Adam Kanigowski (University of Maryland)
Sparse Equidistribution Problems in Dynamics
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Abhishek Shetty
CANCELLED: Discrepancy and Compression: Two Perspectives abstract
Abstract:
Discrepancy theory has been an area that has recently seen a lot of activity due to algorithmic progress on longstanding open problems. This has opened up connections in diverse areas such as machine learning, probability theory, convex geometry and communication complexity. In this talk, we will focus on some new perspectives on a classical connection between discrepancy theory and compression. In the first part of the talk, we will focus on a connection between discrepancy and one-way communication complexity. In particular, we will show that certain natural question in discrepancy i.e. (Matrix) Spencer problem are equivalent to the one-way (Quantum) communication complexity of a natural communication problem (the indexing problem). Using this connection, we will see applications to the Matrix Spencer conjecture. In the second part of the talk, we will see application of algorithmic discrepancy theory to the problem of distribution compression, i.e. the task of producing a small representative data set that approximates a distribution. We will see general algorithms in this setting that lead to diverse applications such as speeding up testing and optimization and approximating attention.
11:15 • EPF Lausanne, BC129
Prof. Dr. Kostiantyn Drach (Universitat de Barcelona/CRM-Barcelona)
(Unmarked) Length spectral rigidity for expanding circle maps abstract
Abstract:
For a smooth expanding map of the circle, its (unmarked) length spectrum is defined as the set of logarithms of multipliers along all periodic orbits. This set is analogous to the set of lengths of all closed geodesics on negatively curved surfaces -- the classical length spectrum. In the talk, I will present a length spectral rigidity result for expanding circle maps. Namely, I will show that a smooth expanding circle map, under certain assumptions on the sparsity of its length spectrum, cannot be perturbed with an arbitrarily small smooth perturbation (depending on the map) so that the length spectrum stays the same. The proof uses the Whitney extension theorem, a quantitative Livcis-type theorem, and a novel iterative scheme. This is joint work with Vadim Kaloshin.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Zhiyu Liu (Zhejiang Univeristy and ETH-ITS)
Irreducible symplectic varieties with a large second Betti number abstract
Abstract:
Irreducible symplectic varieties are one of three building blocks of varieties with Kodaira dimension zero, which are higher-dimensional analogs of K3 surfaces. Despite their rich geometry, there have been only a limited number of approaches to construct irreducible symplectic varieties. In this talk, I will introduce a general criterion for the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations, based on the minimal model program and the geometry of Lagrangian tori. As an application, I will explain how to get a 42-dimensional irreducible symplectic variety with the second Betti number at least 24. This is a joint work with Yuchen Liu and Chenyang Xu.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Johannes Schipp von Branitz (University of Nottingham)
Abstract:
Homotopy type theory is an intuitionistic type theory with the aspiration of becoming a foundation for all of mathematics. In this talk we introduce the basic type theoretic constructions and their semantic interpretation in an infinity topos, before discussing the synthetic analogues of classical homotopy theoretic constructions such as Eilenberg-MacLane spacesand Whitehead\'s theorem.
Samed Düzlü (Universität Regensburg)
Automorphic Forms and Cryptographic Lattice Problems abstract
Abstract:
In lattice-based cryptography, one of the most popular approaches to increase efficiency is to attach structures to lattices. These structures usually come from algebraic number theory: For instance, taking fractional ideals of number fields become lattices inside the associated Minkowski space, on which the ring of integers act by multiplication. Extending this idea, module lattices are defined by taking submodules over the ring of integers inside an m-dimensional vector spaces over the number field. As the structures involve these algebraic number theoretic notions, it seems natural to analyze the corresponding lattice problems using number theoretic techniques. De Boer et al. (CRYPTO'20) carried out this strategy for ideal lattices: Fixing a number field, the set of ideal lattices (up to scaling) is a compact commutative Lie group. Cryptographic problems on the ideal lattices can be translated to the study of the space of ideal lattices. We explain this approach by a slight reformulation in terms of adeles and ideles. Then, the natural generalization of the idele class group to GL(m) corresponds immediately to the class of module lattices of rank m, for the same fixed number field. We describe this correspondence and explain the building blocks to generalize the results of de Boer et al. to module lattices of higher ranks. We finish with a partial result and explanation of the obstacles to conclude an effective solution.
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Anthony Genevois (Institut Montpellierain Alexander Grothendieck)
Quasi-median graphs, right-angled Artin groups, and homotopy abstract
Abstract:
After a general introduction to applications of metric graph theory in geometric group theory, focused on quasi-median graphs, I will explain how one can deduce from such a perspective new quasi-isometric invariants for right-angled Artin groups. This is joint work with Carolyn Abbott and Eduardo Martinez-Pedrosa.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Christopher Criscitiello
Abstract:
Some optimization problems encountered in practice are non-convex, but become geodesically convex (g-convex) when the search space is endowed with the right Riemannian metric. Examples from statistics include Tyler\'s M-estimator for robust covariance estimation, and maximum likelihood estimators for matrix and tensor normal models. Further instances arise in theoretical computer science (e.g., noncommutative polynomial identity testing), quantum information (e.g., tensor scaling), and pure mathematics (e.g., Brascamp-Lieb constants).Motivated by these applications, we investigate the query complexity of geodesically convex optimization. Our main result is a lower bound showing that the curvature of the search space fundamentally increases the difficulty of g-convex optimization compared to its Euclidean counterpart. This, in turn, rules out the possibility of Nesterov acceleration on manifolds, in certain regimes. It also has implications for tensor scaling and related problems.The talk will begin with motivating applications from statistics, followed by a brief review of the necessary geometric tools. We then present the lower bounds, provide intuition for their validity, and explore their consequences for downstream tasks.
16:15 • Universität Bern, IMSV, Alpeneggstrasse 22, 3012 Bern, Hörraum -203
Prof. Dr. Michael Dumbser (University of Trento)
On well-balanced finite difference, finite volume and discontinuous Galerkin schemes for the Einstein-Euler system of general relativity
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Dr. Alejandro Rosales Ortiz (Universität Zürich, Switzerland)
Graduate Workshop Reinforcement
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12