Vorträge

Donnerstag, 08.01.2026: Heisenberg-limited Hamiltonian learning CV systems

Dr. Tim Möbus (Tübingen)

Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works mostly focused on quantum spin systems, where quantum states can be seen as superpositions of discrete bit-strings, relatively little is known about Hamiltonian learning for continuous-variable quantum systems. In this work we focus on learning the Hamiltonian of a bosonic quantum system, a common type of continuous-variable quantum system. This learning task involves an infinite-dimensional Hilbert space and unbounded operators, making mathematically rigorous treatments challenging. We introduce an analytic framework to study the effects of strong dissipation in such systems, enabling a rigorous analysis of cat qubit stabilization via engineered dissipation. This framework also supports the development of Heisenberg-limited algorithms for learning general bosonic Hamiltonians with higher-order terms of the creation and annihilation operators. Notably, our scheme requires a total Hamiltonian evolution time that scales only logarithmically with the number of modes and inversely with the precision of the reconstructed coefficients. On a theoretical level, we derive a new quantitative adiabatic approximation estimate for general Lindbladian evolutions with unbounded generators. Finally, we discuss possible experimental implementations.

Mittwoch, 14.01.2026: TBA

Shelby Cox (MPI Leipzig)

TBA

Freitag, 16.01.2026: Das Pontrjaginsche Maximumsprinzip

Joachim Steck (Universität Tübingen)

Dienstag, 20.01.2026: Towards a general spectral theory of aperiodic point processes in Lie groups

Tobias Hartnick (KIT)

The goal of this talk is to convince researchers working on spectral theory of lattices in Lie groups to help me out with some problems in point process theory. The talks consists of two parts. In the first talk I will take a bird’s eye view and survey various classes of point processes in Lie groups with strong discreteness properties (not assuming any knowledge of point process theory). Following a research programme which I developed with Michael Björklund over the last decade, I will compare properties of these processes with properties of lattices. I will list various results (by many people) and even more open research directions concerning such point processes. In the second part of the talk I will focus on one specific open problem: How to generalize the spectral theory of lattices in Lie groups to aperiodic point processes? I will explain how to obtain fairly complete results in the case of the Heisenberg group using twisted aperiodic Siegel-Radon transforms. In particular, I will review a construction of explicit intertwiners from Schrödinger representations into the Koopman representation of a large class of aperiodic point processes (joint work with Björklund). Finally, I will point out some of the difficulties which arise in the semisimple case when trying to construct similar intertwiners from principal series. I hope that the audience will be able to help me out with overcoming these difficulties.

Donnerstag, 22.01.2026: TBA

Cameron Peters (Vancouver)

Freitag, 23.01.2026: Die Hamilton-Jacobi-Bellman-Gleichung

Joachim Steck (Universität Tübingen)

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: A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations

Olivia Vicanek Martinez (Universität Tübingen)

Asymptotically Euclidean 3-dimensional initial data sets were shown to carry asymptotic foliations of closed hypersurfaces with constant spacetime mean curvature (Cederbaum-Sakovich, 2021). In order to prove the inverse implication of this result and hence the geometric characterization of being asymptotically Euclidean, we start from the purely geometric foliation and construct asymptotic coordinates from it, exploiting the properties of the induced Laplacian of the foliation leaves via a delicate analysis. We show that these coordinates are asymptotically Euclidean, and moreover seem geometrically meaningful and well-adapted to the center of mass. This is joint work with A. Piubello.

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.