Munich Mathematical CalendarCalendar with mathematical talks near Munich2023-12-05T18:34:01Ztag:mathcal.ma.tum.de,2013-04-10:/feed/filter2/year2023/month1204.12.2023 15:00 Behnaz Rahmani (University of Auckland): Understanding complex oscillations in a model of intracellular calcium dynamics2023-11-27T09:14:02ZBehnaz Rahmani (University of Auckland)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231127101126Oscillations of free intracellular calcium concentration are thought to be important in the control of a wide variety of physiological phenomena, and there is long-standing interest in understanding these oscillations via the investigation of suitable mathematical models. Many of these models have the feature that different variables or terms in the model evolve on very different time-scales, which often results in the accompanying oscillations being temporally complex. This talk will discuss attempts to explain a particular type of complex oscillation seen in a model of calcium dynamics in hepatocytes (liver cells), and in particular will talk about challenges for the application of geometric singular perturbation theory and numerical bifurcation analysis in this context.
04.12.2023 16:30 Serguei Popov : Two-dimensional conditioned trajectories and (Brownian) random interlacements2023-11-27T09:50:17ZSerguei Popov tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231016073310In this talk, we will discuss two dimensional random interlacements, both in discrete and continuous setups. We also discuss some (surprising) properties of their "noodles", which are (two-dimensional) simple random walks conditioned on never hitting the origin in the discrete case and Brownian motions conditioned on never hitting the unit disk in the continuous case. Of particular interest will be the properties of so-called vacant sets.
05.12.2023 16:15 Peter Wildemann (Cambridge): Reinforced Random Walk and a Supersymmetric Spin System on the Tree2023-12-01T05:59:24ZPeter Wildemann (Cambridge)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231201065651Motivated by predictions about the Anderson transition, we study two distinct but related models on regular tree graphs: The vertex-reinforced jump process (VRJP), a random walk preferring to jump to previously visited sites, and the H^{2|2}-model, a lattice spin system whose spins take values in a supersymmetric extension of the hyperbolic plane. Both models undergo a phase transition, and our work provides detailed information about the supercritical phase up to the critical point: We show that their order parameter has an essential singularity as one approaches the critical point, in contrast to algebraic divergences typically expected in statistical mechanics. Moreover, we locate an additional multifractal intermediate phase on large finite trees. This talk is based on arxiv:2309.01221 and is joint work with Rémy Poudevigne.
06.12.2023 12:00 Richard Guo (University of Cambridge): Harnessing Extra Randomness: Replicability, Flexibility and Causality2023-11-27T09:39:28ZRichard Guo (University of Cambridge)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231006070644Many modern statistical procedures are randomized in the sense that the output is a random function of data. For example, many procedures employ data splitting, which randomly divides the dataset into disjoint parts for separate purposes. Despite their flexibility and popularity, data splitting and other constructions of randomized procedures have obvious drawbacks. First, two analyses of the same dataset may lead to different results due to the extra randomness introduced. Second, randomized procedures typically lose statistical power because the entire sample is not fully utilized.
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To address these drawbacks, in this talk, I will study how to properly combine the results from multiple realizations (such as through multiple data splits) of a randomized procedure. I will introduce rank-transformed subsampling as a general method for delivering large sample inference of the combined result under minimal assumptions. I will illustrate the method with three applications: (1) a “hunt-and-test” procedure for detecting cancer subtypes using high-dimensional gene expression data, (2) testing the hypothesis of no direct effect in a sequentially randomized trial and (3) calibrating cross-fit “double machine learning” confidence intervals. For these problems, our method is able to derandomize and improve power. Moreover, in contrast to existing approaches for combining p-values, our method enjoys type-I error control that asymptotically approaches the nominal level. This new development opens up the possibility of designing procedures that explicitly randomize and derandomize: extra randomness is introduced to make the problem easier before being marginalized out.
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This talk is based on joint work with Prof. Rajen Shah.
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Bio: Richard Guo is a research associate in the Statistical Laboratory at the University of Cambridge, mentored by Prof. Rajen Shah. Previously, he was the Richard M. Karp Research Fellow in the 2022 causality program at the Simons Institute for the Theory of Computing. He received his PhD in Statistics from University of Washington in 2021, advised by Thomas Richardson. His research interests include graphical models, causal inference, semiparametric methods and replicability of data analysis. Dr. Guo will start as a tenure-track assistant professor in Biostatistics at the University of Washington in 2024.
06.12.2023 13:00 Stefan Bauer (TUM): Der Vortrag von Stefan Bauer (TUM) "Learning Causal Representations: Explainable AI for Structured Exploration" entfällt leider.2023-12-05T07:44:57ZStefan Bauer (TUM)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20230928124522...
11.12.2023 15:00 Martin Rasmussen (J-v-N Visiting Professorship TUM, Imperial College London): Random dynamical systems with bounded noise: a boundary mapping approach2023-11-28T15:19:16ZMartin Rasmussen (J-v-N Visiting Professorship TUM, Imperial College London)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231127101416We consider discrete-time random dynamical systems with
uniform spherical noise and introduce a geometric approach to study
the compound behaviour of such systems. The key insight of this
novel approach is that the boundary of attractors can be
represented as invariant sets of a deterministic finite-dimensional
mapping, the so-called boundary mapping, that acts on the unit
tangent bundle of the phase space. We address questions regarding
the persistence of attractors and the nature of bifurcations in
this context.
12.12.2023 14:00 Luis Scoccola (Oxford): What do we want from invariants of multiparameter persistence modules?2023-11-30T09:17:15ZLuis Scoccola (Oxford)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231130101413Various constructions relevant to practical problems such as clustering and graph classification give rise to multiparameter persistence modules (MPPM), that is, linear representations of non-totally ordered sets. Much of the mathematical interest in multiparameter persistence comes from the fact that there exists no tractable classification of MPPM up to isomorphism, meaning that there is a lot of room for devising invariants of MPPM that strike a good balance between discriminating power and complexity of their computation. However, there is no consensus on what type of information we want these invariants to provide us with, and, in particular, there seems to be no good notion of “global” or “high persistence” features of MPPM.
With the goal of substantiating these claims, as well as making them more precise, I will give an overview of the theory of multiparameter persistence, including joint works with Bauer and Oudot. I will mention no-go results for invariants of MPPM as well as recent work of Bjerkevik, which contains relevant open questions regarding the global structure of MPPM.
Remote participation: https://conf.dfn.de/webapp/#/?conference=979176504
12.12.2023 16:00 Alexander Armbruster: Simpler constant factor approximation algorithms for weighted flow time -- now for any p-norm2023-12-05T18:34:01ZAlexander Armbrustertag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231205193032A prominent problem in scheduling theory is the weighted flow time problem on one machine. We are given a machine and a set of jobs, each of them characterized by a processing time, a release time, and a weight. The goal is to find a (possibly preemptive) schedule for the jobs in order to minimize the sum of the weighted flow times, where the flow time of a job is the time between its release time and its completion time. It had been a longstanding important open question to find a polynomial time O(1)-approximation algorithm for the problem and this was resolved in a recent line of work. These algorithms are quite complicated and involve for example a reduction to (geometric) covering problems, dynamic programs to solve those, and LP-rounding methods to reduce the running time to a polynomial in the input size. In this paper, we present a much simpler (6+ϵ)-approximation algorithm for the problem that does not use any of these reductions, but which works on the input jobs directly. It even generalizes directly to an O(1)-approximation algorithm for minimizing the p-norm of the jobs' flow times, for any 0<p<∞ (the original problem setting corresponds to p=1). Prior to our work, for p>1 only a pseudopolynomial time O(1)-approximation algorithm was known for this variant, and no algorithm for p<1. For the same objective function, we present a very simple QPTAS for the setting of constantly many unrelated machines for 0<p<∞ (and assuming quasi-polynomially bounded input data). It works in the cases with and without the possibility to migrate a job to a different machine. This is the first QPTAS for the problem if migrations are allowed, and it is arguably simpler than the known QPTAS for minimizing the weighted sum of the jobs' flow times without migration.
14.12.2023 16:30 Wolfgang Lück : Survey on aspherical manifolds2023-10-13T10:06:03ZWolfgang Lück tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231013120423We give a survey over aspherical closed manifolds. Aspherical is the purely homotopy theoretic condition that the universal covering is contractible. There are many well-known examples such as closed Riemannian manifolds with non-positive sectional curvature, but also very exotic examples such as closed aspherical manifolds that do not admit a triangulation. We discuss some prominent conjectures, e.g., the Borel Conjecture about the topological rigidity, and the Singer Conjecture about the concentration of L^2-Betti numbers in the middle dimension.
18.12.2023 15:00 Alexander Schell (ETH Zürich): Functional Analytical Insights into Rough Path Theory and its Expanding Frontiers in Data Science and Machine Learning2023-12-05T08:32:27ZAlexander Schell (ETH Zürich)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231127101806The theory of rough paths, conceived in the 1990s, has recently evolved significantly beyond its origins in controlled and stochastic differential equations, witnessing a remarkable surge in applications within the realms of data science and machine learning. The central concept behind these advances is the signature transform, a map that captures a multidimensional data stream by sending it to the sequence of its iterated integrals.
Intended as an easily accessible invitation to the field, this talk offers a natural functional-analytical perspective on the signature transform and, going beyond theoretical abstraction, gives a brief outlook on how related ideas from rough path theory can be applied to some contemporary challenges within stochastic analysis and statistical machine learning.
18.12.2023 16:30 Christian Hirsch: TBA2023-10-16T05:35:31ZChristian Hirschtag:mathcal.ma.tum.de,2013-04-10:/talk/created/20231016073424TBA