Wochenplan des Fachbereichs Mathematik und Informatik

Given a Hilbert C*-correspondence over C(X), one can construct the associated Cuntz--Pimsner algebra. In the case that the correspondence is full, nonperiodic, and minimal, the resulting C*-algebra is simple and unital. An example of such a correspondence is obtained by taking the right Hilbert C(X)-module of continuous sections of a vector bundle over X and twisting the left multiplication by a minimal homeomorphism. As is the case of crossed products by minimal homeomorphisms, one can identify ``orbit-breaking" C*-subalgebras. In this talk I will discuss these Cuntz--Pimsner C*-algebras and their orbit-breaking subalgebras, their relationship to one another, and when they can be classified by Elliott invariants. This is joint work with Adamo, Archey, Forough, Georgescu, Jeong and Viola.

The topic of the talk will be a paper, I wrote in collaboration with Jan-Frederik Pietschmann (TU Chemnitz) and Andreas W. Püschel and Danila Di Meo (both WWU, Institute for molecular cell biology). A preprint is available on: https://arxiv.org/abs/1908.02055

A random planar map is a canonical model for a discrete random surface which is studied in probability theory, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2D Riemannian manifold with roots in the physics literature. In a joint work with Xin Sun, we prove a strong relationship between these two natural models for random surfaces. Namely, we prove that the random planar map converges in the scaling limit to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.

Further information

A very important open question in the study of NIP fields is the following: do they always admit a non-trivial henselian valuation? Qp is a good example, since it is NIP and its valuation is definable. In this talk, I will explore algebraic extensions of Qp and classify which ones are NIP. On the way, it will give some insight about NIP fields in the general case.

Abstract:
We will describe natural infinite collections of random (Brownian) loops, some of their nice features, and how they are related to some basic ideas and concepts from physics. We will in particular focus on some underlying intriguing random geometric objects in d-dimensional space, and how their construction and behavior drastically differ when d=3, 4 and 5.

About Wendelin Werner:
Wendelin Werner (born 1968) is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics. He is professor at ETH Zurich.

In 2006, he received the Fields Medal for his contribution to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory. He was also honoured with the Rollo Davidson Prize in 1998, the Fermat Prize in 2001, the Grand Prix Jacques Herbrand of the French Academy of Sciences in 2003, the Loève Prize in 2005, the SIAM George Pólya Prize in 2006 and the Heinz Gumin Prize in 2016. He is a member of the French Academy of Sciences, the Academy of Sciences Leopoldina and the Berlin-Brandenburg Academy of Sciences.

Further information

Further information