Bo\'az Klartag (The Weizmann Institute of Science)
Isoperimetric inequalities in high-dimensional convex sets
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Paul Dütting
Nearly Tight Regret Bounds for Profit Maximization in Bilateral Trade abstract
Abstract:
Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a broker, in a regret minimization framework. At each time step, a new seller and buyer arrive, and the broker has to propose a mechanism that is incentive-compatible and individually rational, with the goal of maximizing profit.We propose a learning algorithm that guarantees a nearly tight $\\tilde{O}(\\sqrt{T})$ regret in the stochastic setting when seller and buyer valuations are drawn i.i.d. from a fixed and possibly correlated unknown distribution. We further show that it is impossible to achieve sublinear regret in the non-stationary scenario where valuations are generated upfront by an adversary. Our ambitious benchmark for these results is the best incentive-compatible and individually rational mechanism. This separates us from previous works on efficiency maximization in bilateral trade, where the benchmark is a single number: the best fixed price in hindsight.A particular challenge we face is that uniform convergence for all mechanisms\' profits is impossible. We overcome this difficulty via a careful chaining analysis that proves convergence for a provably near-optimal mechanism at (essentially) optimal rate. We further showcase the broader applicability of our techniques by providing nearly optimal results for the joint ads problem.Preprint available from on arXiv (https://arxiv.org/abs/2509.22563).Forthcoming in FOCS 2025.Joint work with Simone di Gregorio (Sapienza), Federico Fusco (Sapienza), Chris Schwiegelshohn (Aarhus).Short bio: Paul Dütting is a Staff Research Scientist at Google Switzerland whose research focuses on the intersection of Algorithms and Economics. He was previously an Associate Professor of Mathematics at the London School of Economics (LSE), where he now holds a visiting faculty role. He received several awards for his work, including two Best Paper Awards at the ACM Conference on Economics and Computation and a Best Paper Award at the ACM The Web Conference.
11:00 • EPF Lausanne, BC 420
Jerson Caro (Boston University)
Abstract:
Title: Counting and Finding Rational Points on Surfaces Abstract: A celebrated result of Coleman gives an explicit version of Chabauty\'s theorem, bounding the number of rational points on curves over number fields via the study of zeros of p-adic analytic functions. While many developments have extended and refined this result, obtaining analogous explicit bounds for higher-dimensional subvarieties of abelian varieties remains a major challenge. In this talk, I will sketch the proof of such an explicit bound for surfaces contained in abelian varieties -- a step toward a higher-dimensional Chabauty-Coleman method. This is joint work with Héctor Pastén. I will also describe an application of this method to a computational problem: determining an upper bound for the number of unexpected quadratic points on hyperelliptic curves of genus 3 defined over Q. I will illustrate the method through an explicit example where this set can be computed. This is joint work with Jennifer Balakrishnan.
14:15 • Universität Basel
Hugo Moeneclaey (University of Gothenburg)
Synthetic Stone Duality: A Synthetic Approach to Condensed Mathematics abstract
Abstract:
Synthetic Stone duality is an extension of Homotopy Type Theory (HoTT) by 5 well-chosen axioms. These axioms are validated by the interpretation of HoTT in the higher topos of light condensed anima. Therefore, any results we prove in synthetic Stone duality can be interpreted as a result about light condensed anima.First, we will explain the general concept of synthetic mathematics, with an emphasis on geometry, HoTT, higher topoi and cohomology. Then we will present the 5 axioms of Synthetic Stone duality and give detailed proofs of some of their elementary consequences, to give a feeling of how it is to work with them. We will then give an overview of our synthetic version of Theorem 3.2 from Peter Scholze Lecture Notes on condensed mathematics (itself adapted from Roy Dyckhoff). Our version states that the cohomology of a compact Hausdorff space with countably presented coefficients can be computed from a cover of X by a Stone space.If time permits, we will sketch applications of this result to the shape modality, which gives a convenient interface between topological spaces and their homotopy types.
Dominik Francoeur (Madrid)
Intersection-saturated groups and groups with micro-supported actions abstract
Abstract:
A group is said to possess the Howson property if the intersection of any two finitely generated subgroups is again finitely generated. When a group fails to have the Howson property, one can try to characterise how far it is from having it. Such considerations give rise to the notion of intersection-saturated groups, introduced recently by Delgado, Roy and Ventura. In this talk, we\'ll see a new construction for intersection-saturated groups, based on so-called micro-supported actions, that allows one in particular to produce finitely presented amenable examples.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Lukas Koch
Uniform Lipschitz estimates for regularised optimal transport abstract
Abstract:
<p><span style="caret-color: #000000; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">I will discuss how to obtain Lipschitz estimates for regularised optimal transport problems using a variational approach. In particular, this </span><br style="caret-color: #000000; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="caret-color: #000000; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">gives Lipschitz regularity for entropic optimal transport independent of the regularisation parameter. A crucial step in the approach are local </span><br style="caret-color: #000000; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><span style="caret-color: #000000; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">L^\\infty-estimates, which are of independent interest. The talk is based on joint work with Rishabh Gvalani (ETH).</span></p>
16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Guido Lob (Liceo cantonale di Locarno)
Die Mathematik als Hilfsmittel des Taschenrechners abstract
Abstract:Der Taschenrechner ist ein Wunderwerk: In wenigen Augenblicken erwacht ein Plastikrechteck zum Leben und kann uns Werte für Wurzeln, Logarithmen, Trigonometrischen Funktionen und vieles weiteres liefern.Was verbirgt sich hinter diesem scheinbar einfachen, aber so mächtigen Gerät? Es sind nicht nur Taylor-Polynome: Es gibt viele weitere mathematische Eigenschaften und Überlegungen, die in seinem Inneren genutzt werden, um die gewünschten Ergebnisse auf effiziente und elegante Weise zu erzielen.
Präsentation 17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Etienne Ghys (ENS Lyon)
Les merveilles de la géométrie des lettres de l’alphabet abstract
Abstract:
Pendant des siècles, les copistes écrivaient des livres à la main. En 1455 Gutenberg a tout bousculé et on a commencé à fondre des caractères en plomb. Avant de les fondre, il fallait les dessiner. Les graveurs les plus célèbres de la Renaissance ont modifié la forme des lettres pour qu’elles soient lisibles et jolies. Ils ont utilisé les outils dont ils disposaient : des règles et des compas. Il y a quarante ans, tout a basculé avec l’explosion de l’informatique. Comment dessiner les caractères d’imprimerie en respectant le magnifique travail des artistes de la Renaissance ? Cet exposé sera un très rapide survol de l’histoire de la typographie vue par un géomètre.
18:30 • Université de Genève, Uni Dufour, U300