Umut Çetin (London School of Economics)
Mathematics of Market Microstructure
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Olga Kharlampovich (CUNY, Graduate Center and Hunter College)
Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations abstract
Abstract:
We answer the question asked by Louder, McReinolds and Patel and prove the following statement. Let L be a RAAG, H a cubically convex-cocompact subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental group of a hyperbolic 3-manifold.For any finitely generated subgroup H of a limit group L we prove the same results and, in addition, show that there exists a finite-index subgroup K containing H, such that K is a subgroup of a group obtained from H by a series of extensions of centralizers and free products with infinite cyclic group. If H is non-abelian, the K is fully residually H. A corollary is that a hyperbolic limit group satisfies the Geometric Hanna Neumann conjecture. These are joint results with K. Brown and A. Vdovina.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Thomas Rothvoss (University of Washington)
Optimal Online Discrepancy Minimization abstract
Abstract:
We prove that there exists an online algorithm that for any sequence of vectors $v_1,\\ldots,v_T \\in \\setR^n$with $\\|v_i\\|_2 \\leq 1$, arriving one at a time, decides random signs $x_1,\\ldots,x_T \\in \\{ -1,1\\}$ so thatfor every $t \\le T$, the prefix sum $\\sum_{i=1}^t x_i v_i$ is $O(1)$-subgaussian. This improves over the work ofAlweiss, Liu and Sawhney who kept prefix sums $O(\\sqrt{\\log (nT)})$-subgaussian.Our proof combines a generalization of Banaszczyk\'s prefix balancing result to trees with a cloning argument to finddistributions rather than single colorings.This is joint work with Janardhan Kulkarni and Victor Reis.
11:00 • EPF Lausanne
Ernst Hairer (Université de Genève)
Long-time behaviour of numerical integrators for charged particle dynamics abstract
Abstract:
The Boris algorithm is the most popular time integrator for charged particle motion inelectric and magnetic force fields. It is a symmetric one-step method, and it preservesthe phase volume exactly. However, it is not symplectic.In this talk we prove near-conservation of energy over very long times in the specialcases where either the magnetic field is constant or the electric potential is quadratic.When none of these assumptions is satisfied, it is illustrated by numerical examplesthat the numerical energy can have a linear drift or its error can behave like a random walk.We thank Martin Gander for drawing our attention to this problem.The presented results have been obtained in collaboration with Christian Lubich.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Dr. Mateus Sousa (BCAM)
Local and global extremizers for Fourier restriction estimates abstract
Abstract:
In this talk we will see a brief history of sharp Fourier restriction theory and some recent developments related to Fourier restriction estimates on spheres. We will discuss the problem of finding sharp constants for such inequalities, as well as the questions of existence and classification of extremizers of these estimates.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Zijian Guo (Rutgers University)
Adversarially Robust Learning: Identification, Estimation, and Uncertainty Quantification abstract
Abstract:
Empirical risk minimization may lead to poor prediction performance when the target distribution differs from the source populations. This talk discusses leveraging data from multiple sources and constructing more generalizable and transportable prediction models. We introduce an adversarially robust prediction model to optimize a worst-case reward concerning a class of target distributions and show that our introduced model is a weighted average of the source populations\' conditional outcome models. We leverage this identification result to robustify arbitrary machine learning algorithms, including, for example, high-dimensional regression, random forests, and neural networks. In our adversarial learning framework, we propose a novel sampling method to quantify the uncertainty of the adversarial robust prediction model. Moreover, we introduce guided adversarially robust transfer learning (GART) that uses a small amount of target domain data to guide adversarial learning. We show that GART achieves a faster convergence rate than the model fitted with the target data. Our comprehensive simulation studies suggest that GART can substantially outperform existing transfer learning methods, attaining higher robustness and accuracy.Short Bio: Zijian Guo is an associate professor at the Department of Statistics at Rutgers University. He obtained a Ph.D. in Statistics in 2017 from Wharton School, University of Pennsylvania. His research interests include causal inference, multi-source and transfer learning, high-dimensional statistics, and nonstandard statistical inference.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Diane Saint Aubin (Universität Zürich)
What is... Bose-Einstein condensation? abstract
Abstract:
\'\'A Bose-Einstein condensate (BEC) is a state of matter that is formed when a low-density gas of bosons is cooled to near absolute zero. Under these conditions, a majority of the particles occupy the same quantum state and quantum effects become apparent. First predicted by Bose and Einstein a century ago, BECs were realised in laboratories over eight decades later and led to the Nobel price in 2001. Since then, many progresses have been made in the rigorous study and understanding of quantum many-body systems from a mathematical point of view. In this talk we will give an introduction to quantum mechanics and to the mathematical description of quantum many-body systems. We will then present a formal definition of BEC.
16:30 • UZH Zentrum, Building KO2, Room F 150
Prof. Dr. Gianluca Crippa (Uni Basel)
Anomalous dissipation in fluid dynamics abstract
Abstract:
The celebrated Kolmogorov\'s K41 theory of fully developed turbulenceattempts to explain and quantify "wild, but typical" behaviors of"chaotic" fluids, most notably the lack of conservation of the totalenergy. The loss of energy is not due to friction between fluidmolecules, but rather to the limited regularity of the flow.Kolmogorov\'s theory is numerically and experimentally validated to avery large extent, however, very little is known in rigorousmathematical terms. In my lecture, I will present some aspects ofKolmogorov\'s theory, and illustrate recent results (in collaborationwith M. Colombo and M. Sorella) on a related question for the linearadvection equation.
17:15 • Université de Fribourg, room Phys 2.52
Francis Brown (UNIGE & University of Oxford)
Nombres mistérieux - des mathématiques à la physique, et invérsement abstract
Abstract:
Les nombres ont toujours fasciné l’humanité par leur nature mystérieuse et leur omniprésence dans notre quotidien. Certains sont tangibles, comme les nombres entiers, d’autres, comme π ou √2 sont plus insaisissables même si on peut facilement les représenter physiquement. D’autres encore continuent d’intriguer chercheurs et chercheuses en mathématiques et sont au cœur de la recherche actuelle. De leur découverte par le mathématicien et physicien suisse Leonhard Euler au 18ème siècle jusqu’à leur réapparition mystérieuse au cœur de la physique des particules au 20ème siècle, cet exposé vous plongera dans l’univers des valeurs zêta, nombres intrigants apparaissant dans différents domaines en apparence très éloignés.Cet exposé sera suivi d’une discussion avec Francesco Riva, professeur de physique à l’Université de Genève et créateur du jeu Tutti Quantum, durant laquelle le public sera invité à poser ses questions.
18:00 • Université de Genève, Uni Dufour, U300