Workshop on "Combinatorics, Resurgence and Algebraic Geometry in Quantum Field Theory", August 19 - 23, 2024

The study of perturbative quantum field theory has shown a surprising need for the latest advances in algebraic geometry and combinatorics. The field also incorporates the very actively developed theory of resurgence, which has promising potential for applications to both topology and quantum field theory.

This workshop aims to advance this field by bringing together top experts. The goal is to foster discussions on recent results, encourage collaboration, generate new ideas, explore the connections in perturbative quantum field theory, and offer a platform for junior researchers.

This workshop consists of a fixed list of participants. It is not possible to register.

Registration:

The registration is closed as of May 20, 2024.

Speakers:

Bhargav Bhatt (University of Michigan, IAS/Princeton) (tbc)
Jean-Benoit Bost (Université Paris-Saclay)
Ana Caraiani (Imperial College London)
Christopher Deninger (Universität Münster)
Nikolai Durov (Steklov Mathematical Institute)
Hélène Esnault (Freie Universität Berlin)
Ziyang Gao (Leibniz Universität Hannover)
Toby Gee (Imperial College London)
Michael Larsen (Indiana University Bloomington)
Bjorn Poonen (MIT)
Michael Rapoport (University of Bonn)
Peter Scholze (MPIM Bonn)
Jakob Stix (Goethe-Universität, Frankfurt)
Jacob Tsimerman (University of Toronto)
Mingjia Zhang (Princeton University)
Shou-Wu Zhang (Princeton University)
Wei Zhang (MIT)

Survey talk by:

Robin de Jong (Universiteit Leiden)

Organisers:

Christian Blohmann (MPIM Bonn)
Christian Liedtke (TU München)
Wiesława Nizioł (Sorbonne Université)

Workshop on "Dualisable Categories & Continuous K-theory", September 9 - 13, 2024

Algebraic K-theory is an object that sits at the centre of large parts of algebra, geometry, and topology because of its universal role as a receptacle to count other mathematical objects with signs. However, since its invention, a phenomenon often called the Eilenberg swindle - which says that the algebraic K-theory of a category which is too large must necessarily be zero - has been accepted as a fundamental limit to the theory.

Conference on "Homology Growth in Topology and Group Theory", May 13 - 17, 2024

Homology growth is an umbrella term for a number of invariants associated to a topological space. In their simplest incarnation, they measure the growth of Betti numbers in finite covers of the space. Over the years, homology growth became a central topic in group theory and geometric topology. It connects various topological and geometric phenomena, especially in low-dimensional manifolds, with analytically or combinatorially defined invariants, like L^2-Betti numbers. In particular, homology growth plays a central role in controlling the existence of fiberings, over the circle in the topological setting, and over the integers in the algebraic one. The motivation and guiding principles come from the theory of 3-manifolds.Inspired by Agol's resolution of Thurston's Virtual Fibering Conjecture, homology growth and related ideas have been very recently used both in the algebraic setting of cubulated groups, and in higher dimensional negatively curved manifolds. This conference aims to bring together people behind these recent developments, provide an overview of the field and help formulate a coherent system of conjectures to guide us in the years to come.

In case you have any questions, please contact hogro2024$@$mpim-bonn$.$mpg$.$de.

Registration

The registration is closed.

High school students learn how to express the solution of a quadratic equation in one unknown in terms of its three coefficients. Why does this formula matter? We offer an answer in terms of discriminants and data. This lecture invites the audience to a journey towards non-linear algebra.