Title: Algebraic Statistics with a View towards Physics

Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding example is the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

About the speaker: Bernd Sturmfels is Director at the MPI for Mathematics in the Sciences (Leipzig) and Professor at UC Berkeley. His academic dignities are numerous. For example, he is ICM Speaker 2022, Honorary Doctor of Goethe University Frankfurt, Einstein Visiting Fellow at TU Berlin, George David Birkhoff Laureate in Applied Mathematics and member of the Berlin-Brandenburg Academy of Sciences.

Title: Universality in Random Matrix Theory beyond Wigner-Dyson-Mehta

Abstract:  Following E. Wigner’s pioneering discovery, the eigenvalues of large random matrices tend to exhibit a universal behaviour; most prominently the gap distribution converges to the celebrated Wigner-Dyson-Mehta statistics. In this talk an overview of more recent universality results concerning other physically relevant quantities is given, in particular the random matrix version of the Eigenstate Thermalisation Hypothesis and the normal fluctuation of the Quantum Unique Ergodicity is explained.

About the speaker:  László Erdös is a professor at the Institute of Science and Technology Austria (ISTA) in Klosterneuburg and one of the world's leading mathematicians, particularly in the field of random matrices. His academic honours are numerous. For example, he received an ERC Advanced Grant for his research on random matrices, he is a recipient of the Leonard Eisenbud Prize of the American Mathematical Society and a member of the Hungarian and Austrian Academies of Sciences as well as the Academia Europaea.

Title: Analysis on arithmetic manifolds

Abstract: An arithmetic manifold is a Riemannian manifold with additional arithmetic structure: it is acted on by a commutative algebra of "arithmetically defined'' operators. The most classical example is the complex upper half plane modulo the action of a congruence subgroup of SL(2,ℤ). The investigation of the analytic properties of the Laplace eigenfunction on such manifolds offers a fascinating interplay of analysis, number theory and automorphic forms.

About the speaker: Valentin Blomer is a professor at the University of Bonn and is one of the world's leading mathematicians in the field of number theory. He has received numerous academic prizes and awards. For example, he was awarded the Lichtenberg Professorship of the Volkswagen Foundation and an ERC Advanced Grant.
In addition to mathematics, he still finds time to pursue his second passion: music. He studied piano at the Frankfurt University of Music and Performing Arts and regularly performs as a soloist, chamber musician and song accompanist in Germany, Belgium, Switzerland, Slovenia, Japan and Canada.

Title: Rationality problems

Abstract: I will discuss several aspects of rationality, in algebraic geometry over nonclosed fields, and in presence of actions of finite groups. New obstructions based on ideas of motivic integration, which in turn go back to work of V. Batyrev and M. Kontsevich, allowed to settle several classical problems. I will explain these connections.

About the speaker: Yuri Tschinkel is Professor at the Courant Institute of Mathematical Sciences at New York University and Executive Vice President of the Mathematics and Physical Sciences Division of the Simons Foundation. He is a leading mathematician of our time with significant contributions in algebraic geometry and number theory. Yuri Tschinkel has has done research and has taught at several leading mathematical institutes worldwide and he is a member of prestigious academies of sciences, including the Leopoldina and the Academia Europaea.