Prof. Dr. Dimitry Dolgopyat (University of Maryland)
Statistical properties of random dynamical systems abstract
Abstract:
We survey results about statistical properties of random dynamical systems and describe a number of open questions.
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Emily Roff (University of Edinburgh)
Abstract:
The past decade has seen a proliferation of homology theories for graphs. In particular, large literatures have grown up around magnitude homology (due to Hepworth and Willerton) and path homology (Grigor’yan, Lin, Muranov and Yau). Though their origins are quite separate, Asao proved in 2022 that in fact these homology theories are intimately related. To every directed graph one can associate a certain spectral sequence—the magnitude-path spectral sequence, or MPSS—whose page E^1 is exactly magnitude homology, while path homology lies along a single axis of page E^2. In this talk, based on joint work with Richard Hepworth, I will explain the construction of the sequence and argue that each one of its pages deserves to be regarded as a homology theory for directed graphs, satisfying a Künneth theorem and an excision theorem, and with a homotopy-invariance property that grows stronger as we turn the pages of the sequence. The \'nested’ family of homotopy categories associated to the pages is not yet well understood. But I will describe a new cofibration category structure on the category of directed graphs, associated to page E^2 of the MPSS.
Amélie Loher (University of Cambridge)
Abstract:
We discuss local regularity properties of solutions to non-local equations arising in kinetic theory. We will focus on the Strong Harnack inequality for global solutions to a non-local kinetic equation in divergence form. We will explain the connection to the Boltzmann equation and we will mention a few consequences on the asymptotic behaviour of the solutions.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Jeremy Blanc
Closed normal subgroups of the group of polynomial automorphisms abstract
Abstract:
The group of polynomial automorphisms of the affine plane has been studied a lot since decades. In 1942, Jung and van der Kulk proved that it is generated by affine automorphisms (linear maps and translations) and triangular automorphisms, which are automorphisms preserving one variable. It has moreover the structure of an amalgamated product over these two subgroups. The group is not simple as it contains the subgroup of automorphisms of Jacobian 1. This latter normal subgroup also contains some complicated normal subgroups, as proven by Danilov in 1974. The simplicity of this group, viewed as an infinite dimensional algebraic group, or equivalently the existence of closed normal subgroups was however often since Iskovskikh in 1966, which had produced an incomplete proof. I will give the answer to this question and explain the history and the details of the proofs.
14:15 • EPF Lausanne, CM 0 10
Dr. Younghan Bae (Univ. of Michigan)
Complex abelian varieties and their moduli VII abstract
Abstract:
Fourier-Mukai transformations on compactified Jacobians
14:30 • Zoom
Frederic Koehler (University of Chicago)
Pseudolikelihood, Score Matching, and Dynamics abstract
Abstract:
In his 1975 paper "Statistical Analysis of Non-Lattice Data", Julian Besagproposed the pseudolikelihood method as an alternative to the standardmethod of maximum likelihood estimation. This method has beenvery influential and successful in applications like learning graphical modelsfrom data, and also inspired another related and important method called score matching. I will discuss some recent work which connects the statisticalefficiency of these estimators to the computational efficiency of related samplingalgorithms.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Michelle Bucher (Université de Genève)
Continuous cocycles on the Furstenberg boundary and applications to bounded cohomology abstract
Abstract:
Group cohomology comes in many variations. The standard Eilenberg-MacLane group cohomology is the cohomology of the cocomplex {f:Gq+1→ ℝ | f is G-invariant} endowed with its natural homogeneous coboundary operator. Now whenever a property P of such cochains is preserved under the coboundary one can obtain the corresponding P-group cohomology. P could be: continuous, measurable, L0, bounded, alternating, etc. Sometimes these various cohomology groups are known to differ (eg P=empty and P=continuous for most topological groups), in other cases they are isomorphic (eg P=empty and P=alternating (easy), P=continuous and P=L0 (a highly nontrivial result by Austin and Moore valid for locally compact second countable groups)).In 2006, Monod conjectured that for semisimple connected, finite center, Lie groups of noncompact type, the natural forgetful functor induces an isomorphism between continuous bounded cohomology and continuous cohomology (which is typically very wrong for discrete groups). I will focus here on the injectivity and show its validity in several new cases including isometry groups of hyperbolic n-spaces in degree 4, known previously only for n=2 by a tour de force due to Hartnick and Ott. Monod recently proved that all such continuous (bounded) cohomology classes can be represented by measurable (bounded) cocycles on the Furstenberg boundary. Our main result is that these cocycles can be chosen to be continuous on a subset of full measure. In the real hyperbolic case, this subset of full measure is the set of distinct tuples of points, easily leading to the injectivity in degree 4.This is joint work with Alessio Savini.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Jia-Jie (JJ) Zhu (WIAS Berlin)
Kernel Approximation of Wasserstein and Fisher-Rao Gradient flows abstract
Abstract:
Gradient flows have emerged as a powerful framework for analyzing machine learning and statistical inference algorithms. Motivated by several applications in statistical inference, generative models, generalization and robustness of learning algorithms, I will provide a few new results regarding the kernel approximation of gradient flows, such as a hidden link between the gradient flows of kernel maximum-mean discrepancy and relative entropies. These findings not only advance our theoretical understanding but also provide practical tools for enhancing machine learning algorithms. I will showcase inference and sampling algorithms using a new kernel approximation of the Wasserstein-Fisher-Rao (a.k.a. Hellinger-Kantorovich) gradient flows, which have better convergence characterization and improved performance in computation.The talk is based on the joint works with Alexander Mielke.
16:00 • EPF Lausanne, CM 1 517
Dr. Gabriel Berzunza (University of Liverpool )
Fringe trees for random trees with given vertex degrees abstract
Abstract:
In this talk, we consider fringe trees of random plane trees with given vertex statistics (i.e., a given number of vertices of each degree). The main results are laws of large numbers and central limit theorems for the number of fringe trees of a given type.The key tool for our proofs is an extension to the multivariate setting of a theorem by Gao and Wormald (2004), which provides a way to show asymptotic normality by analyzing the behaviour of sufficiently high factorial moments.Our results also apply to random simply generated trees (or conditioned Galton–Watson trees) by conditioning on their degree statistic.Joint work with Cecilia Holmgren and Svante Janson (Uppsala University)
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43