Weekly Bulletin

The FIM provides a Newsletter called FIM Weekly Bulletin, which is a selection of the mathematics seminars and lectures taking place at ETH Zurich and at the University of Zurich. It is sent by e-mail every Tuesday during the semester, or can be accessed here on this website at any time.

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FIM Weekly Bulletin

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Monday, 15 April
Time	Speaker	Title	Location
17:30 - 19:00	Dr. Miguel Moreira MIT	Abstract The cohomology of moduli spaces of 1-dimensional sheaves, together with a special filtration called the perverse filtration, can be used to give an intrinsic definition of (refined) Gopakumar-Vafa invariants. While there are methods to calculate the Betti numbers of these moduli spaces in low degree, understanding the perverse filtration is more challenging. One way to compute it is to fully determine the cohomology ring. In this talk I will explain an approach to describing the cohomology rings of moduli spaces and moduli stacks in terms of generators and relations, which allowed us to determine them for curve classes up to degree 5 (for moduli spaces) and 4 (for moduli stacks). I will explain the P=C conjecture, which is an analogue of the P=W conjecture in a Fano and compact setting. This is joint work with Yakov Kononov, Woonam Lim and Weite Pi. Algebraic Geometry and Moduli Seminar The cohomology ring of moduli spaces of 1-dimensional sheaves on CP2	Zoom

Tuesday, 16 April
Time	Speaker	Title	Location
15:15 - 16:15	Mario Gauvrit Université Paris Cité	Abstract We investigate Morse index stability for a sequence of Yang-Mills connections on closed 4-manifolds under bubble-tree convergence. As critical points of a conformally invariant energy, Yang-Mills connections share close ties with harmonic maps in various aspects. Simultaneously, their analysis is simpler as long as we work in an appropriate gauge, the so-called Coulomb gauge. Motivated by applications in constructing non-stable solutions of the Yang-Mills equations, this work extends recent methods developed by Da Lio-Gianocca-Rivière for index stability to the Yang-Mills framework, using sharp decay estimates to prove that the neck regions account for a positive contribution to the second variation. Analysis Seminar Morse index stability for Yang-Mills connections	HG G 43
16:30 - 17:30	Yuriy Tumarkin Universität Zürich	Abstract ''If you take a square and glue the opposite sides together, you get a flat torus. What happens if you start with a different polygon instead, say a regular octagon? The result is a translation surface, a central object in the field of Teichmüller Dynamics. Of particular interest is the straight-line flow on a translation surface, a simple to define dynamical system that arises from the study of billiards in polygons. In this talk I will give a friendly introduction to a few of the key concepts of the field, such as the moduli space of translation surfaces, and the idea of using renormalisation to study the dynamics on a translation surface. Zurich Graduate Colloquium What is... a translation surface?	KO2 F 150

Wednesday, 17 April
Time	Speaker	Title	Location
13:30 - 14:30	Prof. Dr. Sébastien Biebler Université Paris Cité	Abstract One of the main goals in the theory of dynamical systems is to describe the dynamics of a "typical" map. For instance, in the case of diffeomorphisms of a given manifold, it was conjectured by Smale in the 60s that uniform hyperbolicity was generically satisfied. This hope was however fast discouraged by exhibiting dynamical systems displaying in a robust way dynamical configurations which are obstructions to hyperbolicity: robust homoclinic tangencies (this is the so-called Newhouse phenomenon) and robust heterodimensional cycles. In this talk, I will explain these phenomena and their extensions to the complex setting. In particular, I will show how to construct robust heterodimensional cycles in the family of polynomial automorphisms of C^3. The main tool is the notion of blender coming from real dynamics. Ergodic theory and dynamical systems seminar Non-density of hyperbolicity in complex dynamics in several variables	HG G 19.1
13:30 - 15:00	Prof. Dr. Danilo Lewanski University of Trieste	Abstract Via virtual localisation techniques, Johnson, Pandharipande and Tseng proved that the integral of the Hodge class over the moduli space of admissible covers vanishes under certain sufficient technical conditions: either strong negativity or negativity together with boundedness would suffice. What happens when these conditions are lifted? The answer (in a certain setting) was provided in previous work with Borot, Do, Karev and Moskovsky: the vanishing of a single summand gets replaced by the vanishing of the sum of many. This was achieved as a byproduct of the topological recursion procedure. By deformation techniques in topological recursion, other three families of these relations arose, two of which genus dependent. Based on joint work with Gaëtan Borot and Maksim Karev, tested thanks to the admcycles Sage package. Algebraic Geometry and Moduli Seminar A fair amount of weighted intersection numbers summing up to zero	HG G 43
15:30 - 16:30	Isacco Nonino University of Glasgow	Abstract When studying smooth structures on a 4-dimensional topological manifold M, there are three main topics one has to cover: existence, uniqueness and behavior of their diffeotopy groups. I will explain the reasons why the 4 dimensional case is so interesting and wild, and remark the striking difference between the compact and non-compact settings. I will then give an overview on the recent work on diffeotopy groups of exotic smoothings of R4, and show how the results were generalized to a wider class of non-compact 4 manifolds. Geometry Seminar Smooth structures on non-compact 4-manifolds	HG G 43
16:00 - 17:00	Prof. Dr. Vincent Perrier Inria, France	Abstract Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the vorticity for the first order wave system or divergence preservation for the Maxwell system or the induction equation. In this talk, I will address this problem with the classical discontinuous Galerkin method. Based on discrete de-Rham ideas, I will show that by considering an adapted approximation space (but still discontinuous) for vectors , divergence or curl can be easily preserved under mild assumption on the numerical flux Zurich Colloquium in Applied and Computational Mathematics How to preserve a divergence or a curl constraint in a hyperbolic system with the discontinuous Galerkin method	HG E 1.2
17:15 - 18:15	Prof. Dr. Vincent Vargas Universität Genf	Abstract Gaussian multiplicative chaos (GMC) on the circle is a canonical (random) multifractal measure on the circle which appears in a wide variety of contexts and most recently in relation to Liouville conformal field theory. In this talk, I will present the first results concerning the decay and renormalization of the Fourier coefficients of GMC. In particular, one can show that GMC is a so-called Rajchman measure which means that its Fourier coefficients go to zero when the frequency goes to infinity. Numerous questions remain open. Based on a joint work with C. Garban. Seminar on Stochastic Processes Harmonic analysis of Gaussian multiplicative chaos on the circle (CANCELLED)	HG G 43

Thursday, 18 April
Time	Speaker	Title	Location
10:15 - 12:00	Umut Çetin London School of Economics	Abstract Nachdiplomvorlesung Mathematics of Market Microstructure	HG G 43

Friday, 19 April
Time	Speaker	Title	Location
14:15 - 15:15	Prof. Dr. Mladen Dimitrov Université de Lille	Abstract We will give an overview of the local geometry of the Coleman-Mazur eigencurve at classical points. If time permits we will explain possible generalizations in higher dimension, namely in the Hilbert modular setting. Number Theory Seminar On the Geometry of the Eigencurve	HG G 43
15:15 - 16:15	Joshua Warren Yale University	Abstract Abstract: Studies of the relationships between environmental exposures and adverse health outcomes often rely on a two-stage statistical modeling approach, where exposure is modeled/predicted in the first stage and used as input to a separately fit health outcome analysis in the second stage. Uncertainty in these predictions is frequently ignored, or accounted for in an overly simplistic manner when estimating the associations of interest. Working in the Bayesian setting, we propose a flexible kernel density estimation (KDE) approach for fully utilizing posterior output from the first stage modeling/prediction to make accurate inference on the association between exposure and health in the second stage, derive the full conditional distributions needed for efficient model fitting, detail its connections with existing approaches, and compare its performance through simulation. Our KDE approach is shown to generally have improved performance across several settings and model comparison metrics. Using competing approaches, we investigate the association between lagged daily ambient fine particulate matter levels and stillbirth counts in New Jersey (2011–2015), observing an increase in risk with elevated exposure 3 days prior to delivery. The newly developed methods are available in the R package KDExp. ZüKoSt Zürcher Kolloquium über Statistik A Bayesian framework for incorporating exposure uncertainty into health analyses with application to air pollution and stillbirth	HG G 19.1
16:00 - 17:30	Dr. Julia Schneider Universität Zürich	Abstract We describe the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field, proving that if it contains a point of degree 6, then it is not generated by elements of finite order. We then use this result to study Mori fibre spaces over the field of complex numbers and deduce that the Cremona group of rank at least 4 admits any group (of cardinality at most $\|\mathbb{C}\|$) as a quotient. Moreover, we prove that the 3-torsion in the abelianization of the Cremona group of rank at least 4 is uncountable. This is based on a joint work with J. Blanc and E. Yasinsky. Algebraic Geometry and Moduli Seminar Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank	HG G 43

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