Past talks
2024
22 May – Lucia Cavallaro (Radboud University Nijmegen)
Title: Network Features in Complex Applications
Abstract: This talk shows how Network Science can be applied to (i) analyze criminal networks and (ii) miniaturize Artificial Neural Networks (ANNs). In the first part, key findings confirm that Betweenness Centrality is the most effective node ranking strategy for rapidly disrupting the information flow within these networks. Additionally, even with a large fraction of missing links (up to 30%), representing interceptions missed by Law Enforcement Agencies (LEAs), the networks remain reliable for investigative purposes. In the second part, an efficient sparsification strategy using Erdős-Rényi random networks to streamline the training of ANNs is proposed. Initial results are promising, with Sparse ANNs significantly reduced in size (up to 70% sparsity) while experiencing minimal accuracy loss. Future research will explore using Network Science techniques to gain insights into how ANNs operate.
17 April – Heather Harrington (Max Planck Institute for Molecular Cell Biology and Genetics and University of Oxford)
Title: Topology of spatio-temporal trajectories
Abstract: Many processes in the life sciences are inherently multi-scale and dynamic. Spatial structures and patterns vary across levels of organisation, from molecular to multi-cellular to multi-organism. With more sophisticated mechanistic models and data available, quantitative tools are needed to study their evolution in space and time. Topological data analysis (TDA) provides a multi-scale summary of data. We review single and multi-parameter persistent homology. Recent work by Kim and Memoli proposed a filtration for the case of dynamic metric spaces, requiring three parameter persistence. In-progress work by Lesnick, Bender and Gäfvert combines Gröbner bases algorithms to compute minimal presentations of multiparameter persistence. Here we build on this work and present an algorithm, GBlandscapes, which computes 3-parameter persistent homology landscapes. We highlight the utility of two and three parameter persistence landscapes with concrete case studies arising in biological systems.
20 March – Justin M. Curry (University at Albany, SUNY)
Title: Algebraic and Geometric Models for Space Communications
Abstract: In this talk I will describe a new model for time-varying graphs (TVGs) based on persistent topology and cosheaves. In its simplest form, this model presents TVGs as matrices with entries in the semi-ring of subsets of time; applying the classic Kleene star construction yields novel summary statistics for space networks (such as STARLINK) called "lifetime curves." In its more complex form, this model leads to a natural featurization and discrimination of certain Earth-Moon-Mars communication scenarios using zig-zag persistent homology. Finally, and if time allows, I will describe recent work with David Spivak and NASA, which provides a complete description of delay tolerant networking (DTN) in terms of an enriched double category.
6 March – Maximilian Engel (UvA Amsterdam and FU Berlin)
Title: Shear-induced chaos via stochastic forcing: a tale of finding positive Lyapunov exponents
Abstract: We discuss the phenomenon of shear-induced chaos, coined by Wang and Young about twenty years ago and referring to chaotic behavior as a result of shear being magnified by some forcing, in the context of stochastic perturbations. As a latest result, we show the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation, perturbed by additive white noise, under sufficiently strong shear strength. This completes a series of related results for simplified situations which we can exploit by studying suitable limits of the shear and noise parameters. Some general ideas concerning conditioned random dynamics, computer-assisted proofs and continuity of Lyapunov exponents will be highlighted along the way.
21 February – Ágnes Backhausz (Eötvös Loránd University and Alfréd Rényi Institute of Mathematics, Budapest)
Title: From graph limits to random matrices
Abstract: The main motivation of graph limit theory is to understand the structure of large networks and graphs by using various tools from analysis and probability theory. Starting from different distance notions for graphs, one can define convergence notions for graph sequences. We can also construct limit objects, which are not graphs, but continuous (or measurable) functions or operators. In the talk we present the main concepts of graph limit theory for sparse, intermediate and dense graph sequences, together with some applications (e.g. for eigenvectors of certain random matrices), when solving the problem in the limit and translating it back leads to essentially new results about finite, discrete structures.
7 February – Aad van der Vaart (TU Delft)
Title: Gaussian processes in Bayesian statistics: a review and some recent results
Abstract: A nonparametric Bayesian statistical method puts a prior probability distribution on an infinite-dimensional parameter and next obtains a posterior distribution over the unknowns using an ordinary Bayesian analysis. The approach is quite elegant, and popular in applied settings, for instance in inverse problems or machine learning, when it is desired to obtain not only a point estimator, but also a quantification of the uncertainty in this estimator. In this talk we discuss the validity of the approach and its determinants from a non-Bayesian point of view. Gaussian processes are a first choice as priors for functions. We review theoretical results on posterior distributions resulting from such priors when used to model a regression function or density function, or a functional parameter in an inverse problem described by a differential equation. We review the role of the small ball probability of the Gaussian process as a determinant of the contraction rate of the posterior distribution, the importance of the length scale of the process, and the accuracy of credible sets for uncertainty quantification. We present recent results on approximating a posterior distribution by distributed computing, and on using linear methods to solve inverse problems resulting from some nonlinear partial differential equations.
2023
6 December – Eva Miranda (Universitat Politècnica de Catalunya)
Title: The Weinstein conjecture
Abstract: The Weinstein conjecture (1979) concerns the existence of periodic orbits of Reeb vector fields. Over the years, the conjecture has undergone significant developments. In this talk, I will provide a historical overview of the Weinstein conjecture and discuss variations for singular contact manifolds. The Weinstein conjecture for singular structures matches in nature a number of problems in celestial mechanics. I will relate the singular Weinstein conjecture with the existence of escape orbits in celestial mechanics and fluid dynamics. Time permitting, I will conclude with a counterexample to the singular Weinstein conjecture.
This talk is based on joint works with Josep Fontana-McNally, Cédric Oms, and Daniel Peralta-Salas (some of them ongoing).
29 November – Pol van Hoften (VU Amsterdam)
Title: Some "dynamical systems'' in characteristic p.
Abstract: The goal of this talk is to give a leisurely introduction to the mathematics surrounding Oort's Hecke orbit conjecture. Towards the end, I hope to say something about the proof in my joint work with Marco D'Addezio. We will start by discussing the action of SL_2(R) on the Poincare upper half plane H by Mobius transformations, and from there discuss the modular curve SL_2(Z)\ H and its Hecke operators.
15 November – Jürgen Jost (Max Planck Institute for Mathematics in the Sciences)
Title: Generalized Curvatures and the Geometry of Data
Abstract: Curvature is the most important concept of Riemannian geometry, and it has been extended to metric spaces. Here, I shall develop a notion of curvature that also applies to discrete spaces (as occurring as data samples), links curvature to the concept of hyperconvexity and offers a geometric view on topological data analysis.
1 November – Special event with Daniele Avitabile and Meron Vermaas (VU Amsterdam)
11 October – Leo Tzou (UvA)
Title: Geodesic Lévy Flight and the Foraging Hypothesis
Abstract: The Lévy Flight Foraging Hypothesis is a widely accepted dogma which asserts that animals using search strategies allowing for long jumps, also known as Lévy flights, have an evolutionary advantage over those animals using a foraging strategy based on continuous random walks modelled by Brownian motion. However, recent discoveries suggest that this popular belief may not be true in some geometric settings. In this talk we will explore some of the recent progress in this direction which combines Riemannian geometry with stochastic analysis to create a new paradigm for diffusion processes.
27 September – Inbar Klang (VU Amsterdam)
Title: Manifold topology via isovariant homotopy theory
Abstract: Homotopy theory has proven to be a robust tool for studying non-homotopical questions about manifolds; for example, surgery theory addresses manifold classification questions using homotopy theory. In joint work with Sarah Yeakel, we are developing a program to study manifold topology via isovariant homotopy theory. I'll introduce isovariant homotopy theory, explain how it relates to the study of manifolds via their configuration spaces, and talk about an application to fixed point theory.
13 September – Francesco Fassò (University of Padova)
Title: A mathematical view to the synchronization in unforced dissipative mechanical systems
Abstract: Synchronization phenomena in systems governed bydifferential equations (which include famous examples such as Huyghens coupled pendula and swarms of flashing fireflies) constitute a large and actively studied research field, particularly in applied sciences, and a world of fascination. A mathematical comprehension of the mechanisms that lead to such behaviours is however still incomplete. In this talk I will restrict to a particular class of such systems (unforced dissipative mechanical systems, which include systems of pendula attached to a damped moving platform or to a viscoleastic cable) and explain the mathematical tools (from dynamical systems theory) which can be used to provide rigorous results on the synchronization phenomenain such systems, and the practical difficulties which one encounters in trying to apply them.
24 May – Krystal Guo (UvA)
Title: Strongly regular graphs with a regular point
Abstract: Arising from Hoffman and Singleton's study of Moore graphs, strongly regular graphs play an important role in algebraic graph theory. Strongly regular graphs can be construct from geometric objects, such as generalized quadrangles and certain geometric properties, such as having a regular point, can be studied in the context of graphs. We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, thereby, answering a question posed by Gardiner, Godsil, Hensel, and Royle. As a by-product of our characterisation, we are able to give new constructions of infinite families of strongly regular graphs and compute many small sporadic examples, in particular, we find 135478 new strongly regular graphs with parameters (85,20,3,5) and 27 039 strongly regular graphs with parameters (156, 30, 4, 6).
This is joint work with Edwin van Dam.
10 May – Renee Hoekzema (VU)
Title: Cutting and pasting manifolds
Abstract: Scissor’s congruence is a classical setup in mathematics that featured in one of Hilbert’s problems in 1900. It asks whether two polytopes can be obtained from one another through a process of cutting and pasting. In the 1970s this question was posed instead for smooth manifolds: which manifolds A and B can be related to one another by cutting A into pieces and gluing them back together to get B? Manifold cut and paste invariants describe when this is possible. In this talk I introduce this these ideas and describe recent work that ‘upgrades’ cut and paste invariants from groups to spaces using the machinery from algebraic K-theory. This is joint work with Mona Merling, Laura Murray, Carmen Rovi and Julia Semikina.
26 April – Instead of the colloquium, there will be an inaugural lecture starting at 15:45 (sharp) in the Aula: Assia Mahboubi (VU/Inria) - Computer assisted mathematics. See this page for more information.
22 March – Raffaella Mulas (VU Amsterdam)
Title: Graphs and Hypergraphs: From spectral theory to extremal combinatorics
Abstract: Spectral graph theory studies the qualitative properties of a graph that can be inferred from the eigenvalues and the eigenvectors of an associated operator. It has a long history, is widely used in applications, and the first part of this talk will focus on it. We will then consider a generalization of spectral graph theory to the case of hypergraphs, as well as an application to networks of genetic expression. Finally, in the last part of the talk, we will focus on a much more theoretical topic and we will talk about an extremal combinatorics problem for hypergraphs that was introduced by Paul Turán in 1941.
22 February – Marcello Seri (University of Groningen) [Slides]
Title: Geometricintegration in celestial mechanics via the contact glasses
08 February – Walter van Suijlekom (RU) [Slides]
Title: Geometric spaces at finite resolution
Abstract: After a gentle introduction to the spectral approach to geometry, we extend the framework in order to deal with two types of approximation of metric spaces. On the one hand, we consider spectral truncations of geometric spaces, while on the other hand, we consider metric spaces up to finite resolution. In our approach, the traditional role played by C*-algebras is taken over by so-called operator systems. Essentially, this is the minimal structure required on a space of operators to be able to speak of positive elements, states, pure states, etc. We illustrate our methods in concrete examples obtained by spectral truncations of the circle and of metric spaces up to finite resolution. The former yield operator systems of finite-dimensional Toeplitz matrices, and the latter give suitable subspaces of the compact operators. We also analyze the cones of positive elements and the pure-state spaces for these operator systems, which turn out to possess a very rich structure.
2022
14 December – Daniel Labardini Fragoso (National Autonomous University of Mexico (UNAM) and University of Cologne) [Slides]
Title: Hyperbolic geometry and cluster algebras
Abstract: It has been more than twenty years since Fomin and Zelevinsky discovered cluster algebras. Often appearing as a new kind of symmetry, or as a novel way to combinatorially organize mathematical objects, cluster algebras have had deep interactions with many subjects in Mathematics and Theoretical Physics. In this talk I will illustrate how cluster algebras appear in hyperbolic geometry as coordinate rings of Teichmüller spaces. Time permitting, I shall also illustrate how the representation theory of quivers and the generating functions of perfect matchings of bipartite graphs can help to obtain expressions of many important functions in these coordinate rings.
30 November – Laura Scarabosio (Radboud) [Slides]
Title: Bayesian calibration and comparison of models of tumour cell dynamics
Abstract: Mathematical modeling is a powerful tool to predict cancer dynamics under some environmental conditions. However, in order to have quantitative predictions, model parameters need to be calibrated from data. In this talk, we address calibration of mathematical models of tumour growth using Bayesian inversion. The Bayesian approach allows not only to estimate the parameters, but also to quantify how much we can rely on these estimates. After recalling the main concepts in Bayesian inversion, we will apply them to a novel mathematical model for tumour growth, which takes into account systematically how different conditions in the tumour microenvironment affect cancer progression. We will see how a filtering-based approach allows for an efficient learning from time-resolved data, consisting, in our case, of fluorescence measurements of in-vitro cultured cells. Moreover, we will use Bayesian tools to compare our new mathematical model with a standard one, showing potential advantages of the first one.
This is joint work with Sabrina Schönfeld and Christina Kuttler (TUMunich), and with Alican Ozkan (Harvard University) and Marissa Nichole Rylander (UT Austin).
16 November – Hanne Kekkonen (TU Delft) [Slides]
Title: Statistical guarantees for inverse problems
Abstract: Bayesian methods for inverse problems have become increasingly popular in applied mathematics in the last decades. They provide inherent uncertainty quantification via Bayesian credible sets, and can often be efficiently implemented using MCMC methodology. For linear inverse problems Bayesian methods are closely related to the classical Tikhonov regularisation but for non-linear and non-convex problems they give genuinely distinct algorithmic alternatives.
In this talk I will discuss recent progress in Bayesian non-parametric statistics that allows us to give rigorous statistical guarantees for posterior consistency, and illustrate the theory with a variety of concrete inverse problems.
02 November – Rianne de Heide (VU) [Slides]
Title: E is the new P
Abstract: The last decade there has been much attention in the media to the fact that many scientific results are not reproducible, especially in medicine and psychology this is widely acknowledged. Part of the problem is due to the mathematics used for hypothesis testing. The standard methodology is the "p-value based null hypothesis significance testing", despite a myriad of problems surrounding it. We present the E-value, a notion of evidence which overcomes some of the issues.
12 October – Lauran Toussaint (VU) [Slides]
Title: Sphere eversions & the h-principle
Abstract: The h-principle is a collection of techniques to study the space of solutions of partial differential relations. One of the early results of this kind is due to Smale who classified (immersed) spheres in Euclidean space.
It has the remarkable consequence that the sphere can be turned inside out, in a smooth way (without cutting or tearing). I will discuss some ways that have been invented to visualize this sphere eversion, and a few ideas for proving such results.
28 September – Frank van der Meulen (VU) [Slides] [Handout]
Title: Backward Filtering Forward Guiding for Markov models
Abstract: Markovian processes are among the most popular models for time-varying phenomena. Their stochastic dynamics are usually specified up to un unknown parameter vector. If this parameter is known, forward evolving a Markov process is usually explicit. The statistical problem focusses on the inverse problem, where one gets (partial) observations from the process and tries to infer the parameter. For some combinations of observation schemes and Markov process this is simple, for most not. I will start from the very simplest case: finite state Markov chains. Then I will explain the difficulties introduced by increasingly more difficult processes. Finally I hope to explain the basics of Backward Filtering Forward Guiding: a framework to overcome these difficulties.
14 September – Stefano Luzzatto (ICTP) [Slides]
Title: Chaos Theory: Determinism and Randomness in Nature and Mathematics
Abstract: In 1908, Poincaré asked "Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.”. A hundred years later it can be said that we understand, to some extent, the answer to this question. I will give some historical background and describe some simple mathematical models which help us to understand the nature of chaotic and unpredictable systems.
25 May – Lennart Meier (Utrecht University)
Title: From elliptic genera to topological modular forms
Abstract: Elliptic genera are invariants of manifolds constructed from elliptic integrals or elliptic curves, first considered by Ochanine, Witten and Hirzebruch. They have very nice geometric properties, which motivates them independently of their origin. I will talk about refining elliptic genera to a transformation of homology theories. This allows to generalize the input to manifolds with a map to fixed target space, and also promises new proofs of classic properties.
A short survey article on the topic is the Notices article of Ochanine „What is an elliptic genus?“
11 May – Patricia Yanguas (Universidad Pública de Navarra) [Slides]
Title: Formal stability of elliptic equilibria. Applications.
Abstract: The subject of this talk is the study of the nonlinear stability of elliptic equilibria in Hamiltonian systems with n degrees of freedom. We provide a criterion to obtain formal stability. This result generalizes previous approaches, such as exponential stability in the sense of Nekhoroshev when there is directional quasi-convexity. It is also applicable to highly degenerate systems. Moreover, in the case of formal stability, the solutions are proven to be bounded near the equilibrium over exponentially long times. The theory is illustrated with some applications to systems with three or more degrees of freedom: the spatial circular restricted three-body problem; the attitude motion of a satellite describing a circular orbit in space with respect to its centre of mass in a central gravitational field; the Levitron.
This presentation is based on joint work with Daniela Cárcamo and Claudio Vidal Díaz (Universidad del Bío-Bío, Concepción, Chile) and Jesús F. Palacián (Universidad Pública de Navarra, Pamplona, Spain).
06 April – Alexander Lohse (Universität Hamburg)
Title: Heteroclinic Dynamics: Switching, Multicycles and Stability
Abstract: In the past decades heteroclinic structures have been studied as dynamical objects that organize complicated bifurcation scenarios in various settings. They can display an intricate range of stability and attraction properties tied to different dynamical behavior within a system. In order to understand a heteroclinic network it is often desirable to first understand its substructures — typically smaller networks or heteroclinic cycles. Recently, the concept of an omnicycle (or multicycle) has gained attention: a closed sequence of nodes and connections in a network where nodes and/or connections may appear multiple times. The stability properties of these objects are linked to switching behavior on (parts of) the initial network. In this talk we aim to present basic concepts in this context as well as some new ideas and open questions.
30 March – Eric Beutner (VU) [Slides]
Title: Justifying conditional inference in time series models
Abstract: Often we are interested in parameters that change over time and that do depend on the past. Thus, if we want to infer such parameters from observations we need to take into account past observations. Or in statistical/probabilistic terms we must condition on past values. Thereby, we lose randomness. Yet, randomness is what is needed to quantify the uncertainty inherent in inferential procedures for unknown parameter. In this talk we present an asymptotic approach that allows to condition on the past and to preserve enough randomness for statistical inference at the same time. Merging a concept that generalizes weak convergence of measures is briefly discussed and shown to be helpful for providing an asymptotic solution to the above problem.
09 March – Babette de Wolff (VU) [Slides]
Title: Delayed feedback stabilization of periodic orbits and spatio-temporal patterns
Abstract: In 1992, the physicist Pyragas proposed a time delayed feedback scheme to stabilize periodic solutions of ordinary differential equations. The feedback scheme (now known as ‘Pyragas control’) preserves periodic orbits with a given period, but drastically changes the dynamics in their neighborhoods and hence has the potential to make the periodic orbits stable.
While the success of Pyragas control has been confirmed in many experiments, mathematical results on Pyragas control are still relatively rare. This is mostly because the controlled system becomes a delay differential equation (DDE) which generates an infinite dimensional dynamical system and hence poses analytical challenges.
In the first part of this talk, I will discuss some fundamental observations in the mathematical analysis of Pyragas control, while also giving a short introduction to delay differential equations. The second part of this talk concerns feedback stabilization in systems with symmetries. I will discuss how Pyragas control can be adapted to stabilize spatio-temporal patterns, and how the functional analytical framework of DDE can be adapted in this setting.
23 February – Alex Best (VU) [Slides]
Title: The "why" of p-adic integration
Abstract: In many problems in number theory a field of numbers known as the p-adics (for a given prime number p) are used to make progress.
These play an analogous role to the real numbers and many techniques that are familiar from real or complex settings carry over, sometimes in similar ways, but often with striking differences.
In this colloquium talk I'll try to motivate how these numbers arise naturally from simple mathematical problems. I'll focus on the theory of p-adic integration, and how calculating these integrals can be useful for solving hard problems, even some that don't appear to involve prime numbers at all.
I'll also try to explain some applications of these ideas in other areas, such as in discrete dynamical systems.
09 February – Yufei Zhao (MIT) [Slides]
Title: Equiangular lines and eigenvalue multiplicities
Abstract: Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle.
A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity.
My talk will discuss these problems and their connections, along with extensions and open problems (e.g., what is the maximum possible second eigenvalue multiplicity of a connected bounded degree graph?).
Joint work with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang