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Monday, 27 April
Time	Speaker	Title	Location
15:15 - 16:30	Kai Cieliebak	Abstract A well-studied and intriguing question concerns the relation between symplectic and algebraic surfaces in the projective plane. In ongoing work with Zhengyi Zhou we address this question one dimension higher. In particular, we prove that each degree two symplectic hypersurface in complex projective space P3 is symplectomorphic to P1 times P1 with its standard structure. The proof uses the moduli space of nodal rational curves of degree two. Symplectic Geometry Seminar Symplectic quadrics in projective 3-space	HG G 43

Tuesday, 28 April
Time	Speaker	Title	Location
15:15 - 16:15	Dr. Charlotte Dietze Laboratoire Jacques-Louis Lions Sorbonne Université	Abstract We prove eigenvalue asymptotics and concentration of eigenfunctions of the Laplace-Beltrami operator for certain singular Riemannian metrics. This is motivated by the study of propagation of sound waves in gas planets. The talk is based on joint works with Yves Colin de Verdière, Maarten de Hoop and Emmanuel Trélat, and with Larry Read. Analysis Seminar Spectral theory for singular Riemannian metrics	HG G 43
16:30 - 18:30	Zheng Fang Institut für Mathematik, Universität Zürich	Abstract <p>The monkey walk is a self-interacting random walk that occasionally relocates to a site from its own past. I will discuss the simplest case where the relocation time is chosen uniformly from all its past times, and where between relocations the walk behaves like a simple random walk. This model provides an example of how relocation can drastically alter long-time behavior of the simple random walk, i.e., instead of diffusing on the usual \(\sqrt{n}\) scale, the walk spreads only on the much slower \(\sqrt{\log n}\) scale. The talk will focus on intuition, the role of the uniform relocation rule, and the main ideas that turn the memory-driven walk into a problem about random recursive trees and its corresponding effective time. This talk is based on Cécile Mailler and Gerónimo Uribe Bravo’s work on random walks with preferential relocations and fading memory (2019).</p> Zurich Graduate Colloquium What is... random walk with relocation?	KO2 F 150

Wednesday, 29 April
Time	Speaker	Title	Location
13:30 - 14:30	Leon Staresinic Universität Zürich	Abstract <div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><span style="color: #000000;">Interval Translations Maps (ITMs) are a natural generalisation of the well-known Interval Exchange Transformations (IETs). They are obtained by dropping the bijectivity assumption for IETs. As such, they are exactly the finite piecewise isometries of the interval. There are two types of ITMs, finite-type and infinite-type ones. They are classified by their non-wandering sets: it is a finite union of intervals for finite-type maps, and contains a Cantor set for infinite-type maps.</span></div> <div style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><br> <div><span style="color: #000000;">One of the basic questions in the field is: How prevalent is each type of map in the parameter space? In this work, we show that the set of finite-type maps contains an open and dense subset of the parameter space of ITMs with a fixed number of intervals, which resolves in positive the topological version of a long-standing conjecture due to Boshernitzan and Kornfeld.</span></div> <div> </div> <span style="color: #000000;">This is a joint work with Kostiantyn Drach and Sebastian van Strien.</span></div> Ergodic theory and dynamical systems seminar The Topological Boshernitzan-Kornfeld Conjecture	HG G 19.1
16:30 - 17:30	Prof. Dr. Helmut Harbrecht Universität Basel	Abstract This presentation aims to provide an overview of shape optimization in case of random input parameters. Besides the minimization of the expected objective, we also consider the minimization of failure probabilities. We show that in some situations the objective and its gradient are deterministic despite the random input. We can thus derive cheap, deterministic algorithms to minimize the objective. Several applications and numerical computations are given. Zurich Colloquium in Applied and Computational Mathematics Shape optimization under uncertainty	HG G 19.2
17:15 - 18:45	Dr. Yujin Kim California Institute of Technology	Abstract Random surfaces play a central role in probability and mathematical physics for decades. Physically, they often arise as models of interfaces: boundaries between distinct regions of space. The Solid-on-Solid (SOS) model is a canonical discrete model for interfaces separating stable (equilibrium) coexisting phases in three dimensions, such as the boundary of a solid that has crystallized in a liquid solution. In this talk, we present the fascinating geometry of the SOS model at "low temperature", conditioned to be non-negative ("above a wall": think of substration on a hard surface). In this setting, the SOS model resembles a wedding cake, being comprised of a sequence of shrinking, stacked layers whose boundaries form a collection of nested loops. Our work sheds light on the fluctuations of these loops away from their Wulff shape scaling limits, and in particular suggests a scaling limit for these fluctuations. Based on joint works with Patrizio Caddeo, Milind Hegde, Eyal Lubetzky, and Christian Serio. Seminar on Stochastic Processes The low temperature SOS model above a wall and 1:2:3 scaling	Y27 H12

Thursday, 30 April
Time	Speaker	Title	Location
16:00 - 17:00	Letizia Issini Université de Genève	Abstract Divergence of groups is a quasi-isometry invariant that measures how difficult it is to connect two points while avoiding a large ball around the identity. It is easy to see that divergence is linear for direct products. I will discuss how the presence of direct products as subgroups can be used to show that certain groups have linear divergence. This applies to some groups that admit a micro-supported action on a Hausdorff topological space, i.e., groups containing elements with arbitrarily small support. Joint work in progress with D. Francoeur and T. Nagnibeda Geometry Graduate Colloquium Divergence in groups with micro-supported actions	HG G 43
17:15 - 18:15	Prof. Dr. Walter Schachermayer University of Vienna	Abstract The classical Hsu-Robbins-Erdös Theorem provides a sharpening of Kolmogoroff’s strong law of large numbers. It pertains to the i.i.d. case where boundedness in L^2 turns out to be a necessary and sufficient condition for complete convergence. We give a lacunary/hereditary version of this theorem in the spirit of Komlos. Interestingly, to obtain a necessary and sufficient version in our context, one necessarily has to go beyond martingale techniques as predicted some 40 years ago by David Aldous. Rather one has to rely on approximation by exchangeable sequences. Joint work with Istvan Berkes (Budapest) and Yannis Karatzas (New York). Talks in Financial and Insurance Mathematics A Komlos version of the Hsu-Robbins-Erdös law of large numbers	HG G 43

Friday, 1 May
Time	Speaker	Title	Location
16:00 - 17:30	Prof. Dr. Jérémy Guéré Université Grenoble Alpes	Abstract First, I will review the construction of atoms, beginning with an overview at the formal level before addressing the technical difficulties that necessitate the use of non-Archimedean fields. I will also discuss the behavior of the Hodge structure under Iritani's blow-up formula. Then, I will introduce a new atomic invariant and provide the proof for the following theorem: if a smooth complex cubic fourfold is rational, then its primitive cohomology is isomorphic, as a rational Hodge structure, to the shifted middle cohomology of a projective K3 surface. The proof relies on explicit computations for surfaces that I will present. Algebraic Geometry and Moduli Seminar On the irrationality of cubic fourfolds	HG G 43

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