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, 3 March
Time	Speaker	Title	Location
15:15 - 16:30	Felix Schlenk Neuchâtel University	Abstract Twenty five years ago, Paul Biran introduced polarizations of closed symplectic manifolds and showed that their Lagrangian skeleta exhibit remarkable rigidity properties. He in particular found that their complements contain only small balls. I will introduce similar polarizations of certain open 4-dimensional symplectic manifolds. This leads to several symplectic embedding results, that in turn lead to new Lagrangian non-removable intersections and a novel phenomenon of Legendrian barriers. For instance, given any connected symplectic 4-manifold $(M,\omega)$ and a 4-ball of smaller volume, their exists an explicit finite union of Lagrangian discs in the 4-ball such that their complement symplectically embeds into~$(M,\omega)$, extending a result by Sackel--Song--Varolgunes--Zhu and Brendel. Other applications are new Lagrangian intersection results and relative versions of the Arnold chord conjecture. The talk will be non-technical and focus on the geometric constructions. This is joint work with Emmanuel Opshtein. Symplectic Geometry Seminar Singular polarizations of open symplectic 4-manifolds, with applications	HG G 43

Tuesday, 4 March
Time	Speaker	Title	Location
15:15 - 16:15	Dr. Mitchell Taylor ETH Zurich, Switzerland	Abstract A subspace $E \subset L2(\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C \geq 1$ such that for any $f,g \in E$ we have $\inf_{\|\| \lambda \|\| =1} \|\| f- \lambda g \|\| \leq C \|\| \|f\| - \|g\| \|\|$ In this case, if \|f\| is known, then f is uniquely determined up to an unavoidable global phase factor $\lambda$ moreover, the phase recovery map is C-Lipschitz. Phase retrieval appears in several applied circumstances, ranging from crystallography to quantum mechanics. In this talk, I will present some elementary examples of subspaces of L2(µ) which do stable phase retrieval and discuss the structure of this class of subspaces. The material in this talk is based on joint work with M. Christ and B. Pineau as well as with D. Freeman, T. Oikhberg and B. Pineau. Analysis Seminar Stable phase retrieval in function spaces	HG G 43
16:00 - 17:00	Sorrachai Yingchareonthawornchai ETH Institute for Theoretical Studies	Abstract Many fundamental problems in theoretical computer science lie at the intersection of combinatorial structures and algorithmic efficiency. In this talk, I will highlight two classical problems from distinct areas—graph connectivity and adaptive data structures—both of which have deep mathematical foundations and long-standing open questions. First, I will discuss the vertex connectivity problem which asks to compute the minimum number of vertices that must be removed to disconnect a graph. The problem is closely related to flow algorithms and combinatorial optimization. From a computational perspective, finding the vertex connectivity of a graph has been extensively studied. I will highlight new algorithmic ideas in the past few years that lead to the new breakthrough in the area. Next, I will turn to the Dynamic Optimality Conjecture, one of the biggest open questions in data structures, which asks whether splay trees achieve near-optimal adaptive search performance. Despite decades of research, the conjecture remains unresolved, but recent techniques from extremal combinatorics and algorithm analysis offer promising directions. I will highlight the role of extremal combinatorics in analyzing adaptive search strategies and explore new techniques that bring us closer to resolving this conjecture. More information: https://eth-its.ethz.ch/activities/its-fellows--seminar/Sorrachai-Yingchareonthawornchai.html ETH-ITS Fellows' Seminar Recent Advances in Vertex Connectivity and The Dynamic Optimality Conjecture	SEW F 21 Scheuchzerstrasse 70
16:15 - 18:30	Stefano Galanda Dipartimento di matematica - DIMA, Universita di Genova	Abstract The Algebraic approach to quantum theories was developed in the end of last century in order to provide a solid mathematical description to the theory of the standard model of particle physics and especially its generalization on curved spacetime backgrounds. Despite its original purpose, the formalism also emerged as a suitable framework for formulating the thermodynamic limit of models in statistical mechanics. The goal of this talk is to provide a gentle introduction to the algebraic approach by first presenting its main motivations and then outlining some of its mathematical foundations. In particular, we will present this approach as an abstract generalization of the mathematical framework of Quantum Mechanics. Zurich Graduate Colloquium What is... Algebraic Quantum Field Theory?	KO2 F 150

Wednesday, 5 March
Time	Speaker	Title	Location
10:15 - 12:00	Adam Kanigowski University of Maryland	Abstract Nachdiplomvorlesung Sparse Equidistribution Problems in Dynamics	HG G 43
13:30 - 14:30	Dr. Marc Abboud Université de Neuchâtel	Abstract The family of Markov surfaces M_D is a family of cubic affine surfaces parametrised by the complex line (here D is the parameter) that is related to the character variety of the punctured torus. It has sparked a lot of work in algebraic geometry, algebraic differential equations and low-dimensional topology. The mapping class group of the punctured torus acts on the character variety and preserves this family. Its image is a finite index subgroup of the group of automorphisms of M_D for every parameter D. We show the following result: for certain algebraic parameters D if two automorphisms of M_D with positive entropy share a Zariski dense set of periodic points then they share a common iterate. The proof uses tools from arithmetic dynamics such as the arithmetic equidistribution theorem of Yuan and Zhang and tools from quasi-Fuchsian representation theory. Ergodic theory and dynamical systems seminar Unlikely intersections problem for automorphisms of Markov surfaces	HG G 19.1
16:00 - 17:30	Prof. Dr. Aaron Pixton University of Michigan	Abstract Algebraic Geometry and Moduli Seminar The lambda_g formula	Zoom
17:15 - 18:45	Prof. Dr. Erich Baur Berner Fachhochschule, Technik und Informatik	Abstract Seminar on Stochastic Processes Graduate Workshop Reinforcement	Y27 H12

Thursday, 6 March
Time	Speaker	Title	Location
16:15 - 18:00	Dr. Victor Navarro-Fernández Department of Mathematics, Imperial College London	Abstract We study a passive scalar equation on a two-dimensional periodic box, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at an exponential rate, independent of any underlying diffusivity. Furthermore, we show that the velocity field enhances dissipation, and we establish sharp decay rates that, for large times, are deterministic and remain uniform in the diffusivity constant. Our approach is purely Eulerian and relies on a suitable modification of Villani's hypocoercivity method. This is a joint project with C. Seis (Universität Münster). PDE and Mathematical Physics Exponential mixing with random cellular flows via hypocoercivity	Y27 H 46
17:15 - 18:15	Dr. Aleksei Minabutdinov ETH Zurich	Abstract Transversality is an important sufficient condition for identifying the solution in infinite horizon economic and financial models. Without such a condition, there exists a continuum of functions that satisfy the Hamilton-Jacobi-Bellman (HJB) functional equation. In this paper, we explore this manifold of solutions with numerical and analytical methods. Using a standard continuous-time model, we demonstrate that, without explicitly imposing the transversality condition, widely used numerical algorithms, including the (Deep) Galerkin-type methods, may converge to arbitrary points of this manifold, leading to significant and uncontrollable biases. Using an example of the AK-Ramsey model with logarithmic utility (a prototypical model for many financial mathematics and macro/environmental economics applications), the paper demonstrates that the area of direct applicability of projection-type algorithms is narrower than one might expect based on contemporary literature. We propose a novel approach using a functional transformation of the original HJB equation to effectively incorporate the transversality condition, ensuring convergence to the actual value function. Talks in Financial and Insurance Mathematics Transversality Condition Matters: Ensuring Uniqueness of Deep Learning Solutions in Economics and Finance	HG G 43

Friday, 7 March
Time	Speaker	Title	Location
10:15 - 12:00	Boris Bukh Carnegie Mellon University	Abstract Nachdiplomvorlesung Discrete Geometry	HG G 43
14:15 - 15:15	Dr. Seoyoung Kim UBasel	Abstract We start with a double sextic family of K3 surfaces with four parameters with Picard number $16$. Then by geometric reduction (specializing at fiber) processes, we obtain three, two and one parameter families of K3 surfaces of Picard number $17, 18$ and $19$ respectively. All these families turn out to be of hypergeometric type in the sense that their Picard-Fuchs differential equations are given by hypergeometric or Heun functions. We will study the geometry of 2-parameter families and related finite hypergeometric series in detail. We will then discuss some relevant modularity questions. This is a joint work with A. Clingher, A. Malmendier, and N. Yui. Number Theory Seminar Certain families of K3 surfaces and their modularity	HG G 43
16:00 - 17:30	Dr. Michele Graffeo SISSA	Abstract The Hilbert scheme of points on a quasi-projective variety is a classical object in algebraic geometry. However, its geometry is nowadays still not completely accessible. On the other hand, the motive of a variety X is an invariant attached to X carrying a lot of information about its geometry, and it is considered as a universal Euler characteristic. In a joint project with Monavari, Moschetti and Ricolfi we give general formulas to compute the motive of the Hilbert scheme of points, provided the knowledge of a finite amount of data (that we gave explicitly in some cases). In my seminar I will present our formulas and I will show many applications. Algebraic Geometry and Moduli Seminar The motive of the Hilbert scheme of points	HG G 43
16:15 - 17:15	David M. Blei Columbia University	Abstract Analyzing nested data with hierarchical models is a staple of Bayesian statistics, but causal modeling remains largely focused on "flat" models. In this talk, we will explore how to think about nested data in causal models, and we will consider the advantages of nested data over aggregate data (such as data means) for causal inference. We show that disaggregating your data---replacing a flat causal model with a hierarchical causal model---can provide new opportunities for identification and estimation. As examples, we will study how to identify and estimate causal effects under unmeasured confounders, interference, and instruments. Preprint: https://arxiv.org/abs/2401.05330 This is joint work with Eli Weinstein. ETH-FDS seminar Joint talk ETH-FDS Seminar - Research Seminar on Statistics: "Hierarchical Causal Models"	HG D 7.2
16:15 - 17:15	David M. Blei Columbia University	Abstract Analyzing nested data with hierarchical models is a staple of Bayesian statistics, but causal modeling remains largely focused on "flat" models. In this talk, we will explore how to think about nested data in causal models, and we will consider the advantages of nested data over aggregate data (such as data means) for causal inference. We show that disaggregating your data---replacing a flat causal model with a hierarchical causal model---can provide new opportunities for identification and estimation. As examples, we will study how to identify and estimate causal effects under unmeasured confounders, interference, and instruments. Preprint: https://arxiv.org/abs/2401.05330 This is joint work with Eli Weinstein. Research Seminar in Statistics Joint talk ETH-FDS Seminar - Research Seminar on Statistics:"Hierarchical Causal Models"	HG D 7.2

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