(*) The lectures of Prof. Wilhelm Schlag have been canceled.

Contents of the lecturers:

Minicourse Lecturer: Robert Seiringer
Title: Mathematical Foundations of Density Functional Theory
Abstract: Density Functional Theory (DFT) attempts to describe all the relevant information about the ground state of a many-body quantum system in terms of its one-body reduced density. It is widely and successfully used in practice for computations in quantum chemistry. In these lectures, we shall explain the mathematical structure of DFT, and review known bounds on the universal density functional (including the Lieb-Thirring Inequality for the kinetic energy, and the Lieb-Oxford Inequality for the electrostatic energy). We shall also outline recent results concerning the validity of the local density approximation, and the equivalence of various possible formulations of the uniform electron gas. Much (but not all) of the material of the lectures is contained in the review paper https://arxiv.org/pdf/1912.10424

Minicourse Lecturer: Mitia Duerinckx
Title: New methods for mean-field limits of classical particle systems
Abstract: One major open problem in mathematical physics still concerns the justification of the Vlasov-Poisson equation as the mean-field limit for systems of classical particles with Coulomb interactions. In this course, we shall review this classical problem, describe some previous approaches, and present a new dual hierarchical method that we recently developed with D. Bresch and P.-E. Jabin. If time allows, we might also discuss related questions regarding correlation estimates and corrections to mean field.

Minicourse Lecturer: Yoshiko Ogata
Title : Operator algebraic approach to topological orders
Abstract : Recently, topological phases of matters have attracted a lot of attention. One characteristic feature of topological phases is the existence of anyons. In this talk, I explain the operator algebraic approach to anyons.

Speaker: To Tat Dat
Title: The Phi43 measure on compact Riemannian 3-manifolds
Résumé: In this talk, I present a joint work with Dang, Bailleul and Ferdinand in which we construct the Phi43 quantum field theory measure on a compact Riemannian 3-manifold, as an invariant measure of a stochastic partial differential equation. This gives an example of nonperturbative, interacting, non topological quantum field theory constructed on 3-manifolds.

Speaker: Maxime Van De Moortel
Title: Strong Cosmic Censorship Conjecture and black hole dynamics.
Abstract: In the wake of major breakthroughs in General Relativity during the 1960s, Roger Penrose introduced Strong Cosmic Censorship, a profound conjecture regarding the deterministic nature of the theory. Nearly six decades later, Penrose's conjecture remains one of the most captivating unsolved problems in mathematical physics, particularly within the realm of general relativity. Perhaps the most critical arena for testing the conjecture is the spacetime region hidden behind the event horizon: the interior of black holes. The key challenge is to prove the dynamical formation of singularities for solutions to the Einstein equations in this context. We will discuss
recent results on Strong Cosmic Censorship leveraging modern techniques in the theory of quasilinear waves equations at the crossroad of PDEs and Lorentzian geometry.

Speaker: Jia Shi
Title: Non-radial implosion for compressible Euler and Navier-Stokes in T3 and R3
Abstract: We will discuss the smooth, non-radial solutions of the compressible Euler and Navier-Stokes equation that develop an imploding finite time singularity. The construction is motivated by the radial imploding solutions from Merle--Raphaël--Rodnianski--Szeftel, and Cao-Labora--Buckmaster--Gomez-Serrano but is flexible enough to handle both periodic and non-radial initial data. This is a joint work with Gonzalo Cao-Labora, Javier Gomez-Serrano, and Gigliola Staffilani.

Speaker: Marcin Napiórkowski
Title: Free energy asymptotics of the quantum Heisenberg model
Abstract: The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. Based on an effective theory called spin wave approximation,  it is believed that low temperature properties of the model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction.

Speaker: Le Van Phu Cuong Title: Energy minimising maps and branched optimal transport
Abstract: In their seminal work, Brezis, Coron, and Lieb showed an equivalence between sphere-valued minimising harmonic maps having prescribed topological singularities at given points in R3 and minimal connections between those points, which are solutions of Monge-Kantorovich having those points as marginals. This work was later recast and generalised by Almgren, Browder, and Lieb, who interpreted the minimal connection problem as a suitable Plateau’s problem for integral rectifiable currents, having those points as the prescribed boundary. In this talk, we will investigate more general energies for maps with values into Cartesian products of spheres, and investigate their connections to Plateau’s problem for currents (or flat chains) with coefficients in suitable groups. In particular, we establish the equivalence for energy minimising configurations of those maps with irrigation Gilbert-Steiner problems. This talk is based on joint work with S. Baldo (Verona), A. Massaccesi (Padova), and G. Orlandi (Verona).

Flash talks on Tuesday 

• Chanjin You (Penn State): Phase mixing estimates for the nonlinear Hartree equation of infinite rank
• Vũ Hồ Thảo Thuận (Monash University): Hamiltonian approach to 2-layer dispersive stratified fluids
• Võ Hoàng Hưng (Saigon University): Liouville Theorems for infinity Laplacian with gradient and KPP type equation
• Nguyễn Tiến Tài (University of Science, VNU Ha Noi) Nonlinear Rayleigh-Taylor instability in fluid mechanics and beyond
• Jinyeop Lee (University of Basel): On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs

Flash talks on Wednesday 

• Florian Haberberger (LMU Munich): The free energy of dilute Bose gases at low temperatures
• Ben Li (University of Warsaw): Beliaev damping through Friedrichs model
• Nguyễn Tòng Xuân (NYU Shanghai): Local Central Limit Theorem for long-range potentials with continuous spins
• Nguyễn Thị Nguyên Khoa (ENS Paris-Saclay): Development and assessment of physics-informed deep learning methods: towards multiphysics simulation in industrial contexts