Mini Course

The index of a pair of projections on a Hilbert space was introduced in 1973 by Brown-Douglas-Filmore and connected to the integer quantum Hall effect by Avron-Seiler-Simon in 1994. For […]

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 […]

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 […]

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 […]

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 […]

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. […]

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 […]

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 […]

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, […]

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 […]

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 […]

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 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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 = […]

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 […]

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 […]

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 […]

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. […]

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 […]

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 […]

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 […]