HCM Graduate Colloquium, Summer Term 2024

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Organisers: Michel Alexis, Regula Krapf, Fred Lin, Luise Puhlmann, Christoph Thiele, Radu Toma

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
17.04.2024	Sid Maibach (IAM)	An Exposition to Random Conformal Geometry
24.04.2024	Antonia Ellerbrock (DM)	Cost Allocation for Set Covering: the Happy Nucleolus
29.05.2024	Sil Linskens (MI)	Grothendieck's Homotopy Hypothesis
12.06.2024	Tba	Tba
03.07.2024	Tba	Tba

Abstracts

April 17, 2024: Sid Maibach (IAM)

Title: An Exposition to Random Conformal Geometry

Abstract. In this talk I will present an overview of the research area sometimes titled "random conformal geometry". This is the study of random objects that are symmetric under holomorphic coordinate changes, making them well-defined objects on Riemann surfaces. The key objects I will introduce are "Schramm–Loewner evolution" random curves, "Gaussian free field" random functions, and concepts from conformal field theory. These appear universally in the study of systems at critical temperature on 2D lattices as the spacing of the lattice goes to zero. As an example of such a system I will discuss the Ising model. I will also briefly touch upon my own research questions about the correspondence between Kähler structures on the moduli spaces of the underlying Riemann surfaces and large deviation principles for the aforementioned random objects. However, instead of going into detail I will illustrate more examples of probabilistic constructions from which these universal objects emerge.

April 24, 2024: Antonia Ellerbrock (DM)

Title: Cost Allocation for Set Covering: the Happy Nucleolus

Abstract. Imagine you were a delivery service operator who wants to visit a certain set of customers. There is a given set of possible tours. Each tour serves a subset of the customers and has a certain cost. You can use as many of these tours as you like. Your task is to set a price for each customer. Of course, you want to charge as much money as possible, but without losing customers. We assume that any group could leave your delivery service and self-fund one of the given tours. Thus, the summed prices of customers in this group should not exceed the cheapest cost for a tour of their own. From here, we will build on previous work in the field of cooperative game theory and develop a fair cost allocation concept with efficient computation.

May 29, 2024: Sil Linskens (MI)

Title: Grothendieck's Homotopy Hypothesis

Abstract. In 1983, Grothendieck wrote the influential manuscript Pursuing stacks. In this work he formulated the famous homotopy hypothesis: “homotopy types = infinity-groupoids”. This was a deep insight, which completely changed our understanding of the place of homotopy theory in broader mathematics. In this talk I will motivate and contextualise the homotopy hypothesis, and then explain its development since 1983.