Dominique Maldague (MIT, USA): "An intersection of CS and harmonic analysis: approximating matrix p to q norms"

In Fourier restriction theory, we bound exponential sums whose frequencies lie in sets with special properties, e.g. random sets or curved sets. Bourgain, Demeter, and Guth developed decoupling inequalities to show that such functions enjoy square root cancellation behavior. This theory lies in the larger context of bounding matrix l^p to l^q norms, which is well-studied in the CS literature. We will discuss a new polynomial time algorithm inspired by Fourier restriction theory of myself, Guth, and Urschel which reduces the multiplicative error of computing matrix 2 to q norms from roughly n^{1/q} to n^{1/2q}, where n is the size of the matrix.

Lars Becker (University of Bonn): "Quantum signal processing and the nonlinear Fourier transform"

We will give a short overview of two topics and their connection. The first is so-called quantum signal processing, a framework for designing quantum algorithms. The second one is the nonlinear Fourier transform, a transformation that diagonalizes certain integrable nonlinear partial differential equations.

Hong Wang (NYU, USA): "Kakeya sets in R^3"

A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction.  Kakeya set conjecture asserts that every Kakeya set has Minkowski and Hausdorff dimension n. We prove this conjecture in R^3 as a consequence of a more general statement about union of tubes. This is joint work with Josh Zahl.

Sun Woo Park (MPIM): "Graph neural networks and covering spaces"

I would like to give a brief overview of some deep learning techniques, their applications, and their limitations. We will focus particularly on how covering spaces are relevant to understanding limitations of conventional neural networks in determining isomorphism classes of graphs (or in particular graph neural networks). A number of works presented in this talk are based on joint collaborations with Yun Young Choi, U Jin Choi, Dosang Joe, Minho Lee, Seunghwan Lee, Joohwan Ko, and Youngho Woo. My hope is to make the talk as accessible as possible, even for those who do not have prior knowledge in deep learning techniques.

Andrew Ng (University of Bonn): "What geometric group theory has to do with your area of interest"

Geometric group theory studies the interplay between the algebraic properties of groups and the geometric properties of spaces that they act on. I will illustrate this close connection in the setting of 3-manifolds and also point out connections with surprisingly diverse areas of mathematics, such as algebraic geometry, number theory, symplectic geometry, and geometric analysis, though no knowledge of any of these topics will be necessary to understand the core of the talk. If there is time at the end I welcome challenges from the audience to show/elaborate on connections between GGT and their favourite area of maths. 

László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany): "Dissipation and mixing: from turbulent flows to weak solutions"

There is a well-known discrepancy in mathematical fluid mechanics between phenomena that we can observe and phenomena on which we have theorems. The challenge for the mathematician is then to formulate an existence theory of solutions to the equations of hydrodynamics which is able to reflect observation. The most important such observation, forming the backbone of turbulence theory, is anomalous dissipation. In the talk, we survey some of the recent developments concerning weak solutions in this context.

Elliot Kaplan (MPIM): "Nullstellensätze and model-theoretic embeddings"

Abraham Robinson realized that properties of a model-theoretic structure are equivalent to algebraic information about extensions of that structure. I will discuss this correspondence and show how it can be used to give quick proofs of some classical theorems about algebraically closed fields, such as Hilbert's (weak) Nullstellensatz and Chevalley's theorem on constructible sets. I will then discuss some recent work on applying these tests to describe the asymptotic behavior differential equations. 

Habib Ammari (ETH, Swiss)
TBA

Andreas Thom (TUD, Germany)
TBA