I will describe the new approach to scattering theory, which extends to time dependent potentials, including nonlinear equations. In particular, recent progress for one dimensional cases, Long-Range scattering and Local-Decay […]
For Schrödinger-type equations with time-dependent, spatially local interactions — including nonlinear cases — there exist solutions that are neither localized nor scattering. These solutions exhibit sub-ballistic spreading, yet are global, […]
We consider stochastic growth models in the Kardar-Parisi-Zhang universality class, like the asymmetric simple exclusion process or the last passage percolation. We will give an overview of older and recent […]
Under suitable assumptions, a Markov chain will converge at large times to its stationary measure, over a time scale known as the mixing time. Markov chains can then be used […]
Tensor networks have become a standard computational tool for simulating quantum many-body dynamics. Their time evolution requires the efficient and accurate update of low-rank tensor factors. In recent years, several […]
The standard approach to studying the liquid-vapor phase transition uses the Maxwell double-tangent construction. Whereas this construction is easily justified physically, deriving it mathematically has proved to be more difficult. […]
The study of the electronic properties of twisted bilayer graphene (TBG) has garnered much attention from the condensed matter community recently. TBG is obtained by stacking two graphene monolayers on […]
Anyons are 2d identical quantum particles with an intermediate exchange symmetry characterized by representations of the braid group. In the abelian case, they can be modeled through the so-called magnetic […]
We investigate a family of radially symmetric Coulomb gas systems at inverse temperature coming from the normal matrix model. The family is characterised by the property that the density of […]
COURSE OVERVIEW Exponential integrators are powerful numerical methods for solving time-dependent partial differential equations. This short course introduces the construction, analysis, and efficient implementation of exponential integrators, providing both theoretical […]
In the setting of non-local quantum computation (NLQC), we study how multiple parties can implement channels on a distributed input system by making use of an entangled resource state, local […]
Effectively describing the long-time dynamical behavior of quantum systems is a long-standing open problem. When the coupling constant λ of the interaction is small, the dynamics of the system up […]
COURSE OVERVIEW Exponential integrators are powerful numerical methods for solving time-dependent partial differential equations. This short course introduces the construction, analysis, and efficient implementation of exponential integrators, providing both theoretical […]
In this talk, I will describe some work in progress about relating the low-lying spectrum of the Davies Lindbladian for qLDPC codes to that of Glauber dynamics on a classical […]
Calderbank-Shor-Steane (CSS) codes, such as the toric code, are a widely studied class of quantum error-correcting codes. Understanding the thermalization time of these systems is important not only for error […]
Registration for the TRR 352 Winter School on Mathematical Physics is now open! The event will take place from March 9-13, 2026, at the Georg-von-Vollmar-Akademie in Kochel am See. Invited […]
A gas of interacting Bosons can be represented using an ensemble of stochastic diffusions – a Brownian loop soup. In this talk, we review the construction of this Feynman representation, […]
Describing the long-time dynamical behaviour of quantum systems is a long-standing open problem. When the coupling constant \lambda of the interaction is small, the dynamics of the system up to […]
We consider a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. After explaining that these Scattering Quantum Walks encompass several known Quantum Walks, […]
We study the dynamical density and current responses of a class of non-interacting, one-dimensional gapless lattice Fermi systems subjected to density-type perturbations slowly varying in space and time, in the […]
Schedule: 14:30 Welcome 15:00 Talk by Nicos Georgiou (Sussex) 16:00 Coffee break 16:30 Talk by Christian Kühn (TU Munich) 18:00 Option for common dinner Titles and abstracts: Nicos Georgiou: Mean-field limit and parameter […]
With the proof of Widom’s conjecture giving new insights on the entanglement properties of the non-relativistic free Fermi gas, it is a natural question whether this situation extends to the […]
The microscopic laws of quantum mechanics give rise to some of the most fascinating macroscopic phenomena in physics, such as superfluidity and superconductivity. The theoretical description of such phenomena is […]
We present the relativistic quantum physics model hierarchy from Dirac-Maxwell to Vlasov/Euler-Poisson that models fast moving charges and their self-consistent electro-magnetic field. Our main interest is (asymptotic) analysis of these […]
November 17-21, 2025 at Haus Chiemgau, Teisendorf The meeting will begin on Monday at 3 pm and conclude on Friday after lunch. Speakers: Lennart Becker (UT) Yoon Jun Chan (UA) […]
Repeated compositions of quantum channels arise naturally in many places across quantum: they arise, for example, in the transfer operator approach to quantum spin chains, and also in the repeated […]
The CRC’s Annual Retreat took place from September 28 to October 1, 2025, at the Georg-von-Vollmar-Akademie in Kochel am See. The retreat was fully dedicated to preparing the application for the next […]
Quantum mechanics, now about a century old, is a very successful physical theory of matter on a small scale. From its first description until today, it has surprised scientists and […]
This talk will provide a basic introduction to the three dimensional Dirac equation that describes an electron interacting with a magnetic field. Over the years a lot of work has […]
I will review the mathematical analysis behind two classes of new exciting materials: Twisted bilayer graphene (TBG) and twisted semiconductors (TMDs) with an emphasis on their mathematical properties and differences. […]
Conventional quantum tomography assumes a high degree of control over the system in question in order to measure many observables. On the other hand, a classical dynamical system may be […]
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This talk discusses numerical integrators for such and other classes of nonlinear parametrizations u(t) = Φ(θ(t)) where […]
Thanks to their high degree of control and tunability, ultracold atomic gases provide a rich platform for the study of quantum many-body effects. Ultracold gases of highly magnetic atoms exhibit […]
We explore a connection between a weak topology on spaces of probability measures, a classical combinatorial problem in matching, and numerical schemes for the solution of PDEs by neural networks.
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by […]
On Thursday, May 08, 2025, at 12:15 pm, Prof. Dr. Shi Jin (Shanghai Jiao Tong University) will give a talk on “Quantum Computation of partial differential equations and related problems” at TUM, Boltzmannstr. 3, 85748 Garching Forschungszentrum, room […]
Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. Separately, hardware containing native continuous-variable (CV, oscillator) systems […]
In this talk we consider discrete Gaussian free fields with ergodic random conductances on ℤd, d ≥ 2, where the conductances are possibly unbounded but satisfy a moment condition. As […]
Let X be a simple random walk in Znd with d≥3 and let tcov be the expected time it takes for X to visit all vertices of the torus. In joint work with Prévost and Rodriguez […]
Program: 11:00 am – Dr. Larry Read, LMU München: Proof of the oval conjecture (Part 1) lunch 1:30 pm – Matthias Baur, M.Sc., Universität Stuttgart: Proof of the oval conjecture (Part 2) […]
In relativity, nothing can travel faster than the speed of light. But there are often emergent speed limits, such as the speed of sound, that limit practical information transfer. In […]
In this talk, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form. We follow a […]
State-sum constructions have numerous applications in both mathematics and physics. In mathematics, they yield invariants for knots and manifolds and serve as a powerful organizing principle in representation theory. To […]
In this talk, we consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary […]
We consider a system of closed random walk trajectories interacting by mutual repulsion. This probabilistic model is motivated by its connections to statistical mechanics models, such as the Bose gas, […]
It is a remarkable property of random matrices, that their resolvents tend to concentrate around a deterministic matrix as the dimension of the matrix tends to infinity, even for a […]
January 21-24, 2025 at Christkönigshaus, Stuttgart Speakers: Jonas Peteranderl (LMU) Sara Terveer (LMU) François Visconti (LMU) Paul Gondolf (Tub) Yifei Li (Tub) Tom Wessel (Tub) Pablo Costa Rico (TUM) […]
Fix some graph or uniform hypergraph F and then consider the following simple process: start with a large complete (hyper)graph Kn on n vertices and iteratively remove (the edge set […]
Phase transitions are natural phenomena in which a small change in an external parameter, like temperature or pressure, causes a dramatic change in the qualitative structure of the object. To […]
Of great interest in plasma physics is to determine whether excited charged particles in a non-equilibrium state will relax to neutrality or transition to a nontrivial coherent state. Due to […]
Bardeen-Cooper-Schrieffer (BCS) theory is a successful model of superconductivity. In this talk, I will begin by providing an overview of how BCS theory connects with other models of superconductivity, highlighting […]
Quantum systems typically reach thermal equilibrium when in weak contact with a large external bath. Understanding the speed of this thermalisation is a challenging problem, especially in the context of […]
Competitive games of complete information famously always have Nash equilibria, but it is well-known that correlation (“advice”) can yield new equilibria, sometimes with preferable collective properties (social welfare, fairness, …). […]
Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f: \to (-1,1)$ as the upper left entry of a product of $SU(2)$ matrices parametrized by […]
Quantum walks (QWs) can be viewed as quantum analogs of classical random walks. Mathematically, a QW is described as a unitary, local operator acting on a grid and can be […]
We study the generalised Lloyd model, that is, a random Schrödinger operator on the lattice Zd of the form H = −∆ + λV, λ > 0, with Vi = […]
The CRC’s Annual Retreat was held from October 6–10, 2024, at the Explorer Hotel Garmisch in Farchant. Nearly 60 members, including both established researchers and early-career scientists, gathered for a […]
This talk will provide a partial overview of how to model molecular observables and spectral responses. We shall start with the essential quantum mechanical concepts and formalisms that are used […]
The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the […]
Branching Brownian motion, branching random walks, and the F-KPP equation have been the subject of intensive research during the last couple of decades. By means of Feynman-Kac and McKean formulas, […]
(Pseudo)spectral methods are popular for solving a wide variety of differential equations and generic optimization problems. Due to favourable approximation properties, such as rapid convergence for smooth functions, they are […]
The classification of states of quantum lattice systems is a well -defined mathematical endeavour which started with the discovery of the quantum Hall effect. In this talk, I will discuss […]
The stability of topological indices of condensed matter systems in the p resence of interactions is not expected to hold universally. In this colloquium, I will first discuss the mathematical […]
The operator-algebraic description of quantum mechanical systems can be used to mathematically deal with systems, where the usual Hilbert space description becomes inconvenient or breaks down. In this talk I […]
For many problems in quantum mechanics it is important to have a good grasp of the operators modelling the system. The landscape function was introduced as a tool to compute […]
We study the contact process on scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where the neighbourhood of each vertex is updated with a rate depending on its […]
We prove a thermodynamically stable Lieb-Robinson bound (LRB) for bosons with long-range interaction on lattices. The condition is that the initial state admits (i) uniformly bounded density from above and […]
Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to […]
We introduce a new approach to justify mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of […]
In Bernoulli percolation, the incipient infinite cluster (IIC) is a version of the “open cluster of the origin at criticality conditioned to be infinite”. Since this event should have probability […]
Regularisation by noise in the context of stochastic differential equations (SDEs) with coefficients of low regularity, known as singular SDEs, refers to the beneficial effect produced by noise so that […]
In this seminar, we will discuss the estimation of group action using the non-commutative Fourier transform. We’ll explore an interesting relationship between the non-commutative Fourier transform and this estimation problem. […]
In this talk, I will try to motivate the subject of constructive quantum field theory which was born in the 70’s as an attempt to give rigorous constructions of quantum […]
The talk reviews the state of affairs in the mathematically rigorous foundations of the special-relativistic Vlasov-Maxwell equations. The progress is made possible by a recent formulation of a well-posed Lorentz […]
In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, […]
Although many-body quantum simulations have greatly benefited from high-perfor- mance computing facilities, large molecular systems continue to pose formidable challenges. Mixed quantum-classical models, such as Born-Oppenheimer molecular dynamics or Ehren- […]
The Fröhlich polaron models a charged quantum particle interactiong with a polar cystal. Since the moving particle has to drag along a ‘cloud’ of polarization, it appears heavier than it […]
It is known through classical works of Kac, Salem, Zygmund, Erdös and Gal that lacunary sums behave in several ways like sums of independent random variables, satisfying, for instance, a […]
In this talk – based on a joint work with J. Lampart, N. Leopold, and D. Mitrouskas – I will talk about the mean field limit of the renormalized Nelson […]
The meeting of the junior members of TRR 352 took place from December 13-15, 2023, at the Haus der bayerischen Landwirtschaft in Herrsching/Ammersee. Program Titles & Abstracts Speakers: Alberto Brollo (TUM) Florian Haberberger […]
We consider a random walk in a truncated cone K_N , which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study […]
In this talk, we investigate random convex interfaces which are generated as convex hulls of random point sets. We are interested in their asymptotic behavior when the size of the […]
Interacting Bose gas at zero temperature is often described by the Bogoliubov approximation. It involves quasiparticles, called phonons, with a rather curious dispersion relation responsible for superfluidity. The Fermi Golden […]
In 2001 Bolthausen, den Hollander and van den Berg obtained the asymptotics of the probability that the volume of a Wiener sausage at time t is smaller than expected by […]
The Abelian sandpile model on a graph G is a Markov chain whose state space is a subset of the set of functions with integer values defined on the vertices […]
First CRC meeting in the Bavarian Alps From October 11 to 15, 2023, the kick-off meeting of our CRC took place in Farchant near Garmisch. Around 60 participants came together […]
The KPZ fixed point is conjectured to be the universal space-time scaling limit of the models belonging to the KPZ universality class and it was rigorously constructed by Matetski, Quastel […]
We introduce a currently hot topic in probability theory, the theory of scaling limits for random fields of gradients in all dimensions. The random fields are a class of model […]
I will present a new approach to finding the asymptotic states of Nonlinear Wave Equations with general initial data. In particular, we show for a large class of equations, that […]
The homogeneous electron gas (jellium) where electrons interact with each other and with a positive background charge is one of the simplest model system in condensed matter physics. Still, the […]
We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle […]
In this talk, we describe the kinetic equation for the Bogoliubov excitations of the Bose-Einstein Condensate. We find three collisional processes: One of them describes the 1↔2 interactions between the […]
Propagation and generation of “chaos” is an important ingredient in rigorous control of applicability of kinetic theory, in general. Chaos can here be understood as sufficient statistical independence of random […]
We consider Markovian open quantum dynamics (MOQD) in continuous space. We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed […]
In this talk I will describe the vacuum sector of the Weinberg-Salam (WS) model of electroweak forces. In the vacuum sector the WS model yields the U(2)-Yang-Mills-Higgs equations. We show […]
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs […]
Unraveling the origin of unconventional superconductivity is one of the driving forces behind quantum simulations with Fermions in optical lattices. In these strongly correlated materials, the necessary pairing of charge […]
We consider the infrared problem in translation-invariant Nelson-type models describing a single quantum mechanical particle linearly coupled to a field of scalar bosons at fixed total momentum. Physical examples include […]
The correspondence principle, as stated by Niels Bohr in 1923, is at the root of the traditional results in semi-classical analysis. It offers a natural insight into the world of […]
Schrödinger’s equation is a beautiful piece of mathematics. It f its on just one line and is supposed to accurately describe the behavior of most atoms and molecules of our […]
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical […]
A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the […]
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., […]
