Nairobi workshops in Algebraic Geometry
Chiara Bonadiman, Jared Ongaro, Diletta Martinelli and Balazs Szendroi: Live and remote: Nairobi workshops in algebraic geometry, EMS Magazine, June 2022
2024 Workshop
Date: 16 December 2024
Organised by Damian Maingi
8am-1pm Nairobi time, Chiromo Campus, University of Nairobi, and online
- 8:00 Geoffrey Mboya: Graded Rings and the Geometry of Elliptic Curves
- 9:00 Balazs Szendroi (remote talk): Ehrhart theory of polytopes and graded rings
- 9:50 Elvice Omondi: Induced Hom-Nambu-Lie algebras
- 10:40 Livia Campo (remote talk): Weighted projective spaces and hypersurfaces
- 11:30 Francesco Malaspina (remote talk): Castelnuovo-Mumford regularity and splitting criteria for vector bundles
- 12:20 Salash Tolan Nabaala (remote talk): Functor Formalisms in Noncommutative Algebraic Geometry
Supported by Balazs Szendroi's grant at the University of Vienna.
Some abstracts
- Francesco Malaspina: Castelnuovo-Mumford regularity and splitting criteria for vector bundles. In this talk, we will introduce some notions of Castelnuovo-Mumford regularity and show how they can be used to prove splitting criteria for vector bundles on some projective varieties.
- Geoffrey Mboya: Graded Rings and the Geometry of Elliptic Curves. This talk delves into the graded ring R(E,H) associated with an elliptic curve E and a divisor H=P. Using the Riemann–Roch theorem, we compute the spaces of sections of multiples of E, and identify the graded structure of R(E,P) through generators x,y,z with poles of orders 1,2, and 3. By exploring the algebraic relations among these generators, we recover the classical Weierstrass equation. We extend the analysis to divisors H=kP for k=2,3,4,5, revealing embeddings of E into projective spaces. Each embedding is characterized by distinct geometric features: a double cover of the projective line, a plane cubic, intersections of quadrics, and sections of Grassmannians. These constructions provide insights into the relationship between the graded ring and the geometry of E; a tip of the iceberg that is the theory of graded ring geometry in higher dimensions and their extended versions.
- Elvice Omondi: This talk is about induced ternary Hom-Nambu-Lie algebras arising from Hom-Lie algebras (generalised Lie algebras). The talk alslo gives some results giving conditions on when morphisms of Hom-Lie algebras can still remain morphisms for the induced ternary Hom-Nambu-Lie algebras. Examples in dimension 3 are provided to show this way of constructing ternary structures and such morphisms. Joint work with: Sergei Silvestrov, Jared Ongaro and Abdennour Kitouni.
- Salash Tolan Nabaada: This work explores the use of 2-functor formalisms within noncommutative algebraic geometry, with a particular emphasis on the application of topos theory in constructing and interpreting these formalisms. We present results and proposals that advance our understanding of how functors encapsulate geometric information in algebraic settings. In this context, a 2-functor formalism refers to a pair of adjoint functors in a class of symmetric monoidal categories. This class of adjoint pairs is obtained from the essential image of a pseudofunctor, which ensures that each functor in the image has a right adjoint with which it maintains some specific relationship relative to the symmetric monoidal structure of their domains and codomains.
- Livia Campo: In this talk I will introduce weighted projective spaces (wps) and we will see them in action in explicit examples. Wps are singular projective spaces, whose structure leads to interesting behaviours of their subvarieties (like hypersurfaces). This is the stepping stone for the study and the birational classification of Fano varieties.
2023 Workshop
Dates: 3-7 July 2023
Christophe Ritzenthaler (CIMPA/Université de Nice) gave a series of lectures on the geometry of plane (not necessarily smooth) curves and some arithmetic results related to their maximal number of points over finite fields. Restricting to smooth curves, the cases of degree 1, 2, and, using some experiments with Magma, degree 3 (elliptic curves) were studied. Applications to cryptography and coding theory were also discussed. Finally the speaker sketched a proof of the fact that the asymptotic proportion of elliptic curves over F_q with q+1 points goes to 0 when q goes to infinity.
Supported by CIMPA.
2022 Workshop
Dates: 26-28 October 2022
Balazs Szendroi (University of Vienna) gave a series of lectures entitled "Algebraic Geometry through examples". Presentations were also given by Nairobi students Peter Oluoch, Frederick Koech and Benson Kipng'ong'o
Supported by the University of Vienna
Link to a paper paper on Biochemical reaction networks by Alicia Dickenstein
2021 Workshop
Dates: 23-31 August 2021
The event took place online, virtually hosted by the Department of Mathematics, Chiromo Campus, University of Nairobi
The event was dedicated to the memory of Professor Marco Andrea Garuti
The event was partly sponsored by the University of Trento, Italy. It was organised in collaboration with the Abram Gannibal Project
Organizers: Jared Ongaro (University of Nairobi), Diletta Martinelli (University of Amsterdam), Balazs Szendroi (University of Oxford)
Three mini-courses with several exercise sessions were given
Balazs Szendroi (Oxford): Computational Algebraic Geometry with Macaulay 2
Danilo Lewanski (IHES Paris): Hurwitz theory
Diletta Martinelli (Univeristy of Amsterdam): An introduction to toric varieties
Joint talks with the African Mathematical Seminar were given by senior speakers Diane Maclagan (University of Warwick) and Bernd Sturmfels (MPI Leipzig/UC Berkeley)
Teaching assistants were Aurelio Carlucci, University of Oxford; Bianca Gouthier (University of Bordeaux), Margherita Pagano (Univerity of Leiden), Chiara Bonadiman (University of Trento)
2019 Workshop
Dates: 2-11 September 2019
Organizers: Jared Ongaro, University of Nairobi; Balazs Szendroi, University of Oxford
Main speakers: Dominic Joyce FRS, University of Oxford; Miles Reid FRS, University of Warwick
The workshop consisted of lecture courses given by Prof Joyce and Prof Reid, accompanied by examples classes lead by doctoral students, and some research talks
Some of Prof Joyce's course material can be found HERE
The 2019 workshop was supported by a grant to the Centre for Quantum Geometry of Moduli Spaces at Aarhus University, Denmark, funded by Danish National Research Foundation, alongside continued support from partner institutions: University of Oxford , University of Warwick and University of Nairobi
2018 Workshop
Pre-workshop school: 21-24 August 2018, Workshop: 27-31 August 2018
Location: Department of Mathematics, Chiromo Campus, University of Nairobi
Workshop organizers: Damian Maingi (University of Nairobi), Diletta Martinelli (University of Edinburgh), Jared Ongaro (University of Nairobi), Balazs Szendroi (University of Oxford)
Organizers of the pre-workshop week: Aurelio Carlucci (University of Oxford), Alberto Cazzaniga (Stellenbosch University/AIMS South Africa), Diletta Martinelli (University of Edinburgh)
The workshop was organised in a partnership of the Nairobi Algebraic Geometry Group, the University of Oxford, the Africa Oxford Initiative and the Clay Mathematics Institute. Further support has been received from IMU CDC
Workshop speakers: Jim Bryan, University of British Columbia, Canada; Alessio Corti, Imperial College London, UK; Laura Costa, University of Barcelona, Spain; Mbolo Esoye, Northwestern, USA; Marco Garuti, University of Padova and AIMS-Cameroon; David Ssevviiri, Makerere University, Uganda
2017 Workshop
Dates: 14-16 June 2017
This was an activity organized around visits by Ran Tessler and Balazs Szendroi to the University of Nairobi. The visits were supported by the Institute of Theoretical Studies, ETH Zurich and the University of Oxford. Two mini-courses were given
Ran Tessler (Zurich): Moduli of curves and Witten's conjecture
Balazs Szendroi (Oxford): Introduction to moduli problems and moduli spaces
2016 Workshop
Dates: 8-11 August 2016
Venue: Chiromo Campus, University of Nairobi
Speakers included Enrico Fatighenti, Sara Muhvic and Miles Reid from the University of Warwick, and David Ssevviiri from Makerere University
Organizers: Gavin Brown (Warwick), Damian Maingi and Jared Ongaro (Nairobi) and Balazs Szendroi (Oxford)
Supported by a MARM grant from the London Mathematical Society, and by the Universities of Nairobi and Warwick
2015 Workshop
Dates: 10-13 August 2015
Organizers: Gavin Brown (Warwick), Damian Maingi (Nairobi), Jared Ongaro (Nairobi), Balazs Szendroi (Oxford)
Gavin Brown (University of Warwick): Riemann-Roch and graded rings I-II
Ben Davison (EPFL Lausanne): The cohomology of the space of semistable representations of a quiver I-II
Andre Saint Eudes Mialebama Bouesso (AIMS SA): Groebner bases over some quotient rings
Damian Maingi (University of Nairobi): Vector bundles associated to monads on multiprojective spaces
Renzo Cavalieri (Colorado State University): From Hurwitz Numbers to Tropical Geometry I-II
David Stern: Algebraic geometry in Africa? (talk and discussion)
Balazs Szendroi (University of Oxford): Hilbert schemes of points on surfaces I-II
Jared Ongaro (University of Nairobi): Plane Hurwitz numbers
Ben Kikwai (ICTP): Refined node polynomials via long edge graphs
Praise Adeyemo (University of Ibadan): Cohomological Consequences of the Pattern Map
