Mathematical Colloquium
Upcoming talks:
| Tue 27 May 2025, 16:30: Afonso Bandeira (ETH Zürich) Towards a sharp non-asymptotic theory for structured random matrices (and tensors) |
| Matrix Concentration inequalities such as Matrix Bernstein inequality (Oliveira and Tropp) have played an important role in many areas of pure and applied mathematics. These inequalities are intimately related to the celebrated noncommutative Khintchine inequality of Lust-Piquard and Pisier. While these tend to be optimal when the underlying matrices are commutative, they are known to be sub-optimal in several other instances. Recently, we have leveraged ideas from Free Probability to fully remove the sub-optimal dimensional dependencies in these inequalities in a range of instances, yielding sharp bounds in many settings of interest. In this talk I will describe these results, some of the recent and ongoing work that it has sparked, and several open problems. Includes joint work with: March Boedihardjo (MSU); Ramon van Handel and Giorgio Cipolloni (Princeton); Petar Nizic-Nikolac, Anastasia Kireeva, Kevin Lucca, and Dominik Schroder (ETH); Xinmeng Zeng (Stanford); Dustin Mixon (OSU); Dmitriy Kunisky (Johns Hopkins); Thomas Rothvoss (U Washington); Haotian Jiang (U Chicago); Sivakanth Gopi (MSR). ______________________ Invited by Prof. Holger Rauhut |
| Theresienstr. 39, München. Room A 027 |
| Tue 3 Jun 2025, 16:30: Lauriane Chomaz (Universität Heidelberg) Stabilization by quantum fluctuations in ultracold gases of magnetic atoms : experimental observations and theory descriptions |
| Thanks to their high degree of control and tunability, ultracold atomic gases provide a rich platform for the study of quantum many-body effects. Ultracold gases of highly magnetic atoms exhibit unique interaction properties that lead to striking behaviors, both at the mean-field level and beyond [1]. A decade ago, a universal stabilization mechanism driven by quantum fluctuations was discovered in these gases. This mechanism prevents the systems from collapsing when the mean-field interactions become attractive, and instead allows exotic states of matter to arise, including ultradilute quantum droplets, crystallized quantum states, and especially the so-called supersolids [2]. In my colloquium, I will present the seminal observations of these states and how they emerged from the long-standing progress in the field. I will discuss the theoretical description of these systems via an effective mean-field theory, including the effect of quantum fluctuations via a higher-order effective interaction. I will outline our current understanding of the properties of these states and highlight open questions. [1] L. Chomaz & al, Dipolar physics: a review of experiments with magnetic quantum gases, Reports on Progress in Physics 86, 026401 (2023). [2] L. Chomaz, Quantum-stabilized states in magnetic dipolar quantum gases, arXiv preprint 2504.06221 (2025) _____________________ Invited by Prof. Arnaud Triay |
| Theresienstr. 39, München. Room A 027 |
| Tue 17 Jun 2025, 16:30: Eyal Neuman (Imperial College London) Stochastic Graphon Games with Memory |
| We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When the agents' interactions are modeled by a weighted graph, we formulate the corresponding non-Markovian continuum-agent game, where interactions are modeled by a graphon. We also derive the Nash equilibrium of the graphon game explicitly by first reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations, then decoupling it using the spectral decomposition of the graphon operator, and finally solving it in terms of operator resolvents. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of agents increases. This holds both when a given graph sequence converges to the graphon in the cut norm and when the graph sequence is sampled from the graphon. We also bound the convergence rate, which depends on the cut norm in the former case and on the sampling method in the latter. Finally, we apply our results to various stochastic games with heterogeneous interactions, including systemic risk models with delays and stochastic network games. ______________________________ Invited by Prof. Alexander Kalinin |
| Theresienstr. 39, München. Room A 027 |
| Tue 8 Jul 2025, 16:30: Femke Sporn (IPN Kiel) Mathematisches Beweisverständnis in Sekundarstufe und Hochschule - Entwicklung und Förderung |
| Das Beweisen ist für die Mathematik als Disziplin von zentraler Bedeutung und spielt daher auch in der mathematischen Ausbildung eine wichtige Rolle. Lernende sollen die Mathematik als deduktives System begreifen, die Art der Absicherung mathematischer Ergebnisse verstehen, argumentative Herausforderungen erfolgreich bewältigen können und so ein adäquates Verständnis von mathematischen Beweisen aufbauen. Ausgehend von einem theoretischen Rahmenmodell zum mathematischen Beweisverständnis werden Ergebnisse empirischer Studien vorgestellt, die das Beweisverständnis von Lernenden in unterschiedlichen Phasen der mathematischen Ausbildung untersuchen und Möglichkeiten der Förderung aufzeigen. ______________________ Invited by Prof. Stefan Ufer |
| Theresienstr. 39, München. Room A 027 |
All lectures are on Tuesdays at 4:30 pm in lecture hall A027 unless otherwise noticed.
Looking for past events? You may find them in the Munich Mathematical Calendar.