http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Wed, 28 Aug 2024 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Alexander Kechris (CalTech) -

]]> http://www-math.umd.edu/research/seminars.html Wed, 04 Sep 2024 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Christoph Schwab (ETH, Zurich) - https://math.ethz.ch/research/applied-mathematics-numerical-analysis-scientific-computing/christoph-schwab.html
Abstract: Centered Gaussian random fields (GRFs) indexed by compacta
as e.g. compact orientable manifolds M
are determined by their covariance operators.
We consider the numerical analysis of sample-wise, compressive
multi-level wavelet-Galerkin approximations of centered GRFs given
as variational solutions to coloring operator equations driven by spatial white noise,
with pseudodifferential covariance operator being
elliptic, self-adjoint and positive from the Hörmander class.

For pathwise approximations with p parameters,
tapered covariance or precision matrices have O(p) nonzero entries,
can be optimally diagonally preconditioned,
and allow O(p) path simulation, covariance estimation and kriging of GRFs.

Joint work with Helmut Harbrecht (Uni Basel).
]]> http://www-math.umd.edu/research/seminars.html Wed, 18 Sep 2024 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Julien Berestycki (University of Oxford, Statistics Department) - https://www.stats.ox.ac.uk/~berestyc/
Abstract: The $N$-branching Brownian motion with selection ($N$-BBM) is a particle system consisting of $N$ independent particles that diffuse as Brownian motions in $\mathbb{R}$, branch at rate one, and whose size is kept constant by removing the leftmost particle at each branching event. It is a simple toy model for the evolution of a population under selection that has generated some fascinating research since its introduction by Brunet and Derrida in the early 200ss.

If one recentre the positions by the left most particle, this system has a stationary distribution. I will show that, as $N\to \infty$ the stationary empirical measure of the $N$-particle system converges to the minimal travelling wave of an associated free boundary PDE. This resolves an open question going back at least to works of e.g. Maillard in 2012.
It follows a recent related result by Oliver Tough (with whom this is joint work) establishing a similar selection principle for the so-called Fleming-Viot particle system.
]]> http://www-math.umd.edu/research/seminars.html Wed, 23 Oct 2024 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Artur Avila (IMPA) -

]]> http://www-math.umd.edu/research/seminars.html Fri, 25 Oct 2024 16:00:00 EDT Where: Kirwan Hall 3206
Speaker: Stephane Mallat (College de France) - https://blog.umd.edu/nwc/fft/2024fft/
Abstract: Score based diffusions generate impressive models of images, sounds and complex physical systems. Are they generalising or memorising ? How can deep network estimate high-dimensional scores without curse of dimensionality ? This talk shows that generalisation does occur for deep network estimation of scores, with enough training data. We prove that these deep networks perform a denoising by shrinking image coefficients in a best basis adapted to the image geometry. The ability to avoid the curse of dimensionality seems to rely on multiscale properties revealed by a renormalisation group decomposition coming from statistical physics. Applications to models of turbulences will be introduced and discussed.
]]> http://www-math.umd.edu/research/seminars.html Wed, 30 Oct 2024 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Amos Nevo (Technion) -
Abstract: Let G be a Lie group, L a lattice in G, and H a closed subgroup of G.
Suppose that L acts on the homogeneous space G/H with dense orbits.
Naturally, we would like to measure how dense these orbits actually are, or equivalently, gauge the efficiency of approximation of a general point on G/H by a lattice orbit.
Departing from traditional classical Diophantine approximation, we will
Assume G to be a non-amenable group, for example the group of isometries of hyperbolic space, or the general linear or affine group.
We will present a solution to this problem for lattice actions
on a large class of homogeneous spaces, emphasizing a sufficient condition for when an optimal result holds, and give some examples. The methods involve dynamical arguments, and the representation theory of the automorphic representation.
We will then briefly describe the extensive scope of this set-up, and explain some more refined problems related to equidistribution and discrepancy of lattice orbits, as time permits.
Based partly on joint work with Alex Gorodnik and Anish Ghosh, and partly on recent joint work with Alex Gorodnik and Mikolaj Fraczyk.
]]> http://www-math.umd.edu/research/seminars.html Wed, 06 Nov 2024 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Adam Kanigowski (UMD) - https://akanigow.math.umd.edu/

Title:  Ergodic and statistical properties of slowly chaotic systems

Abstract: Smooth dynamical systems can be (roughly) divided into three classes: (partially) hyperbolic, parabolic and elliptic. I will shortly discuss some general characteristic features of each of these classes. Then I will focus on the class of parabolic dynamical systems. These systems typically display intermediate type of chaotic behavior (called slow chaos). I will discuss recent developments and results around ergodic and statistical properties for parabolic dynamical systems.
]]> http://www-math.umd.edu/research/seminars.html Wed, 13 Nov 2024 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Maria Chudnovsky (Princeton University) - https://web.math.princeton.edu/~mchudnov/
Abstract: Tree decompositions are a powerful tool in both structural
graph theory and graph algorithms. Many hard problems
become tractable if the input graph is known to have a tree
decomposition of bounded “width”. Exhibiting a particular kind
of a tree decomposition is also a useful way to describe the
structure of a graph.

Tree decompositions have traditionally been used in the context
of forbidden graph minors; studying them in connection with
graph containment relations of more local flavor (such as
induced subgraph or induced minors) is a relatively new
research direction. In this talk, we will discuss recent progress in
this area, touching on both the classical notion of bounded
tree-width, and concepts of more structural flavor.
]]> http://www-math.umd.edu/research/seminars.html Wed, 20 Nov 2024 15:30:00 EST Where: Kirwan Hall 3206
Speaker: Alessio Figalli (ETH Zurich) - https://people.math.ethz.ch/~afigalli/

]]> http://www-math.umd.edu/research/seminars.html Mon, 09 Dec 2024 15:30:00 EST Where: Kirwan Hall 3206
Speaker: Patrick Lutz (UC Berkeley) - https://math.berkeley.edu/~pglutz/
Abstract: The field of computability theory studies the complexity of uncomputable problems. In this study, a special role is played by the Halting Problem—i.e. the problem of determining whether a given program stops after a finite number of steps or runs forever. Not only is it the first problem proved to be uncomputable, it also seems to be the simplest "natural" uncomputable problem. Martin's Conjecture is a long-standing open question in computability theory which partially explains why the Halting Problem plays such a special role. A key idea behind Martin's Conjecture is to view the Halting Problem not just as an individual problem, but as an operator on problems, which takes any problem to a strictly harder one. Martin's Conjecture consists of a classification of such operators, which says, in part, that the Halting Problem is the minimal non-trivial operator. I will discuss the background and motivation for Martin's Conjecture, as well as recent progress by Benjamin Siskind and myself which essentially completes a proof of the conjecture for a special class of operators called "order-preserving."
]]> http://www-math.umd.edu/research/seminars.html Wed, 11 Dec 2024 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Christophe Garban (University of Lyon) - https://math.univ-lyon1.fr/~garban/
Abstract:  One of the main goals of statistical physics is to observe how spins displayed along a lattice Z^d interact together and fluctuate. When the spins belong to a discrete set (for example the celebrated Ising model where spins \sigma_x belong to {-1,+1}), the nature of the phase transitions which arise as one varies the temperature is now rather well understood. When the spins belong instead to a continuous space (for example the unit circle S^1 for the so-called XY model, the unit sphere S^2 for the classical Heisenberg model etc.), the nature of the phase transitions differs drastically from the discrete symmetry setting. The case where the (continuous) symmetry is non-Abelian is currently more mysterious than when the symmetry is Abelian. In the later case, phase transitions are caused by a change of behaviour of certain monodromies in the system called "vortices". They are called topological phase transitions for this reason.  
In this talk, after an introduction to the mathematics of spin systems with a continuous symmetry, I will present some recent results on these spins systems. One proof will happen to rely on an intriguing Bayesian statistics problem (!).
The talk will not require any background in statistical physics/probability and will be based on joint works with Juhan Aru, Paul Dario, Avelio Sepúlveda and Tom Spencer.
]]> http://www-math.umd.edu/research/seminars.html Wed, 05 Feb 2025 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Zbigniew Blocki (Jagiellonian University and UMD) - https://gamma.im.uj.edu.pl/~blocki/
Abstract: Breaking of the Enigma code, encryption used by the Germans in the Second World War, had a huge influence on the outcome of the conflict. Everybody has heard about the Bletchey Park and Alan Turing’s role in it but it is not widely known that in fact it was done by Polish mathematicians led by Marian Rejewski already in December 1932. Only in July 1939 the Polish intelligence shared it with the Allies and only since then the British could follow. We will explain the main mathematical aspects of this work, as well as the historical background.
]]> http://www-math.umd.edu/research/seminars.html Thu, 13 Feb 2025 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Albert Cohen ( Sorbonne University) - https://www.ljll.fr/cohen/
Abstract: Understanding how to optimally approximate general compact sets by finite dimensional spaces is of central interest for designing efficient numerical methods in forward simulation or inverse problems. While the concept of n-width, introduced in 1936 by Kolmogorov, is well taylored to linear methods, finding the correct analogous concept for nonlinear approximation (which typically occurs when using adaptive methods or neural networks) is still the object of current research. In this talk, we shall discuss a general framework that allows to embrace various concepts of linear and nonlinear widths, present some recent results and relevant open problems.
]]> http://www-math.umd.edu/research/seminars.html Wed, 19 Feb 2025 15:15:00 EST Where:

]]> http://www-math.umd.edu/research/seminars.html Wed, 26 Feb 2025 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Amanda Hirschi (Sorbonne Université) - https://amandahirschi.com/
Abstract: Two simply-connected smooth 4-manifolds are homeomorphic if and only if their product with S^2, are diffeomorphic. The Donaldson 4-6 question ask whether this fact can be lifted to the symplectic category. Explicitly, it conjectures that the underlying smooth manifolds of two (simply-connected) symplectic manifolds are diffeomorphic if and only if their product with S^2, equipped with the standard area form, are symplectic deformation equivalent. I will describe one example of a smooth 4-manifold admitting two symplectic forms which remain deformation inequivalent after taking the product with S^2, giving counterexamples to one implication of the conjecture. On the other hand, I will explain why two symplectic manifolds, whose stabilisations are deformation equivalent, have the same Gromov-Witten invariants. This is joint work with Luya Wang.
]]> http://www-math.umd.edu/research/seminars.html Wed, 05 Mar 2025 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Katrin Tent (University of Münster) - https://www.uni-muenster.de/FB10srvi/persdb/MM-member.php?id=482
Abstract: The Cherlin-Zilber Conjecture states that any infinite simple group of finite Morley rank is an algebraic group over an algebraically closed field. I will explain how work on this conjecture naturally leads to the Burnside problem, namely the question whether any finitely generated group of bounded exponent is finite. I will then indicate the ideas behind our proof with Atkarskaya and Rips which gives the currently best known lower bound for the exponent for infinite Burnside groups.
]]> http://www-math.umd.edu/research/seminars.html Wed, 12 Mar 2025 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Pazit Haim-Kislev (Institute for Advanced Study) - https://www.ias.edu/scholars/pazit-haim-kislev
Abstract: Symplectic capacities are, roughly speaking, a means of measuring the "size" of symplectic manifolds, arising from various themes in Hamiltonian dynamics and symplectic topology. Viterbo's conjecture, an isoperimetric-type question introduced in 2000, asserted that the ball has the largest capacity among all convex domains with the same volume. Despite its simple formulation, this conjecture remained unresolved for many years, sparking extensive research, partly due to its encapsulation of the nontrivial interplay between convex and symplectic geometries. In this talk, I will present a counterexample to Viterbo's conjecture, based on joint work with Yaron Ostrover, and discuss its implications for further research.
]]> http://www-math.umd.edu/research/seminars.html Wed, 26 Mar 2025 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Davesh Maulik (MIT) - https://math.mit.edu/directory/profile.html?pid=177
Abstract: Given a compact Riemann surface, nonabelian Hodge theory relates topological and algebro-geometric objects associated to it. Namely, complex representations of the fundamental group are in correspondence with algebraic vector bundles, equipped with an extra structure called a Higgs field. This gives a transcendental matching between two very different moduli spaces associated with the Riemann surface: the character variety (parameterizing representations of the fundamental group) and the Hitchin moduli space (parameterizing Higgs bundles). In 2010, de Cataldo, Hausel, and Migliorini proposed the P=W conjecture, which predicted that the Hodge theory of the character variety is determined by the topology of the Hitchin space, imposing surprising constraints on each side. In this talk, I will introduce the conjecture and review its recent proofs; time permitting, I will try to explain how this phenomenon relates to other geometric questions.
]]> http://www-math.umd.edu/research/seminars.html Wed, 09 Apr 2025 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Robert Simon (London School of Economics) - https://www.lse.ac.uk/Mathematics/people/Robert-Simon
Abstract: We show that there is an infinite graph of finite degree defined by a Borel
equivalence relation on a probability space such that it can be coloured
properly with 17 colours but only in ways that induce paradoxical
decompositions. We show that there are problems of optimization such that
every epsilon-optimal solution for small enough positive epsilon induces a paradoxical decomposition.




]]> http://www-math.umd.edu/research/seminars.html Wed, 16 Apr 2025 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Jeff Adams (IDA-CCS and UMD) - https://www.math.umd.edu/~jda/
Abstract: This talk is an update on the Atlas of Lie Groups and Representations project which was started at UMD in 2002. One of the main problems in representation theory is to describe the unitary dual: the set of irreducible unitary representations of a Lie group. I will describe an algorithm for computing the unitary dual of, and discuss our computer calculations of E_7 and (partially completed) E_8. I will also discuss recent progress on proving Arthur's conjectures about the unitarity of Arthur packets for real reductive groups. This work is joint with the members of the Atlas project - among others, Lucas Mason-Brown, Stephen Miller, Marc van Leeuwen, Annegret Paul and David Vogan, as well as Dougal Davis and Kari Vilonen.
]]>