Vorträge

Dienstag, 16.12.2025: Anosov representations and convex-cocompact groups II

Giacomo Gavelli

Donnerstag, 18.12.2025: Mean-field regimes of the Bose-Hubbard Model

Dr. Shahnaz Farhat (Tübingen)

In the first part, I will talk about the many-body quantum Gibbs state for the Bose–Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. We prove an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula. In the second part of the talk, I will talk about the validity of a mean-field approximation for the dynamics of quantum systems in high dimension, using the Bose–Hubbard model on a square lattice. We prove a trace norm estimate between the one-lattice-site reduced density of the Schrödinger dynamics and the mean-field dynamics in the limit of large dimension.

Montag, 12.01.2026: tba

Stefan Friedl

Donnerstag, 22.01.2026: TBA

Cameron Peters (Vancouver)

Freitag, 30.01.2026: Static Black Holes with a Negative Cosmological Constant

PhD Brian Harvie (Universität Kopenhagen)

The classification of stationary black hole solutions of the Einstein field equations, broadly referred to as the "no-hair conjecture", is a challenging and fundamental line of research in general relativity. The problem is more tractable for black hole spacetimes which are static, but even under this stronger assumption the existing results are mostly limited to static black holes with zero or positive cosmological constant. In this talk, I will present a geometric inequality for isolated static vacuum black holes with a negative cosmological constant which has far-reaching implications for their geometry and uniqueness. The inequality relates the surface gravity, area, and topology of a horizon in a static spacetime to its conformal infinity, and equality is achieved only by the Kottler black holes. From this, we deduce several new static uniqueness theorems for Kottler. Namely, we show: (1) the Kottler black hole over the sphere which minimizes surface gravity is unique, (2) the Kottler black hole over the torus is unique, assuming the horizons have non-spherical topology, and (3) uniqueness for the higher-genus Kottler black holes is equivalent to the Riemannian Penrose inequality. This is based on joint work with Ye-Kai Wang.

Freitag, 30.01.2026: TBA

Olivia Vicanek Martinez (Universität Tübingen)

TBA

Freitag, 30.01.2026: Quaternion Kähler manifolds of non-negative sectional curvature

Profl Dr. Uwe Semmelmann (Universität Stuttgart)

Quaternion Kähler manifolds, i.e., Riemannian manifolds with holonomy contained in Sp(m)Sp(1), are Einstein. In the case of positive scalar curvature, there is a longstanding conjecture by LeBrun and Salamon stating that all such manifolds should be symmetric. So far, the conjecture has been confirmed only up to dimension 12. In the first part of my talk I will give an introduction to the geometry of quaternion Kähler manifolds of positive scalar curvature In the second part I will make a few remarks on the proof of the conjecture under the additional assumption of non-negative sectional curvature. This extends earlier work by Berger, who proved that quaternion Kähler manifolds of positive sectional curvature are isometric to the quaternionic projective space. My talk is based on a joint article with Simon Brendle and on earlier work by Simon Brendle.