HCM Graduate Colloquium, Summer Term 2025

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Organisers: Michel Alexis, Regula Krapf, Fred Lin, Christoph Thiele

This seminar is organised as a BIGS event. The goal is to present topics from all areas of mathematics in an elementary and informal way. The talks should be accessible to a general mathematical audience and are mainly aimed at BIGS students.

Everybody (students, postdocs, faculty, guests) is welcome to attend.
If you would like to give a talk please contact us.

The seminar will take place Wednesdays 15:15 - 16:45 in the Lipschitzsaal. The talks will usually take about one hour and there is the subsequent possibility to ask questions. Coffee, tea and cake will be served beforehand between 15:00 and 15:15 in the Plückerraum.

A predecessor of the HCM Graduate Colloquium is the Basic Notions Seminar which took place until 2017:
Basic Notions Seminar Summer Term 2017

Date	Speaker	Topic
23.04.2025	Lars Becker (MI)	Quantum signal processing and the nonlinear Fourier transform
30.04.2025	Sun Woo Park (MPIM)	Graph neural networks and covering spaces
21.05.2025	Andrew Ng (MI)	What geometric group theory has to do with your area of interest
04.06.2025	Elliot Kaplan (MPIM)	Tba.
02.07.2025	Tba.	Tba.

Abstracts

April 23, 2025: Lars Becker (MI)

Title: Quantum signal processing and the nonlinear Fourier transform

Abstract. We will give a short overview of two topics and their connection. The first is so-called quantum signal processing, a framework for designing quantum algorithms. The second one is the nonlinear Fourier transform, a transformation that diagonalizes certain integrable nonlinear partial differential equations.

April 30, 2025: Sun Woo Park (MPIM)

Title: Graph neural networks and covering spaces

Abstract. I would like to give a brief overview of some deep learning techniques, their applications, and their limitations. We will focus particularly on how covering spaces are relevant to understanding limitations of conventional neural networks in determining isomorphism classes of graphs (or in particular graph neural networks). A number of works presented in this talk are based on joint collaborations with Yun Young Choi, U Jin Choi, Dosang Joe, Minho Lee, Seunghwan Lee, Joohwan Ko, and Youngho Woo. My hope is to make the talk as accessible as possible, even for those who do not have prior knowledge in deep learning techniques.

May 21, 2025: Andrew Ng (MI)

Title: What geometric group theory has to do with your area of interest

Abstract. Geometric group theory studies the interplay between the algebraic properties of groups and the geometric properties of spaces that they act on. I will illustrate this close connection in the setting of 3-manifolds and also point out connections with surprisingly diverse areas of mathematics, such as algebraic geometry, number theory, symplectic geometry, and geometric analysis, though no knowledge of any of these topics will be necessary to understand the core of the talk. If there is time at the end I welcome challenges from the audience to show/elaborate on connections between GGT and their favourite area of maths.