Mathematical and Theoretical Physics Seminar (MTPS)

Abbas Saberi (MPIPKS Dresden, University of Tehran)

Emergence at the Edge: Random Matrices Meet Correlated Percolation

Abstract: Random matrix theory and percolation are two foundational frameworks based on ensembles of independent random variables. Despite their deceptively simple formulations, both exhibit rich and nontrivial behavior, leading to widespread applications in describing diverse physical phenomena and advancing interdisciplinary research. In this talk, I will begin with a general overview of these two theories and highlight some of their real-world applications---including the modeling of economic systems, large-scale climate wind variables, and electrical and thermal conduction in polymer nanocomposites. We will then examine the limitations of these classical models in the presence of long-range correlations, which are common in natural systems. Drawing on ideas from correlated percolation, I will show how one can construct a new class of random matrix ensembles that incorporate long-range correlations and uncover novel spectral universality classes. I will conclude with examples demonstrating how these concepts apply to long-range correlated quantum and classical systems.

Maxim Trushin (National University of Singapore)

Exploring Dimensional Crossover: 2D Water Flow, Light, and Electronic Transport

Abstract: Reducing dimensionality often amplifies interaction effects, though their manifestations vary widely across physical systems. In this talk, I will present three distinct examples. First, I’ll show how confining water to monolayer thickness alters its flow behavior, revealing a transition to 2D dynamics governed by dilatational rather than shear viscosity [1]. Second, I’ll demonstrate how surface plasmon polaritons - 2D analogs of light - can be generated via electron-hole recombination in strongly biased graphene, separated from a plasmonic material by a thin boron nitride layer [2]. Third, I’ll discuss how 2D electrons with flat bands and cross-band pairing can enter a highly conductive yet non-superconducting state - an effect absent in three dimensions [3]. These cases highlight the richness of interaction-driven phenomena in reduced dimensions.
[1] Maxim Trushin, Alexandra Carvalho & A. H. Castro Neto Commun. Phys. 6, 162 (2023).
[2] Maxim Trushin arXiv:2505.02358 (2025).
[3] Maxim Trushin et al. Phys. Rev. B 109, 245118 (2024).

Athanasios Chatzistavrakidis (RBI Zagreb)

Basic curvature tensors in geometry and physics

Abstract: The concept of basic curvature first appeared implicitly in the study of deformed infinitesimal symmetries and Cartan-Lie algebroids. Subsequently, it was understood that it plays a crucial role in defining the adjoint and coadjoint representations for Lie algebroids. In physics, the basic curvature tensor first appeared in the BV formulation of twisted Poisson sigma models. Apart from these instances, there are several other related problems in geometry and physics where the basic curvature and its accompanying structures become important. In this talk, I will discuss two selected problems: (i) the basic curvature tensor for Courant algebroid connections and its role in generalised Riemannian geometry and (ii) a unifying framework for supersymmetric Poisson sigma models where global supersymmetry is associated to the coadjoint representation of a Lie algebroid.

Richard Szabo (Heriot-Watt University Edingburgh)

Title: Random partitions, instantons and enumerative geometry

Abstract: Counting partitions in diverse dimensions is a long-standing problem in enumerative combinatorics. It also plays a prominent role in the physics of instanton counting and in algebraic geometry through the computation of Donaldson-Thomas invariants. In this talk I will give an overview of these counting problems, and discuss how recent developments in the computation of instanton/Donaldson-Thomas partition functions clarify some open problems in the enumeration of higher-dimensional partitions.

Christiaan J.F. van de Ven (FAU Erlangen-Nürnberg)

Classical and quantum KMS states on spin lattice systems

Abstract: We study the classical and quantum KMS conditions in spin lattice systems. Specifically, we construct a strict deformation quantization (SDQ) for an S^2-valued spin lattice over Z^d, extending the Berezin SDQ for a single sphere. This allows to promote a classical dynamics on the algebra of classical observables to a quantum dynamics on the algebra of quantum observables. We then compare the notion of classical and quantum thermal equilibrium by showing that any weak*-limit point of a sequence of quantum KMS states fulfils the classical KMS condition, demonstrating that the semiclassical limit of quantum thermal states reproduces classical thermal equilibrium. Finally, using a version of the Kirkwood–Salzburg equations adapted to our setting, we provide sufficient conditions ensuring uniqueness of classical and quantum KMS states at high temperatures.
Joint work with L. Pettinari and N. Drago;
Communications in Mathematical Physics Vol 406, 163 (2025);
https://link.springer.com/article/10.1007/s00220-025-05325-2.

Workshop Mathematical Physics in the Heart of Germany VI

See the workshop website for more information. A registration by email (to spetrat AT constructor.university) would be appreciated.