DECEMBER 7, 2022

• TITLE: Looking at metric spaces as enriched categories

• SPEAKER: Simon Willerton, The University of Sheffield, UK

• TIME: 2:00PM Nairobi

• DATE: DECEMBER 7, 2022

One can think of category theory as having the category of sets as its 'base category' and changing this 'base category' leads to the notion of enriched category. There's a classic observation of Lawvere that metric spaces can be viewed as enriched categories over the base category of non-negative real numbers. Assuming only a basic understanding of what a category is, I'll explain this idea. I'll go on to show how this perspective has lead to new ideas about metric spaces which touch on a wide variety mathematics including measuring diversity, homological algebra, special functions and tight spans. If time permits I'll mention how this is connected to ideas in classical convex analysis.

November 2, 2022

• TITLE: Computational Approaches to Emerging Infectious Diseases

• SPEAKER: Eric Lofgren, Washington State University

• TIME: 2:00PM Nairobi

• DATE: NOVEMBER 16, 2022

This talk will explore the use of computational epidemiology to respond to emerging infectious diseases, including the West African Ebola epidemic as well as COVID-19, as well as highlight existing research work taking place in Eastern and Central Africa where there is potential for the use of computational tools.

November 2, 2022

• Title: Category Theory in Epidemiology

• Speaker: John Baez

• Affiliation: University of California, Riverside

• Time: 3:00PM Nairobi

Abstract:

Category theory provides a general framework for building models of dynamical systems. We explain this framework and illustrate it with the example of "stock and flow diagrams". These diagrams are widely used for simulations in epidemiology. Although tools already exist for drawing these diagrams and solving the systems of differential equations they describe, we have created a new software package called StockFlow which uses ideas from category theory to overcome some limitations of existing software. We illustrate this with code in StockFlow that implements a simplified version of a COVID-19 model used in Canada. This is joint work with Xiaoyan Li, Sophie Libkind, Nathaniel Osgood and Evan Patterson.

September 28, 2022

• Title: Infinite staircases in symplectic embeddings

• Speaker: Ana Rita Pires

• Affiliation: University of Edinburgh, UK

• Time: 3:00PM Nairobi

Abstract:

A classic result due to McDuff and Schlenk asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many corners, determined by the odd-index Fibonacci numbers, that fit together to form an infinite staircase.

I will discuss a general framework for analyzing the question of when the ellipsoid embedding function for other symplectic 4-manifolds is partly described by an infinite staircase, in particular by giving an obstruction to the existence of an infinite staircase that experimentally seems strong. We will then look at the special case of rational closed symplectic toric manifolds, where the targets with infinite staircases seem to be exactly those whose moment polygon is reflexive. Finally, I will mention some results about the non-rational case, where there are a whole lot more infinite staircases to be found.

This talk is based on various projects joint with Dan Cristofaro-Gardiner, Tara Holm, Alessia Mandini, Maria Bertozzi, Tara Holm, Emily Maw, Dusa McDuff, Grace Mwakyoma, Morgan Weiler, and Nicki Magill.

October 5, 2022

• Title: The Eilenberg-Ganea problem and quasi-isometry types of groups.

• Speaker: Luis Jorge Sánchez Saldaña

• Affiliation: Universidad Nacional Autónoma de México

• Time: 3:00PM Nairobi

Abstract:

Given a group G, we can define the cohomological dimension as the length of the shortest projective resolution of the trivial G-module Z. On the other hand, we can also define the geometric dimension of G as the minimum dimension of a contractible free G-CW-complex. A famous theorem of Eilenberg and Ganea from the 1960’s, and a theorem of Stallings, these two dimensions are equal except for the possibility of a group with cohomological dimension 2 and geometric dimension 3. Sixty years latter it is still not known whether such a group exists. There are generalizations of the cohomological and geometric dimension, concretely, given a group G and a family of subgroups of F we can define the F-cohomological and F-geometric dimension. It turns out that in this generalized setting there is an Eilenberg-Ganea type theorem, and surprisingly, there are examples of groups and families of subgroups such that the corresponding dimensions are distinct. The examples are due to Brady-Leary-Nucinkis, Fluch-Leary, SS, and Martínez-Pedroza-SS. Moreover, in latter work we proved that there are as many of this examples as real numbers up to quasi-isometry (in particular up to isomorphism). In this talk we will expand all said in this abstract.

August 3, 2022

• Title: The weighted Cauchy-type Riemann-Liouville Fractional Problem

• Speaker: Tadesse Abdi

• Affiliation: Addis Ababa University, Ethiopia

• Time: 3:00PM Nairobi

Abstract:

Several papers devoted to the study of existence and uniqueness of solutions of Cauchy-type Fractional Differential Equations use either fixed point theorems or the monotone iterative method. Motivated by these approach, in this work we attempt to establish uniqueness of solutions of Cauchy-type Fractional Differential Equation by using direct methods in fractional calculus. Results pertaining to estimates of derivatives and relative estimates of solutions are obtained in view of Riemann-Liouville Fractional Derivatives and Fractional Integrals. In the sequel a prototype example is given with Volterra Population Growth Model for a closed system.

July 27, 2022

• Title: Enumeration of k-noncrossing trees and related combinatorial structures

• Speaker: Isaac Owino Okoth

• Affiliation: Maseno University, Kenya

• Time: 3:00PM Nairobi

Abstract:

A k-noncrossing tree is a noncrossing tree where each node receives a label in {1, 2, . . . , k} such that the sum of labels along an ascent does not exceed k + 1, if we consider a path from a fixed vertex called the root. The trees were introduced by Pang and Lv in 2010 and are known to be enumerated by Fuss-Catalan numbers. Enumeration of these trees according to number of leaves, degree of a given vertex, degree sequence, number of descents, number of boundary edges and height of these trees have not been done. In this talk, we use bijections and symbolic method to enumerate these trees according to root degree and number of forests. We will also present bijections between the sets of these structures and the sets of other combinatorial structures such as k-noncrossing increasing trees, k-plane trees, k-binary trees and weakly labelled k-trees.

July 20, 2022

• Title: An analytic approach to the study of random digraphs

• Speaker: Naina Ralaivaosaona

• Affiliation: Stellenbosch University, South Africa

• Time: 3:00PM Nairobi

Abstract:

Directed graphs (or digraphs) are graphs in which the edges are oriented. These structures are just as important as the undirected graphs; they occur naturally in many applications. For example, a special class of digraphs known as Directed Acyclic Graphs (DAGs) are the underlying structures of Bayesian Networks. Random undirected graphs have been studied extensively in the literature since the seminal work of Erdős and Rényi in 1959. One of the most spectacular results in the theory of random graphs is the so-called sharp threshold phenomenon. This phenomenon is also known to occur for random digraphs. However, the structure of digraphs through the critical phase remains largely unknown. Recently, we considered an analytic approach to the analysis of digraphs using generating functions and advanced contour integration techniques. In this talk, I will introduce these techniques and discuss some of the results that we obtained from them. This talk is based on joint work with Dovgal, De Panafieu, Rasendrahasina, and Wagner.

July 13, 2022

• Title: An analytic approach to the study of random digraphs

• Speaker: Naina Ralaivaosaona

• Affiliation: Stellenbosch University, South Africa

• Time: 3:00PM Nairobi

Abstract:

Directed graphs (or digraphs) are graphs in which the edges are oriented. These structures are just as important as the undirected graphs; they occur naturally in many applications. For example, a special class of digraphs known as Directed Acyclic Graphs (DAGs) are the underlying structures of Bayesian Networks. Random undirected graphs have been studied extensively in the literature since the seminal work of Erdős and Rényi in 1959. One of the most spectacular results in the theory of random graphs is the so-called sharp threshold phenomenon. This phenomenon is also known to occur for random digraphs. However, the structure of digraphs through the critical phase remains largely unknown. Recently, we considered an analytic approach to the analysis of digraphs using generating functions and advanced contour integration techniques. In this talk, I will introduce these techniques and discuss some of the results that we obtained from them. This talk is based on joint work with Dovgal, De Panafieu, Rasendrahasina, and Wagner.

June 29, 2022

• Title: Real fibered morphisms of real del Pezzo surfaces

• Speaker: Matilde Manzaroli

• Affiliation: University of Tübingen, Germany

• Time: 3:00PM Nairobi

Abstract:

A morphism of smooth varieties of the same dimension is called real fibered if the inverse image of the real part of the target is the real part of the source. It goes back to Ahlfors that a real algebraic curve admits a real fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, in a joint work with Mario Kummer and Cédric Le Texier, we are interested in characterising real algebraic varieties of dimension n admitting real fibered morphisms to the n-dimensional projective space. We present a criterion to construct real fibered morphisms that arise as finite surjective linear projections from an embedded variety; this criterion relies on topological linking numbers. We address special attention to real algebraic surfaces. We classify all real fibered morphisms from real del Pezzo surfaces to the projective plane and determine when such morphisms arise as the composition of a projective embedding with a linear projection.

June 15, 2022

• Title: The tropical symplectic Grassmannian

• Speaker: George Balla,

• Affiliation: RWTH Aachen University

• Time: 3:00PM Nairobi

Abstract:

Given a 2n-dimensional vector space V with a symplectic form w, we call its linear subspace L isotropic if any two vectors u,v in L are orthogonal with respect to w, i.e., w(u,v) = 0. The symplectic Grassmannian SpGr(k,2n) is the space of all isotropic subspaces of V of dimension k. It is a projective subvariety of the usual Grassmannian Gr(k,2n), and its defining ideal under the Plücker embedding is generated by the usual Plücker relations plus some additional linear relations called symplectic relations. After introducing this object, I will discuss its tropicalization, which is a way of passing from algebraic geometry to polyhedral geometry. This work builds on the work of D. Speyer and B. Sturmfels on the tropical Grassmannian from 2004. Some of their results hold in our setting too, but there are key differences, some of which we will see during the talk. I will also briefly discuss an application of the tropical Grassmannian to evolutionary biology via phylogenetics, and an interpretation in the symplectic world. No prior knowledge will be assumed. This talk is based on joint work with Jorge Alberto Olarte.

May 25, 2022

• Title: Coupled oscillators: Networks, symmetry, and synchrony

• Speaker: Prof. Christian Bick,

• Affiliation: University of Amsterdam

• Time: 3:00PM Nairobi

Abstract:

Many systems that are essential for our everyday lives - from power grid networks to coupled neural cells in the brain - can be seen as coupled oscillatory processes. Importantly, their function (or malfunction) depends on the collective dynamics of all oscillator, such as synchrony, where all oscillators evolve in unison. We analyze collective dynamics in networks of coupled oscillators. Symmetries in such networks naturally give rise to synchrony patterns. We discuss network symmetries, synchrony patterns, and the emergence of collective chaotic dynamics.

SLIDES: https://www.dropbox.com/s/dfctnsb1y1tvi9z/TalkCoupledOscKigali.pdf?dl=0

May 11, 2022

• Title: The combinatorics of the infinite

• Speaker: Prof. David Fernández Bretón

• Affiliation: Instituto Politécnico Nacional in Mexico

• Time: 3:00PM Nairobi

Abstract:

Set Theory is a branch of mathematics that is traditionally associated with its foundations; however, another major aspect of Set Theory is that it provides us with the tools to formally study the combinatorial features of mathematical structures that are infinite in size. In this talk I will present a few examples (primarily drawn from Ramsey theory) of this phenomenon, illustrating instances where Set-Theoretic tools and ideas help us prove theorems, as well as instances where some natural questions turn out to be undecidable from the Set-Theoretic axioms.

December 15, 2021

• Title: Power series representing posets

• Speaker: Dr Eric Dolores Cuenca

• Affiliation: Yonsei University, Korea

• Time: 3:00PM Nairobi

Abstract:

In this work we construct a function from finite partially ordered sets to power series, with the property that the n-coefficient counts the number of n-labelings of the poset. As a result we discover a non-recursive algorithm to compute the values of order polynomials of series-parallel posets. Given a power series f(x), we describe an algorithm to recover, if possible, a poset whose order series is the power series f(x). We introduce a family of posets, called Wix\'arika posets, and show that they satisfy a new variant of Stanley's reciprocity theorem. As an application we obtain new identities for binomial coefficients and properties of the negative hypergeometric distribution

December 8, 2021

• Title: 2-modular representations of the Conway simple groups as binary codes

• Speaker: Prof. Bernardo Rodrigues

• Affiliation: University of Pretoria, SA

• Time: 3:00PM Nairobi

Abstract:

In the talk, we introduce and discuss an elementary tool from representation theory of finite groups for constructing linear codes invariant under a given permutation group G. The tool gives theoretical insight as well as a recipe for computations of generator matrices and weight distributions. In some interesting cases a classification of code vectors under the action of G can be obtained. As explicit examples we examine binary codes related to the 2-modular reduction of the Leech lattice and Conway groups.

Parts of this talk are from joint work with Wolfgang Knapp.

December 1, 2021

• Title: What is a Hopf algebra, and why should we care?

• Speaker: Prof. Ken Brown

• Affiliation: University of Glasgow, UK

• Time: 3:00PM Nairobi

Abstract:

I will explain what a Hopf algebra is, give a little of their history, exhibit a number of examples, and explain why these objects are important for many areas of mathematics.

November 24, 2021

• Title: Wide intervals and mutation

• Speaker: Dr Rosanna Laking

• Affiliation: University of Bonn, Germany

• Time: 3:00PM Nairobi

Abstract:

Torsion pairs in the category modA of finite-dimensional modules over a finite-dimensional algebra have played an important role in many aspects of modern representation theory, including the study of cluster theory, t-structures and stability conditions. If we consider the collection of all torsion pairs ordered by inclusion of the torsion class, then we obtain a complete lattice. In recent work by Asai and Pfeiffer, the so-called `wide’ intervals in this lattice are studied from the perspective of lattice theory. These intervals arise naturally both in relation to stability conditions and also in tau-tilting theory. In this talk we will discuss how the torsion pairs in modA are parametrised by 2-term cosilting complexes in the unbounded derived category D(ModA) and how wide intervals correspond to their mutations. This talk is based on ongoing joint work with Lidia Angeleri Hügel, Jan Stovicek and Jorge Vitória.

November 17, 2021

• Title: Morley's theorem in infinitary logic

• Speaker: Prof. Christian Espíndola

• Affiliation: University of Reunion Island, France.

• Time: 3:00PM Nairobi

Abstract:

Morley's theorem asserts that any countable finitary theory which has a unique model (up to isomorphism) in an uncountable cardinal will necessarily have a unique model (up to isomorphism) in all uncountable cardinals. This type of behavior is similar to the case of algebraically closed fields of given characteristic, or vector spaces, and the phenomenon (called categoricity) had been conjectured by Los and demonstrated by Morley in his thesis. In this talk we will start reviewing the basics of model theory and then present a generalization of Morley's theorem to the case of infinitary theories. If they have finite quantifiers, the phenomenon is known as the Shelah categoricity conjecture. If, on the contrary, they have infinite quantifiers, the phenomenon is no longer valid but can be recovered by modifying the notion of size of the model. We will present examples of all these types of theories and study their categoricity spectrum. No prior knowledge of model theory will be assumed.

October 20, 2021

• Title: On Maximal non-Manis extensions

• Speaker: Prof. Simplice Tchamna

• Affiliation: Georgia College & State University, USA

• Time: 3:00PM Nairobi

Abstract:

We introduce and study the concept of maximal Non-Manis extension. A ring extension R ⊆ S is said to be maximal non-Manis if R is not a Manis subring of S and each proper S-overring of R is a Manis subring of S. Several properties of maximal non-Manis extensions are established. We show that if R ⊆ S is maximal non-Manis extension and R is integrally closed in S, then R ⊆ S is a Prüfer extension. We investigate conditions under which the extension R[X] ⊆ S[X] (respectively R(X) ⊆ S(X)) is maximal non-Manis. Examples of maximal non-Manis extensions are provided.

October 13, 2021

• Title: Dividend maximization for a homogeneous insurance portfolio in the presence of reinsurance

• Speaker: Dr Christian Kasumo

• Affiliation: Mulungushi University, Zambia

• Time: 3:00PM Nairobi

Abstract:

We consider an optimal dividend problem for an insurance company whose surplus is modeled by a jump-diffusion model representing a homogeneous insurance portfolio. The company is allowed to pay dividends to the shareholders as well as to enter into reinsurance treaties involving a combination of proportional and excess-of-loss reinsurance arrangements. Our main objective is to find an optimal dividend and reinsurance policy that maximizes the total expected discounted dividend payouts. We derive the Hamilton-Jacobi-Bellman equation and transform the resulting Volterra integrodifferential equation into a Volterra integral equation of the second kind. We then solve this integral equation numerically using the block-by-block method in conjunction with Simpsons Rule to find the optimal dividend and reinsurance strategies. We have given numerical examples with both light- and heavy-tailed distributions in the jump-diffusion case and obtained the optimal dividend barriers that maximize the total expected discounted dividend payouts. The results indicate that the optimal reinsurance policy in the jump-diffusion case is not to take reinsurance.

November 10, 2021

• Title: Generic regularity in obstacle problems

• Speaker: Prof. Dr. Alessio Figalli

• Affiliation: ETH Zürich, Switzerland

• Time: 3:00PM Nairobi

Abstract:

The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. Explicit examples show that the singular set could be, in general, as large as the regular set. In a recent paper with Ros-Oton and Serra we show that, generically, the singular set has codimension 3 inside the free boundary, solving a conjecture of Schaeffer in dimension $n \leq 4$. The aim of this talk is to give an overview of these results.

November 3, 2021

• Title: A client-server and Web-based graphical user interface design for the mathematical model of cardiovascular-respiratory

• Speaker: Prof. Jean Marie Ntaganda

• Affiliation: Department of Mathematics, University of Rwanda.

• Time: 3:00PM Nairobi

Abstract:

The prediction of cardiac conditions can be done through comparison and analysis of parameters transformed into mathematical model equations. This work aims at presenting the design of a web-based graphical user interface of mathematical model of cardiovascular-respiratory system (ICRSMM) as an appropriate displaying tool. The designed interface offers an easy way of recording and storing parameters in a database. Those parameters are computerized to generate automatic results in a graphic representation, which is an effective way used in medicine to allow physicians, nurses and other experienced health personnel to analyze and discuss results. The solution provides an adequate and friendly environment that eases the task of recording the results in a graphic representation. This gives a clear picture of analysis to determine a healthy or unhealthy cardiovascular-respiratory system of a person exercising. However, such a complex solution comes in to put an accent of consideration to an area of research that still needs more discoveries and exploration.

October 27, 2021

• Title: On Galois representations with large image

• Speaker: Prof. Christian Maire

• Affiliation: Institut FEMTO-ST, France

• Time: 3:00PM Nairobi

Abstract:

This talk is an introduction on Galois representations of a number field specially those for which the image is large. We will start with some well-known examples, then follow by the constructions of Greenberg and Katz; and we will end by recent result showing the existence of Galois representations over Q with open image in Gl_m(Z_p), for every odd prime p and integer m.: for very prime p>2 and for every integer m.

In passing we will see the notion of geometric Galois representations and the conjecture of Fontaine-Mazur.

We will try to make this talk accessible to a general audience.

October 6, 2021

• Title: An ordered view of continuous maps

• Speaker: Prof David Holgate

• Affiliation: University of the Western Cape, South Africa

• Time: 3:00PM Nairobi

Abstract:

General Topology provides a set-theoretic basis for the study of properties that are preserved under continuous deformation. The central concept in this regard is a continuous map. You may not have thought about it in such terms before, but two standard theorems in first-year calculus – the Extreme Value Theorem and the Intermediate Value Theorem – are precisely results about topological properties preserved by continuous maps.

A category-theoretic basis for topology has been developed in recent years with closure and interior operators serving as a fundamental tools. Our talk centres on the introduction of the notion of a topogenous order which offers a unifying approach to these interior and closure operators, and gives a fresh insight into continuous maps.

We observe some order-based characterisations of continuous maps and how these naturally lead to the definition of topological properties. The preservation of these properties by continuous maps returns us to an understanding of the Intermediate and Extreme Value Theorems in this context

September 29, 2021

• Title: What is a Quantum Group?

• Speaker: Prof. Dr. Ulrich Krähmer

• Affiliation: Technische Universität Dresden, Germany

• Time: 3:00PM Nairobi

Abstract:

Quantum groups (Hopf algebras) can be defined and motivated in several ways. I will describe one approach that has the advantage of avoiding the use of tensor products of vector spaces altogether, all one needs to know is basic algebra (groups, rings, fields, matrices). I will illustrate the concepts using joint results with Angela Tabiri, Manuel Martins and Blessing Oni on quantum group actions on singular plane curves.

September 22, 2021

• Title: HMS symmetries and hypergeometric systems

• Speaker: Dr Spela Spenko

• Affiliation: Vrije Universiteit Brussel, Belgium

• Time: 3:00PM Nairobi

Abstract:

The derived category of an algebraic variety might be a source of its myriad new (categorical) symmetries. Some are predicted by homological mirror symmetry, as representations of the fundamental group of complex structures of its mirror pair. These finally lead to differential equations. We expositorily unravel a part of this conjectural master plan for a class of toric varieties.

September 15, 2021

• Title: RSK algorithms and partition algebras

• Speaker: Prof Laura Colmenarejo

• Affiliation: North Carolina State University, USA

• Time: 3:00PM Nairobi

Abstract:

I will present a generalization of the Robinson-Schensted-Knuth algorithm to the insertion of two-row arrays of multisets. This generalization leads to new enumerative results that have representation-theoretic interpretation as decomposition of centralizer algebras and the spaces they act on. I will also present a variant of this algorithm for diagram algebras, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra.

September 8, 2021

• Title: Statistical Inference for the Tangency Portfolio in High Dimension

• Speaker: Dr Stanislas Muhinyuzab

• Affiliation: University of Rwanda

• Time: 3:00PM Nairobi

Abstract:

In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a high-dimensional asymptotic regime, i.e. the dimension of the portfolio, k, and the sample size, n, approach infinity such that k/n → c ∈ (0, 1), we deliver the asymptotic distribution of the TP weights.

Moreover, we consider tests about the elements of the TP and derive the asymptotic distribution of the test statistic under the null and alternative hypotheses. In a simulation study, we compare the asymptotic distribution of the TP weights with the exact finite sample density. We also compare the high-dimensional asymptotic test with an exact small sample test. We document a good performance of the asymptotic approximations except for small sample sizes combined with c close to one. In an empirical study, we analyze the TP weights in portfolios containing stocks from the S&P 500 index.

September 1, 2021

• Title: Efficient Computation of the Final Exponentiation in Paring-Based Cryptography

• Speaker: Dr Emmanuel Fouotsa

• Affiliation: University of Bamenda, Cameroon

• Time: 3:00PM Nairobi

Abstract:

The deployment of pairing-based protocols on real world applications requires a very efficient computation of bilinear maps (pairings) over elliptic curves. Their computation is based on the execution of the Miller algorithm followed by a final exponentiation in an extension of a finite field. It is a good remark that part of the computation of the final exponentiation, which involves several squarings, is done in a cyclotomic subgroup. Few works have proposed methods to faster squaring in such subgroups. This expose aims at bringing a detailed explanation on this

August 25, 2021

• Title: 3264 Conics in a Second

• Speaker: Prof. Bernd Sturmfels

• Affiliation: MPI Leipzig and University of California, Berkeley

• Time: 5:00PM Nairobi

Abstract:

This lecture spans a bridge from 19th century geometry to 21st century applications. We start with a classical theme that was featured in the January 2020 issue of the Notices of the American Mathematical Society, namely the 3264 conics that are tangent to five given conics in the plane. We discuss the computation of these conics, by solving a system of polynomial equations with numerical methods that are fast and reliable. We conclude with a problem in statistics, namely maximum likelihood estimation for linear Gaussian covariance models

August 25, 2021

• Title: Subvarieties of Tropical Toric Varieties

• Speaker: Prof. Diane Maclagan

• Affiliation: University of Warwick, UK

• Time: 3:00PM Nairobi

Abstract:

One advantage of toric varieties is that they make sense over any field; in fact over any ring. More is true: we can dispense with most of the ring as well. This leads to the idea of tropical toric varieties. I will introduce these objects, and discuss their subvarieties (and subschemes).

August 18, 2021

• Title: Normal Bases, Galois Correspondence and Finite Field Arithmetic from Algebraic Groups

• Speaker: Tony Ezome

• Affiliation: Masuku University, Franceville, Gabon

• Time: 3:00PM Nairobi

Abstract:

Given a finite Galois extension K/k, a normal basis of K/k is a basis of the form {σ(θ) | σ ∈ Gal(K/k)} where θ ∈ K. Such a θ is called a normal element of K over k. It is known that normal bases are useful for mathematical theory as well as practical applications. For instance, they can be used to realize Galois correspondance and also for an efficient finite fieldarithmetic which is very useful in coding theory and cryptography.

There are papers in the literature describing normal elements of fully ramified Galois extensions of complete local fields with perfect residue field. There are also papers describing normal elements of finite field extensions. In this talk, we are concerned with the case when the normal bases are constructed from one-dimensional algebraic groups. We first explain ho normal bases are used to realise Galois correspondence. Then, we focus on their use for finite field arithmetic. We also explain how extensions of normal bases constructed from Artin-Schreier-Witt theory and Kummer theory give rise to an efficient finite field arithmetic.

June 30, 2021

• Title: The weird and wonderful world of near-vector spaces

• Speaker: Karin-Therese Howell

• Affiliation: Stellenbosch University, South Africa

• Time: 3:00PM Nairobi

Abstract:

Near-vector spaces differ from traditional near-vector spaces in that they possess less linearity as a result of one of the distributive laws not holding in general. This talk will focus on the near-vector spaces first defined by Andre. I will give a brief introduction to the theory and discuss some recent results.

June 23, 2021

• Title: A hybrid neural network GARCH approach to forecasting Zimbabwean inflation volatility

• Speaker: Sure Mataramvura

• Affiliation: University of Cape Town

• Time: 3:00PM Nairobi

Abstract:

This paper provides additional research of modelling and forecasting the inflation volatility present in Zimbabwe, using traditional GARCH models hybridized with Artificial Neural Networks (ANN) and Recurrent Neural Networks (RNN). There are several important conclusions drawn from our results. First, out of the GARCH models, the EGARCH generally performed the best. Second, both the ANN and RNN hybrid models outperformed the traditional GARCH models by a significant margin. Finally, the hybrid ANN models provided more accurate forecasts during volatile periods when compared with hybrid RNN models.

Joint work with Darren Lee and Nigel E.N. Chitambo

June 16, 2021

• Title: Quandles: nonassociative algebraic structures from knot theory

• Speaker: Mohamed Elhamdadi

• Affiliation: University of South Florida

• Time: 3:00PM Nairobi

Abstract:

We will introduce some nonassociative algebraic structures motivated by the mathematics of knots. We will show how to construct invariants of knots from quandles and their low dimensional cohomologies. If time allows, we will discuss "linearization" of quandles from purely algebraic point of view.

June 9, 2021

• Title: On the representation of BSDE-based dynamic risk measures and dynamic capital allocations.

• Speaker: Rodwell Kufakunesu

• Affiliation: University of Pretoria

• Time: 3:00PM Nairobi

Abstract:

We derive a risk representation for dynamic capital allocation when the underlying asset price process includes extreme random price movements. Moreover, we consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. The results are illustrated by deriving a capital allocation representation for dynamic entropic and static coherent risk measures. We also consider the representation of forward entropic risk measures using the theory of ergodic backward stochastic differential equations in a L‘evy framework.

Joint work with : Lesedi Mabitsela and Calisto Guambe.

• Title: Braid groups: presentations and generalisations

• Speaker: Joseph Grant

• Affiliation: University of East Anglia

• Time: 3:00PM Nairobi

Abstract:

Braid groups appear in many parts of mathematics, from knot theory to mathematical physics. They can be studied algebraically using the Artin presentation. I will describe some new presentations which arose in joint work with Marsh, based on the combinatorics of quiver mutation from cluster algebras. Then I will discuss actions of braid groups on categories, and describe some generalisations of braid groups which come from homological algebra.

May 26, 2021

• Title: Extensions of ordered groupoids

• Speaker: Bernard Bainson

• Affiliation: Kwame Nkrumah University of Science and Technology

• Time: 3:00PM Nairobi

Abstract:

Groups are synonymous to symmetry whereas ordered groupoids are to partial symmetry. Ordered groupoids discovered as an algebraic counterpart of Lie pseudogroups has been significantly investigated by algebraists for its beautiful structural properties. In our discussion, we will consider the analogous construction "extensions of groups " for ordered groupoids and characterization of the set of all extensions with abelian kernels using analogous machinery for groups.

This is a joint work with Nick Gilbert, Heriot Watt University.

May 19 , 2021

• Title: The degree of commutativity of an infinite discrete group.

• Speaker: Enric Ventura

• Affiliation: BarcelonaTech, Spain.

• Time: 3:00PM Nairobi

Abstract:

There is a classical result saying that, in a finite group, the probability that two elements commute is never between 5/8 and 1 (i.e., if it is bigger than 5/8 then the group is abelian). The are versions of this result for compact groups working with appropriate measures. We make an adaptation of this notion for finitely generated infinite discrete groups (w.r.t. a fixed finite set of generators) as the limit of such probabilities, when counted over successively growing balls in the group. This asymptotic notion is a lot more vague than in the finite setting, but we are still able to prove some interesting results. I'll concentrate in the following two results (and give an indication of the proof):

(1) with some hypothesis the limit exists and is independent from the set of generators;

(2) a Gromov-like result: “for any finitely generated, residually finite group G of subexponential growth, the commuting degree of G is positive if and only if G is virtually abelian“.

This is joint work with Y. Antolin, A. Martino, M. Tointon, and M. Valiunas.

May 12, 2021

• Title: Controlling OQDS (olive quick decline sindrome)outbreaks caused by Xylella fastidiosa.

• Speaker: Vincenzo Capasso

• Affiliation: University of Milan, Italy

• Time: 3:00PM Nairobi

Abstract:

The motivation of our research has arisen by the outbreak of an epidemic, caused by the pathogen Xylella fastidiosa and known as olive quick decline syndrome (OQDS), which has been seriously affecting olive production of the Apulia region (Italy) since 2013, leading to dramatic socio-economic losses.

Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones, with later installment of more resistant olive cultivars. Unfortunately, both of these practices are having an undesirable impact on the environment (most of these trees were several hundred years old), and on the economy (e.g., costs of the new installments, the loss of production for some years and, the last but not less important the oil quality produced by more resistant cultivars may not match the high standards of the previous ones).

Based on a mathematical model expressed in terms of a simplified reaction diffusion system, it has emerged that the best cost-effective practice consists of the removal of a suitable amount of weed biomass (reservoir of the juvenile stages of the insect vector - P. Spumarius - of X. Fastidiosa) from olive orchards and surrounding areas, without requiring neither the removal nor the substitution of the existing olive trees.

It has to be evidenced that the same kind of disease has been affecting most of the Mediterranean regions, wherever there is a large population of olive trees, in association with the fact that the pathogen X. fastidiosa can infect a large number of productive plants of relevant socio-economic importance (e.g., grapevines, almond trees, citrus plants).

May 5, 2021

• Title: On convergence analysis of fixed-point iterative methods with applications.

• Speaker: Oluwatosin Temitope Mewomo

• Affiliation: University of KwaZulu-Natal, South Africa.

• Time: 3:00PM Nairobi

Abstract:

In this talk, we give a brief introduction to some notable fixed-point iterative methods and their convergence analysis in Hilbert spaces with applications. We show how iterative methods can produce approximate solutions to certain classes of nonlinear problems, fixed points of some non-linear operators and zero point of maximal monotone operators. Finally, we discuss one of our latest results and contributions.

April 28, 2021

• Title: Normal simplices and moduli of weighted hypersurfaces

• Speaker: Dominic Bunnett

• Affiliation: Technical University of Berlin

• Time: 3:00PM Nairobi

Abstract:

A polytope P is called normal if it has the following property: given any positive integer n, every lattice point of the dilation (nP) can be written as the sum of exactly n lattice points in P. In this talk we aim to understand the normality of simplices. The associated toric variety of a simplex is a (possibly fake) weighted projective space. Very ampleness is a property of polytopes, weaker than normality, coming from the algebraic geometry of the associated toric variety. We will focus on the associated geometry lying between the two notions; very ampleness and normality.

In particular, we discuss the implications for the moduli spaces of hypersurfaces in the weighted projective space.

April 21, 2021

• Title: The hidden geometry of magnetic skyrmions

• Speaker: Bernd Schroers

• Affiliation: Heriot-Watt University, UK

• Time: 3:00PM Nairobi

Abstract:

This talk is about a model for topological defects in planar ferromagnetic materials, and the geometrical techniques which can be used to obtain infinitely many exact static solutions. The defects, called magnetic skyrmions in this context, are widely studied in physics because of their potential role in future magnetic information storage. The applicability of techniques from complex geometry and gauge theory is surprising, and leads to interesting links with the theory of gravitational lensing. Finally, the dynamics of magnetic skyrmions in response to an applied current, which is of practical interest, also contains unexpected geometry and can be understood in terms of quaternionic Moebius transformations.

April 14, 2021

• Title: Parameters Estimation in Stochastic Epidemic Models

• Speaker: Denis Ndanguza

• Affiliation: University of Rwanda

• Time: 3:00PM Nairobi

Abstract:

Parameter estimation is a very difficult problem, especially for large systems. In this talk, a deterministic Ebola model is formulated and converted into a stochastic differential equations. In order to estimate the model parameter values, we use the extended Kalman filter technique as the filtering method and sum of square of errors to compute an approximation of the likelihood. From the obtained likelihood function, the maximum likelihood and MCMC methods for parameters estimation are then used. These parameter estimates provide useful information on quantities of epidemiological interest. Finally, we investigate whether an estimate obtained from a biased study differs systematically from the true source population of the study.

April 7, 2021

• Title: Applied Mathematics Applied

• Speaker: Poul G. Hjorth

• Affiliation: Technical University of Denmark

• Time: 3:00PM Nairobi

Abstract:

The ancient and vast art Mathematics is practiced and developed in many ways around the planet. I will discuss here a fairly novel type of collaborative workshop, where applied mathematicians work together to tackle challenges of modelling and computation, posed to the mathematicians by companies and institutions outside academia. Known as Study Groups with Industry (SGI), these workshop began about 50 years ago in the UK, and has since spread around the world. I will describe the format and give some examples of the variety of solutions that I have encountered over the years.

March 31, 2021

• Title: Parity alternating permutations starting with an odd integer

• Speaker: Frether Getachew

• Affiliation: Addis Ababa University, Ethiopia

• Time: 3:00PM Nairobi

Abstract:

A parity alternating permutation of the set [n] = {1, 2, ... , n} is a permutation with even and odd entries alternatively. The talk is about parity alternating permutations (PAPs) having an odd entry in the first position. We will see the numbers that count the PAPs with even as well as odd parity. We also study a subclass of PAPs being derangements as well, parity alternating derangements (PADs). Moreover, by considering the parity of these PADs we look into their statistical property of excedance.

March 24, 2021

• Title: Data Analysis in Smart Agriculture

• Speaker: Dr Oskar Marko

• Affiliation: Biosense Institute, University of Novi Sad, Serbia

• Time: 3:00PM Nairobi

Abstract:

According to FAO's estimates, agricultural production will need to increase by 70% in the next 30 years to feed the world's growing population. Previous agricultural revolutions thrived on innovations kickstarted by the Industrial Revolution in the 19th and the Green Revolution in the 20th century, and now, in the 21st century it is information technologies that are leading the paradigm shift. A wide range of data sources have become available recently. Satellite images from the European Space Agency are providing data every 5 days in 12 spectral bands, drones are becoming more affordable and there are various global open source databases of soil and climate data. All these pieces of information are collected, fused within the cloud and processed using machine learning algorithms. The models derived in this way are used for optimisation of decision-making so that the farmers could increase their profit and sustainability of their production and minimise the risk. The talk will focus on the development of specific machine learning algorithms for management zone delineation, yield prediction and irrigation.

March 17, 2021

• Title: Nodes on Quintic Spectrahedra

• Speaker: Taylor Brysiewcz

• Affiliation: Max Planck Institute for Mathematics, Germany

• Time: 3:00PM Nairobi

Abstract:

A spectrahedron in R3 is the intersection of a 3-dimensional affine linear subspace of dxd real matrices with the cone of positive-semidefinite matrices. Its algebraic boundary is a surface of degree d in C3 called a symmetroid. Generically, symmetroids have (d^3-d)/6 nodes over C and the real singularities are partitioned into those which lie on the spectrahedron and those which do not. This data serves as a coarse combinatorial description of the spectrahedron. For d=3 and 4, the possible partitions are known. In this talk, I will explain how we determined which partitions are possible for d=5. In particular, I will explain how numerical algebraic geometry and an enriched hill-climbing algorithm helped us find explicit examples of spectrahedra witnessing each partition.

March 10, 2021

• Title: Models and Simulations for COVID-19 (not only) in Germany

• Speaker: Prof. Thomas Götz

• Affiliation: University of Koblenz and Landau, Germany

• Time: 3:00PM Nairobi

Abstract:

In this talk we will present modeling and simulation approaches to different aspect of the current Corona pandemic. Differential equation models will be used to analyze the spread of competing virus variants, investigate the effect of household structure and the influence of the resuming travel activities in Europe during summer 2020. The work presented was carried out as a collaboration of University in Koblenz with other German and Sri Lankan colleagues. All the models can be transferred with minor modifications to the situation in other countries.

March 3, 2021

• Title: Modelling the Spread of Schistosomiasis in Humans with Environmental Transmission

• Speaker: Prof. Sansao A. Pedro

• Affiliation: Universidade Eduardo Mondlane, Maputo, Mozambique

Abstract:

Although schistosomiasis containment campaigns have recorded substantial success in most developed countries, sub-Saharan Africa still suffers greatly under the burden of the disease. A basic mathematical model to assess the impact of concomitant immunity in humans and environmental transmission of schistosomiasis disease progression is formulated. Mathematical analysis is carried out to establish the existence of the equilibrium points providing necessary conditions for their local and global stability. Numerical simulations are done to analyze the effects of environmental transmission and processes associated with development of concomitant immunity. Our results suggest that schistosomiasis burden is increased by direct and indirect contribution of individuals with concomitant immunity to the schistosomiasis infection chain, increasing the shedding of miracidia upto the development of cercariae promoting the growth of cercariae, increase in environmental transmission due to cercariae, reducing the clearance rate of cercariae and reducing the development of humans and non-human mammals escape mechanisms from cercariae attack.

This talk is based on the paper: https://doi.org/10.1016/j.apm.2021.01.046

Keywords: Schistosomiasis, Humans, cercariae, Miracidia, Reproduction number and analysis.

February 24, 2021

• Title: A stochastic maximum principle for stochastic control of SDEs with measurable drifts.

• Speaker: Olivier Menoukeu Pamen

• Affiliation: African Institute for Mathematical Sciences/ University of Liverpool,UK

Abstract:

In this talk, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. More precisely, we establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation (in the Sobolev sense) process of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the diffusion process. Then by an approximation argument, we construct a sequence of optimal control problems with smooth coefficients. Finally, we use Ekeland’s variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit.

This talk is based on a joint work with L. Tangpi.

Keywords: Ekeland’s variational principle; first variation process; maximum principle; measurable drift coefficients.

February 17, 2021

• Title: Pricing and hedging of options in non-linear incomplete financial markets

• Speaker: Dr Miryana Grigorova

• Affiliation: University of Leeds

Abstract:

We will start by reviewing some well-known basic examples of complete and incomplete financial market models (in the linear case), in which we will illustrate the application of the so-called BSDE approach (the approach based on Backward Stochastic Differential Equations). We will then focus on some more involved financial models with possible default on the underlying risky asset, combined with different market “imperfections” leading to non-linear expectation operators. We will explain how the pricing and hedging problem of the so-called European option in such market models naturally leads to a stochastic control problem with non-linear expectations/ evaluations.

If time permits, we will explain how the pricing and hedging problem of an American option in such models leads to a mixed stochastic control/stopping problem with non-linear expectations/ evaluations, and to non-linear Reflected BSDEs with constraints.

The talk will be based on joint works with Marie-Claire Quenez, Agnès Sulem, Peter Imkeller, and Youssef Ouknine.

February 10, 2021

• Title: Groups, diagrams and geometries

• Speaker: Colva Roney-Dougal

• Affiliation: University of St Andrews

Abstract:

The study of finitely-presented groups has been ongoing since the work of Hamilton in the 1850s - almost as long as group theory itself! This talk will be a gentle introduction to finitely-presented groups, with an emphasis on algorithms. I’ll describe some finite diagrams, and some potentially infinite geometries, that are naturally associated with any finitely-presented group, and show how results about the diagrams and geometries prove structural results about the group, and vice versa. No detailed background knowledge will be assumed.

February 3, 2021

• Title: Stäckel transform of Lax representation of Liouville integrable Hamiltonian systems

• Speaker: Krzysztof Marciniak

• Affiliation: Linköping University

Abstract:

Suppose M is a smooth manifold and assume that a set of functions on M, each function depending on some parameters, is given. A Stäckel transform is an operation that turns this set of functions into a new set of parameter-dependent functions on M. Stäckel transform, when applied to a Liouville integrable (completely integrable) system produces a new Liouville integrable system, and it transforms a separable (in the sense of Hamilton-Jacobi theory) Liouville system into a new separable Liouville system. It also preserves maximal superintegrability. In this talk we construct a map between Lax equations for pairs of Liouville integrable Hamiltonian systems related by a multiparameter Stäckel transform. Using this map we construct Lax representation for a wide class of separable Hamiltonian systems of Stäckel type by applying the multi-parameter Stäckel transform to Lax equations of suitably chosen systems from the Benenti class of Stäckel systems. For a given separable system, we obtain in this way a set of non-equivalent Lax equations parametrized by an arbitrary function of the spectral parameter.

16 December 2020

AFRICAN MATHEMATICS SEMINAR | MATCH-MAKING SEMINARS

16 December 2020 | Wednesday

15:00 Nairobi

______________________________________

The first speaker: 15.00 EAT (=12.00 UTC).

Apollinaire Touoyem, a PhD student from University of Dschang in Cameroon, is looking for research partner(s) for his work on Optimal ordering and position of supply chain delivery window under forecast updating. The classification of this subject is: Optimization, Stochastic partial differential equation, Financial mathematics, Stochastic process, supply chain.

Anyone interested in joining Apollinaire in his research please send a message to touoyem(at)yahoo.com

______________________________________

The second speaker: 15.30 EAT (=12.30 UTC).

Geoffrey Mboya from University of Nairobi, currently a PhD student at University of Oxford, is looking for speakers or mentors for Mfano, Africa mathematical sciences mentorship scheme, that targets Pre-PhD students in Africa.

The mentor can give

• A Crash course or Introductory/survey talk(s) on any chosen topics in Mathematics

• start a reading group and/or

• Advise student(s) through short mini projects intended to introduce them to research frontiers thus increasing the quality of their graduate application(s).

This would also be an opportunity for Mfano to advertise a pilot Research Experience Visit-Mentor Program in which African students (1 male and 1 female) would be fully funded to come to Oxford for 21 days in the summer of 2021 to get one-on-one mentorship from volunteer members of faculty and postdocs. This pilot would ideally develop into a larger project in the 2021/22 academic year.

Through AfMS, Mfano Africa hopes to reach a larger audience hence welcoming diverse ideas on how to improve the mentorship scheme or find collaborators.

For further contacts and information please write to Geoffrey Mboya, Geoffrey.Mboya(at)maths.ox.ac.uk

9 December 2020

• Title: Algebraic geometry and beyond

• Speaker: Caucher Birkar

• Affiliation: University of Cambridge , UK

Abstract:

In this talk, I will discuss some fundamental aspects of algebraic geometry and then discuss connections with some other areas.

2 December 2020

• Title: Stochastic control for Volterra equations driven by time-changed noises

• Speaker: Giulia Di Nunno

• Affiliation: University of Oslo, Norway

Abstract:

We study a classical control problem for non classical forward dynamics of Volterra type driven by time-changed Levy noises. We consider time-changes that are the abso- lutely continuous type, thus exiting the framework of actual Levy framework. For this we shall consider different information flows and, when necessary, consider these flows either as enlarged filtrations or as partial information. Being the system possibly non- Markovian, we prove stochastic maximum principles of both Pontryagin and Mangasarian type. For this we shall study backward Volterra integral equations with time-change. We illustrate our results with an application to mean-variance portfolio selection.

25 November 2020

• Title: What the emptiness hides

• Speaker: Andrei Okounkov

• Affiliation: Columbia University, USA

Abstract:

The talk will be about vacua, that is, states in which some physical system can exist in infinite space for infinite time. We will see that vacua are full of interesting physics and mathematics. In particular, the parameter or moduli spaces of vacua are very interesting objects of study.

18 November 2020

• Title: The absolute Galois group of the rational numbers

• Speaker: Ravi Ramakrishna

• Affiliation: Cornell University, USA

Abstract:

Most mathematicians are introduced to Galois theory via the study of finite Galois extensions of Q. It turns out if one studies all finite Galois extensions of Q simultaneously, there is a (very large) Galois group that encodes all the finite ones. It has a cohomology theory resembling that of manifolds and the study of this group and its natural representations has become a central tool in modern number theory. I will give an overview of the absolute Galois groups of Q, some questions that have been resolved via studying and some of the many open questions that remain.

11 November 2020

• Title: Decomposable Curves which are Quantum Homogeneous Spaces

• Speaker: Angela Tabiri

• Affiliation: African Institute of Mathematical Sciences (AIMS), Ghana

Abstract:

Let $C$ be a decomposable plane curve over an algebraically closed field $k$ of characteristic 0. That is, $C$ is defined in $k^2$ by an equation of the form $g(x) = f(y)$, where $g$ and $f$ are polynomials of degree at least 2. We use this data to construct 3 pointed Hopf algebras, $A(x, a, g), A(y, b, f)$ and $A(g, f)$, in the first two of which $g$ [resp. $f$] are skew primitive central elements, and the third being a factor of the tensor product of the first two. We conjecture that $A(g, f)$ contains the coordinate ring $O(C)$ of $C$ as a quantum homogeneous space, and prove this when each of $g$ and $f$ has degree at most 5 or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when $g$ has degree 3, $A(x, a, g)$ is a PBW deformation of the localisation at powers of a generator of the downup algebra $A(−1, −1, 0)$.

4 November 2020

• Title: Associated prime ideals of powers of ideals

• Speaker: Roswitha Rissner

• Affiliation: University of Klagenfurt

Abstract:

Primary decompositions play a role in different mathematical areas. For example, in algebraic geometry, decomposing an algebraic set into irreducible components is algebraically encoded in the primary decomposition of the defining ideal $I$. Moreover, the factor ring of the polynomial ring modulo $I^n$ carries information about the derivatives (of order up to $n$) on the algebraic set. Therefore, not only the decomposition of $I$ but also of its powers are of great interest.

Other well-known examples can be found in combinatorial commutative algebra; the associated prime ideal of an edge ideal represent the set of minimal vertex cover of the underlying graph. This speaks to the complexity of the computation of primary decompositions (even in the case of monomial ideals with square-free generators of degree 2) as the computation of minimal vertex covers is NP-hard. Also in this context, associated prime ideal of powers of ideals are desired. The associated prime ideals of powers of edge ideals contain a lot of information about colorings of the graph, that is, the associated prime ideals up to the $k$-th power of an edge ideals contain to chromatically $k+1$-critically subgraphs of the given graph.

This talk is an introduction to the primary decompositions in general and discuss associated primes for powers of certain ideals which show interesting behaviour.

28 October 2020

• Title: Primes in arithmetic progressions: The Riemann Hypothesis - and beyond

• Speaker: James Maynard

• Affiliation: University of Oxford

Abstract:

One of the oldest problems about prime numbers is asking how many primes there are of a given size in an arithmetic progression. Dirichlet's famous theorem shows that there are large primes in any progression unless there is an obvious reason why not, but more refined questions lead quickly to statements equivalent to versions of the Riemann Hypothesis, which unfortunately remains unsolved.

We can prove that the Generalized Riemann Hypothesis is true 'on average', and this can often be used as an unconditional substitute for the Riemann Hypothesis. I'll introduce these ideas and mention some recent work about primes in arithmetic progressions which 'breaks the 1/2 barrier' and shows that something *stronger* that the Riemann Hypothesis holds on average.

21 October 2020

• Title: Real algebraic geometry and computations

• Speaker: Marie-Françoise Roy

• Affiliation: University of Rennes

Abstract:

The talk starts with a basic mathematical problem : How many roots for a real univariate polynomial? This problem was studied by Descartes, Sturm and Hermite and their computational methods are still important today. A vast multivariate generalization is due to Tarski, with his famous quantifier elimination result. Various methods for quantifier elimination will be presented, and their algorithmic complexity will be discussed.

14 October 2020

• Title: Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations

• Speaker: Célestin Kurujyibwami

• Affiliation: University of Rwanda

Abstract:

We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schrödinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schrödinger-type equations, which includes all the other classes considered in the paper. Showing that this superclass is not normalized, we partition it into two disjoint normalized subclasses, which are not related by point transformations. Further constraining the arbitrary elements of the superclass, we construct a hierarchy of normalized classes of Schrödinger-type equations. This gives us an appropriate normalized superclass for the non-normalized class of multidimensional nonlinear Schrödinger equations with potentials and modular nonlinearities and allows us to partition the latter class into three families of normalized subclasses. After a preliminary study of Lie symmetries of nonlinear Schrödinger equations with potentials and modular nonlinearities for an arbitrary space dimension, we exhaustively solve the group classification problem for such equations in space dimension two.

7 October 2020

30 September 2020

• Title: Vitali Selectors of the Real Line and Related Semigroups

• Speaker: Venuste Nyagahakwa

• Affiliation: University of Rwanda

Abstract:

Let R+ be the real line with its additive group structure and Euclidean topology, and let P(R) be the family of all subsets of R. It is well known that there are elements of P(R) which are not measurable in the Lebesgue sense, namely Vitali selectors, Bernstein sets, and much more. In this talk, we are interested in the study of the class of Vitali selectors of R. The Vitali selectors are an example of classical subsets of R which are not measurable in the Lebesgue sense, and without the Baire property. We further develop a theory of semigroups (i.e. families of sets closed under the finite union of sets) under different binary operations. We apply this theory to Vitali selectors of the real line to obtain diverse semigroups consisting of sets, which are not measurable in the Lebesgue sense, and without the Baire property on the real line.

23 September 2020

• Title: Hyperbolic groups of Fibonacci type.

• Speaker: Ihechukwu Chinyere

• Affiliation: University of Essex, UK

Abstract:

Building on previous results concerning hyperbolicity of groups of Fibonacci type we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. The groups not covered in our classification are the notoriously difficult Gilbert-Howie groups H(9,4) and H(9,7). This is joint work with Gerald Williams.

16 September 2020

• Title: Enveloping algebras of infinite-dimensional Lie algebras

• Speaker: Susan J. Sierra

• Affiliation: University of Edinburgh, UK

Abstract:

A Lie algebra is the set of infinitesimal symmetries of some space. Universal enveloping algebras of finite-dimensional Lie algebras are an extremely well-understood class of noncommutative rings and the source of many foundational techniques in noncommutative ring theory. In contrast, universal enveloping algebras of infinite-dimensional Lie algebras are almost entirely mysterious. We will survey what's known about them (relatively little) and what is unknown (most things), focussing on the structure of one-sided and two-sided ideals. This talk will be accessible to a general mathematical audience; we will not assume familiarity with the definition of a Lie algebra or an enveloping algebra.

9 September 2020

• Title: Symplectic PBW Degenerate Flag Varieties; PBW Tableaux and Defining Equations

• Speaker: George Balla

• Affiliation: RWTH Aachen University

Abstract:

We define a set of PBW-semistandard tableaux that are in a weight preserving bijection with the set of monomials corresponding to integral points in the Feigin-Fourier-Littelmann-Vinberg polytope for highest weight modules of the symplectic Lie algebra. We then show that these tableaux parametrize bases of the homogeneous coordinate rings of the complete symplectic original and PBW degenerate flag varieties. From this construction, we provide explicit degenerate relations that generate the defining ideal of the PBW degenerate variety. These relations consist of type A degenerate Plücker relations and a set of degenerate linear relations that we obtain from De Concini's linear relations.

In this talk, we will discuss the main results, meanwhile presenting the ideas of the proofs and providing examples along the way.

2 September 2020

• Title: Spheres Packings in Hyperbolic Space

• Speaker: Taylor Dupuy

• Affiliation: University of Vermont

Abstract:

In John H Conway's book "The Sensual Quadratic Form" he discusses Ford circles. These are a certain circle integral packing of circles in the upperhalf plane which connect the arithmetic of PSL_2(ZZ), Farey Fractions, and the theory of continued fractions (these constructions go way way back to the 1800s). It is natural to ask what happens when we try to go to higher dimensions perhaps replacing the complex numbers with quaternions and circles with 3-spheres. Thinking about the numerology and the structure of the quaternions one will notice that going up in dimensions seems to be a rather tricky problem (if we want to use conformal mapping properties). Using inversive geometry and uniformizations of higher dimensional hyperbolic spaces with via the theory of Clifford algebras developed by Ahlfors, Maass, and Vahlen, we extend these circle packings constructions to higher dimensions and explain what breaks down and what does not break down. This is joint work in progress with Spencer Backman, Anton Hilado (graduate student), and Veronika Potter (undergraduate student).

26 August 2020

• Title: Supervised learning for repeated measurements using the Growth Curve models.

• Speaker: Martin Singull

• Affiliation: Linköping University, Sweden

Abstract:

The Growth Curve model can be applied when measuring one or several response variables repeatedly over time. Our research are mainly focused on supervised learning for Growth Curves and its extensions, i.e., estimation of the bilinear regression model and classification using both the spatial and temporal information hidden in the data.

In this talk, I will present the frontier of the research and what our research group has attained for the last ten years.

19 August 2020

• Title: The sets of flattened partitions with forbidden patterns.

• Speaker: Olivia Nabawanda

• Affiliation: Makerere University, Uganda

Abstract:

The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. We count the number of distinct patterns avoiding flattened partitions over [n]. Surprisingly, several counting sequences, namely Catalan numbers, powers of two, Fibonacci numbers and Motzkin numbers arise. Combinatorial proofs and bijections between patterns avoiding flattened partitions with other combinatorial objects counted by the same numbers are given.

12 August 2020

• Title: Mathematics and art in Africa.

• Speaker: Steven Bradlow

• Affiliation: University of Illinois at Urbana-Champaign

Abstract:

Many motifs in African decorative traditions have distinctive order. Mathematics provides an effective language for describing this order; conversely, the arts and crafts incorporate a rich range of mathematical principles. We will explore this symbiosis in several examples, including Ndebele house decorations, Tonga basketry, and Chokwe sona sand drawings, and will discuss how it can be used as a basis for a masters-level mathematics course.

5 August 2020

• Title: Geometry of the configuration space of Kaleidocycles.

• Speaker: Shizuo Kaji

• Affiliation: Kyushu University

Abstract:

Have you heard of a Kaleidocycle, which is an origami art consisting of tetrahedra joined by their edges to form a ring? (if not, have a look at https://github.com/shizuo-kaji/Kaleidocycle) It exhibits an intriguing turning-around motion. Mathematically, the set of states (the configuration space) of a Kaleidocycle is identified by a certain real-algebraic subvariety of the product of the real Grassmannians: each connecting edges define affine lines in 3-space, and they satisfy geometric conditions specified by a system of quadratic equations.

Each real solution to the system corresponds to a state of the Kaleidocycle. Each one-dimensional subspace of the configuration space corresponds to a motion of the Kaleidocycle. We define a flow on the configuration space using discrete versions of mKdV and sine-Gordon equations. The one-dimensional orbits generated by the flow corresponds to the characteristic turning-around motion.

We discuss some interesting open problems related to the configuration space of the Kaleidocycle, which lie at the intersection of geometry, topology, and integrable systems.

This is joint work with K. Kajiwara and H. Park.

29 July 2020

• Title: A variant of van Hoeij's algorithm for computing hypergeometric term solutions of holonomic recurrence equations

• Speaker: Bertrand Teguia

• Affiliation: University of Kassel

Abstract:

Linear homogeneous recurrence equations with polynomial coefficients are said to be holonomic. Such equations have been introduced in the last century for proving and discovering combinatorial and hypergeometric identities. Given a field K, a term an is called hypergeometric with respect to K, if the ratio a_{n+1}/a_n is a rational function over K. The solutions space of holonomic recurrence equations gained more interest in the 1990s from the well known Zeilberger’s algorithm. In particular, algorithms computing the subspace of hypergeometricterm solutions which covers polynomial, rational, and some algebraic solutions of these equations were investigated by Marko Petkovsek (1993) and Mark van Hoeij (1999). The algorithm proposed by the latter is characterized by a much better efficiency than that of the other; it computes, in Gamma representations, a basis of the subspace of hypergeometric term solutions of any given holonomic recurrence equation, and is considered as the current state of the art in this area. Van Hoeij implemented his algorithm in the Computer Algebra System (CAS) Maple through the command LREtools.

We present a variant of van Hoeij’s algorithm that performs the same efficiency and gives outputs in terms of factorials and shifted factorials, without considering certain recommendations of the original version. Some computations using our implementation in the CAS Maxima are also presented.

22 July 2020

• Title: Random modelling with stochastic partial differential equations.

• Speaker: Marta Sanz-Solé

• Affiliation: University of Barcelona

Abstract:

Randomness and uncertainty are among the most common features in observations of real- world phenomena. Models for random evolutions are very often described using the mathematics of stochastic partial differential equations (SPDEs). Research activity on the theory of SPDEs is very intense nowadays, partly because of external demands from applications but also because of exciting and challenging inside questions. This colloquium lecture will be an introduction to the subject addressed to non-specialists. In the first part, I will present the basics of the theory and in the second part, I will address some interesting questions related to the random wandering of the trajectories of SPDEs.

15 July 2020

• Title: Gap Sets for the Spectra of Cubic Graphs.

• Speaker: Peter Sarnak

• Affiliation: Institute for Advanced Study, Princeton University.

Abstract:

The spectra of large locally uniform geometries have been studied widely and from different points of view,including applications .They include Ramanujan Graphs and Buildings ,

euclidean and hyperbolic spaces and more general locally symmetric spaces. We review some of these briefly highlighting rigidity features.We then focus on the simplest case of finite cubic graphs which prove to be surprisingly rich. As one imposes restrictions on these graphs, planarity, fullerenes,.. their spectra become rigid.

Joint work with Alicia Kollar and Fan Wei.

8 July 2020

• Title: On the computation of polarized class groups of CM-Fields

• Speaker: Sogo Pierre Sanon

• Affiliation: University of Kaiserslautern

Abstract:

Computational number theory is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry. It has applications to cryptography, including RSA, elliptic curve cryptography. Polarized class groups are very important in studying problems that involve polarized abelian varieties.

In this presentation, I will present a new approach to compute Polarized class groups of CM-fields of degree 2 and 4 using complex multiplication theory. I will also present a cryptosystem that shows how elliptic curves and abelian varieties are used in cryptography.

1 July 2020

• Title: Tits Cone Intersections and Applications

• Speaker: Michael Wemyss

• Affiliation: University of Glasgow

Abstract:

I will explain some new structures that can be obtained from ADE Dynkin diagrams, which visually are very beautiful, and have some surprising applications to both two-dimensional and three-dimensional algebraic geometry. Most of the talk will explain how to construct these new objects, will highlight some of the results we can prove about them, whilst containing lots of examples. At the end, I will briefly explain some of our motivation for being interested in them, through noncommutative resolutions, and why these structures in fact control more complicated geometric surgeries called flops. This is joint work with Osamu Iyama.

24 June 2020

• Title: A Mathematical Model for the Transmission of COVID-19 in Sudan

• Speaker: Abdelnasir Bongo

• Affiliation: University of Khartoum

Abstract:

The currently circulating Coronavirus disease 2019 (COVID-19) has reached Sudan by the mid of March 2020 or earlier. From the onset of the virus arrival, the government of Sudan has allocated isolation units across the country and gradually placed a series of measurements to prevent the disease from widespread community transition. In this talk, we will present a mathematical model for the transmission of COVID-19 in Sudan, using a modified version of SEI framework. We placed emphasis on quantifying the impact of the control measurements and the rate of case detecting in slowing down the spread of the disease. We will discuss the model results and consider other simulating scenarios.

17 June 2020

• Title: Projective fibrations through bigraded rings in low dimension.

• Speaker: Geoffrey Mboya

• Affiliation: University of Oxford

Abstract:

Scrolls play a central role in construction of varieties such as K3 surfaces and Fano 3-folds. I will define scrolls in a general toric set-up and describe line bundles on them with accessible examples. Using this background, I will introduce a set-up of probing the geometry of certain projective fibrations polarized by a pair of divisors, one ample and one relatively ample, which together embed the fibration into a "relative key variety" over a base.

Finally, I will give an informal insight on why one would care about this kind of mathematics.

10 June 2020

• Title: Further investigations on a permutation code introduced by Mantaci and Rakotondrajao.

• Speaker: Fufa Beyene

• Affiliation: Addis Ababa University

Abstract:

Permutation codes are interesting because certain algorithms perform better over the codes (vectors) than they do over the permutations themselves. Codes allow for instance to implement efficient algorithms for the exhaustive generation of all permutations or of some given classes of them. To do so, one has often to "read" the properties of the permutation in its code and this gives birth to interesting combinatorial problems.

In 2001, R. Mantaci and F. Rakotondrajao introduced a new code (M-R code) for permutations and in this talk we present some investigations we have conducted over this code and results we have found.

See a detailed abstract here

3 June 2020

• Title: Quantifying Traffic Congestion in Nairobi: A Topological Approach

• Speaker: Eric Bojs

• Affiliation: KTH Royal Institute of Technology in Stockholm, Sweden

Abstract:

African cities are growing. In conjunction with economic prosperity, cities are experiencing what seems to be a never-ending traffic problem. This project aims to give insight into a novel approach for quantifying car traffic in those cities. This is necessary to improve efficiency in resource allocation when trying to fix traffic.

In the form of a case study in Nairobi, the approach consists of a method which relies on topics from the field of Topological Data Analysis, together with the use of large data sources from taxi services in the city. With this, both qualitative and quantitative insight can be given about the traffic. The method was proven useful for understanding how traffic spreads, and to differentiate between levels of congestion: quantifying it.

27 May 2020

• Title: Low-dimensional Hom-Lie algebras

• Speaker: Elvice Ongong’a

• Affiliation: University of Nairobi and Mälardalen University, Sweden

Abstract:

Hom-Lie algebras are considered to be generalization of Lie algebras by having an additional linear map, the twisting map. This gives a generalization of the Jacobi identity into Hom-Jacobi identity. In this talk, we give some preliminaries on Hom-Lie algeras of low dimension and describe isomorphisms of such algebras. We further describe the dimension of the space of possible linear endomorphisms (twists) that turn skew-symmetric low-dimensional algebras into Hom-Lie algebras.

14 October 2020