Lecture Hall M1, 4:00 pm, 27 March, 2024

Speaker: Pablo Candela (Autonomous University of Madrid), http://verso.mat.uam.es/~pablo.candela/

Title: Generalizing Fourier analysis using nilspace theory

Abstract:

Many applications of Fourier analysis in combinatorics rely on the following idea: the averages of a function over certain linear configurations in an abelian group can be usefully analyzed by approximating the function with its dominant Fourier components. A far-reaching extension of this idea was initiated in the seminal work of Gowers on Szemerédi's theorem in the 1990s, leading to the theory known as higher-order Fourier analysis. A fundamental insight in this theory is that for many types of linear patterns, while the dominating Fourier components may not be helpful anymore, one can instead analyze the function effectively by approximating it with components that are based, not on the circle group (like classical Fourier characters), but rather on certain non-commutative extensions, such as nilmanifolds. This has led notably to the discovery of fascinating structures called nilspaces, which are a common generalization of abelian groups and nilmanifolds, and which have yielded further progress in higher-order Fourier analysis. I will give an introduction to this theory and discuss some recent results in this approach involving nilspaces, based on joint work with Balázs Szegedy.

Lecture Hall M1, 4:00 pm, 13 March, 2024

Speaker: Matija Bucić (Princeton University), https://sites.google.com/princeton.edu/matija-bucic

Title: Robust sublinear expanders

Abstract:

Expander graphs are perhaps one of the most widely useful classes of graphs ever considered. In this talk, we will focus on a fairly weak notion of expanders called sublinear expanders, first introduced by Komlós and Szemerédi around 30 years ago. They have found many remarkable applications ever since. In particular, we will focus on certain robustness conditions one may impose on sublinear expanders and some applications of this idea, which include:
- recent progress on the classical Erdős-Gallai cycle decomposition conjecture,
- essentially tight answer to the classical Erdős unit distance problem for "most" real normed spaces, and
- an asymptotic solution to the rainbow Turán problem for cycles, raised by Keevash, Mubayi, Sudakov and Verstraete, with an interesting corollary in additive number theory.

Lecture Hall M1, 2:00 pm, Tuesday, 3 October, 2023

Speaker: Hil Meijer

Title: Data-driven dynamical network models of brain activity in epilepsy patients

Abstract: For patients with refractory epilepsy, surgery may be a treatment option. While preparing for surgery, brain activity is recorded to delineate the tissue responsible for the seizure and to be resected. In this talk, we consider recordings from subdural grid electrodes with single pulse electrical stimulation (SPES). The responses to SPES consist of physiological early responses (ERs) and pathological delayed responses (DRs).
We start with constructing brain networks with several connectivity measures. We show that ER-based effective connectivity reveals more physiological connections than functional connectivity based on cross-correlation or Granger causality. We find that the epileptogenic zone is a densely connected subnetwork. Second, we model the SPES responses using neural mass models of mesoscopic brain activity. Using dynamical systems theory, we characterize a threshold for DRs to appear and their relevance as a clinical biomarker. Finally, we present preliminary results for fitting large-scale individualized patient networks based on SPES responses.

Lecture Hall M1, 4:00 pm, Wednesday, 27 September, 2023

Speaker: Phan Thành Nam

Title: Isoperimetric inequalities and the critical mass in nuclear fission

Abstract: I will discuss the connection from classical isoperimetric inequalities to the critical mass in nuclear fission reactions described via the liquid drop model. In particular, I will address several open questions and recent results on the existence/nonexistence of minimizers according to the change of the nuclear mass.

Phan Thành Nam is a Vietnamese mathematician and mathematical physicist and university professor at the Ludwig Maximilian University of Munich.
Phan Thành Nam studied mathematics and computer science from 2003 at the National University of Vietnam in Ho Chi Minh City, where he received a bachelor's degree in 2007, at the University of Orleans with a master's degree in 2008, and at the University of Copenhagen, where he joined in 2011 Jan Philip Solovej received his doctorate. As a post-doctoral student he worked with Mathieu Lewin at the University of Cergy-Pontoise and the CNRS until 2013 and at the Institute of Science and Technology Austria (IST) with Robert Seiringer until 2016. In 2016 he became an assistant professor at Masaryk University and in 2017 a professor at the University of Munich.
He deals with mathematical physics (many-body quantum mechanics, spectral theory), calculus of variations and partial differential equations as well as numerical analysis.
In 2018 he received the IUPAP Prize for Young Scientists in Mathematical Physics. For 2020/21 he received the EMS Prize (lecture: Excitation spectrum of dilute trapped Bose gases).