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
Title T.B.A.
11:00 • EPF Lausanne
Jerson Caro (Boston University)
Abstract:
Title: TBA Abstract: tba
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.
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