Vorträge in der Woche 19.01.2026 bis 25.01.2026

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: Some Thoughts on the Robinson-Styled Proof of a Minkowski-Type Inequality for Asymptotically Flat Static Manifolds

Huyue Yan (Universität Tübingen)

Using a Robinson-styled method, Florian Babisch obtained an alternative proof of the classical Minkowski inequality based on a divergence identity. Starting from this Euclidean framework, we explore extending the Robinson-styled ansatz to establish a generalized Minkowski-type inequality on asymptotically flat static manifolds. We analyze the additional geometric difficulties arising in this setting and discuss the analytical difficulties they introduce compared to the flat case. In particular, we suggest that the co-area formula may play a role in controlling mixed terms in this context.

Donnerstag, 22.01.2026: Challenges and approaches for the numerical analysis of time-modulated materials

Jörg Nick

Donnerstag, 22.01.2026: TBA

Cameron Peters (Vancouver)

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

Joachim Steck (Universität Tübingen)

Freitag, 23.01.2026: Graph zeta methods for efficient simulations of long-range interacting quantum lattices

Dr. Andreas Buchheit (Universität des Saarlandes)

I first present the Singular Euler—Maclaurin expansion, an extension of the 300-year-old classical Euler-Maclaurin summation formula to long-range interactions on high-dimensional lattices with applications in spin systems [1,2]. This method allows for the exact representation of a discrete lattice in terms of its continuous analog, with corrections given in terms of a generalization of the Riemann zeta function, the so-called Epstein zeta function. With the properties and efficient computation of this function analyzed in [4] and a high-performance implementation available in our library EpsteinLib [5], a new toolset is provided for studying arbitrary long-range interacting lattices. I briefly discuss recent extensions to systems with boundaries [6] as well as to micromagnetics systems [7]. Building on this framework, I subsequently study 2D unconventional BCS superconductors with long-range interactions, finding a rich phase diagram with topologically non-trivial and mixed-parity phases as well as stabilization of Higgs modes in the non-equilibrium dynamics [3]. In the second part of the talk, I present how generalized zeta functions, built from the Epstein zeta function, can allow for the precise evaluation of n-body interaction energies in chemistry given by (n-1) d-dimensional lattice sums, reducing the scaling from exponential to linear in the number of interaction partners n [8]. For cuboidal lattices with a two-body Lennard–Jones potential coupled to a three-body Axilrod–Teller–Muto potential, we demonstrate that increasing the three-body coupling can drive a structural transition from fcc to bcc [8,9]. In long-range-interacting quantum lattices, current graph decomposition methods, such as pCUT, transform the problem of an exponentially growing Hilbert space dimension into the computation of high-dimensional lattice sums associated with graphs, which are usually computed with low-precision Monte Carlo methods. In the final part of the talk, I present ongoing work on computing the arising graph zeta functions efficiently and precisely, laying the foundation for exploring quantum systems in regimes inaccessible to other methods. References: [1] Singular Euler-Maclaurin expansion on multidimensional lattices, Andreas A. Buchheit and Torsten Keßler, Nonlinearity 35 3706 (2022) [2] On the Efficient Computation of Large Scale Singular Sums with Applications to Long-Range Forces in Crystal Lattices, Andreas A. Buchheit and Torsten Keßler, J. Sci. Comput. 90, 53 (2022) [3] Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors, Andreas A. Buchheit, Torsten Keßler, Peter K. Schuhmacher, and Benedikt Fauseweh, Phys. Rev. Research 5, 043065 (2023) [4] Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib, Andreas A. Buchheit, Jonathan Busse, and Ruben Gutendorf, arXiv preprint 2412.16317 (2025) [5] Github Repository: github.com/epsteinlib/epsteinlib, pip install epsteinlib [6] On the computation of lattice sums without translational invariance, Andreas A. Buchheit, Torsten Keßler, and Kirill Serkh, Math. Comp. 94 (2025), 2533-2574 [7] Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics, arXiv:2509.26274 (2025) [8] Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod–Teller–Muto term applied to cuboidal phase transitions, Andres Robles-Navarro, Andreas A. Buchheit, et. al., J. Chem. Phys. 163, 094104 (2025) [9] Epstein zeta method for many-body lattice sums, Andreas A. Buchheit, Jonathan K. Busse, arXiv:2504.11989 (2025)