HCM Graduate Colloquium, Winter Term 2025/26

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Organisers: Michel Alexis, Regula Krapf

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 and postdocs.

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
22.10.2025	Michel Alexis (MI)	Calculus teachers hate him because of this one weird trick, find out why!!
26.11.2025	María Inés de Frutos Fernández (MI)	What is... mathematical formalization?
17.12.2025	David Aretz (MPIM)	A Brief History of Going in Circles: From Belts to Bott
21.01.2026	Annabell Gros (IAM)	Extrema of branching Brownian motion
04.02.2026	Eva-Maria Hekkelman (MPIM)	Tba

Abstracts

October 22, 2025: Michel Alexis (MI)

Title: Calculus teachers hate him because of this one weird trick, find out why!!

Abstract. I’ll present the concept of dyadic decomposition, a simple but stupidly effective technique for quickly estimating various sums and integrals, all without computing a single anti-derivative. We’ll discuss topics ranging from the p-test in Calculus to the Calderon-Zygmund decomposition for estimating averaging operators and the Hardy-Littlewood maximal function.

November 26, 2025: María Inés de Frutos Fernández (MI)

Title: What is... mathematical formalization?

Abstract. Mathematical formalization is the process of digitizing mathematical definitions and results using a "proof assistant" (e.g. Lean), that is, a computer program capable of checking logical statements against a set of inference rules and some basic axioms. In recent years, the community of mathematicians working on formalization has grown rapidly and has reached milestones that demonstrate the ability to formalize results at the frontier of knowledge. In this talk, I will give an introduction to formalization, survey recent formalization projects, and discuss applications to mathematical research, teaching, and communication. No previous knowledge in this area will be assumed.

December 17, 2025: David Aretz (MPIM)

Title: A Brief History of Going in Circles: From Belts to Bott

Abstract. This talk explains why rotating yourself twice is more mathematically respectable than rotating once, why vector bundles repeat every 8 dimensions like a bad sitcom plot, and what all of this has to do with electrons being antisocial. There will be K -theory, Bott periodicity, and a belt. It will all make sense in the end. Probably.

January 21, 2026: Annabell (IAM)

Title: Extrema of branching Brownian motion

Abstract. Branching Brownian motion is a classical model from probability theory that describes the random motion and branching of particles over time. In this talk, we give an introduction to the study of its extreme values. We explore the connection to a particular PDE (the F-KPP equation), discuss the maxima of random variables, and encounter several biologically motivated models. Basic knowledge of probability theory is sufficient to follow the talk.