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)	Nullstellensätze and model-theoretic embeddings
02.07.2025	Luca Poensgen (INS)	A Graphic Novel on How Computers Learn to Solve Nonlinear Problems

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.

June 4, 2025: Elliot Kaplan (MPIM)

Title: Nullstellensätze and model-theoretic embeddings

Abstract. Abraham Robinson realized that properties of a model-theoretic structure are equivalent to algebraic information about extensions of that structure. I will discuss this correspondence and show how it can be used to give quick proofs of some classical theorems about algebraically closed fields, such as Hilbert's (weak) Nullstellensatz and Chevalley's theorem on constructible sets. I will then discuss some recent work on applying these tests to describe the asymptotic behavior differential equations.

July 2, 2025: Luca Poensgen (INS)

Title: A Graphic Novel on How Computers Learn to Solve Nonlinear Problems

Abstract. Even computers struggle — especially with nonlinear or non-convex problems. These pop up in all sorts of places, even when we try to model something as innocent as bending a sheet of paper. Now, mathematicians are excellent at defining wildly abstract spaces and sets — nonlinear and infinite-dimensional. But in the real world, people actually want to find the solution, not just know it's out there sipping tea in some Banach space. That’s where things get tricky. In this talk, we’ll follow a simple toy problem and see how computers manage to tackle it. We’ll dig into the mathematical tools behind the scenes and show how those descriptions help ensure that the rocket doesn’t blow up on launch — or in our case: that the paper bends exactly as simulated. Everything will be supported by visuals. If you already know the Finite Element Method, we’ll give you a quick intro to a $W^{2,2}$-conforming Virtual Element Method — just the basic idea, no heavy lifting required. No experience with FEM or functional analysis? No problem. Bring your curiosity, and let the pictures do the talking.