1. Greg Arone, Stockholm University, Sweden
Title: Polynomial functors in topology

Abstract: Polynomial functors were introduced in algebraic setting by Eilenberg and Mac Lane in the 1950-es. Their definition was adapted to topological (or homotopical) context by Goodwillie in the 1990-ies, as part of his celebrated calculus of functors. Polynomial functors in the sense of Goodwillie (also known as excisive functors) have a rich structure theory, and have become a widely used tool. The talk will be a leisurely overview of polynomial functors. We will aim to give sufficient motivation, review a few applications, and survey the current state of knowledge about their structure.

2. Nguyen Viet Dang, Université de Strasbourg, France 

Title: Quantum gauge theories on surfaces. 

Abstract: Gauge theory, which goes back to Maxwell, is a central topic in physics since it is the basis of the standard model describing elementary particles and forces between them and also in mathematics where it appears in the study of character varieties and knot invariants. In this talk, I will survey ideas and recent works of many authors around quantum gauge theories in 2 dimensions from the point of view of probability and partial differential equations. Comment end  

3. Amnon Neeman, Università degli Studi di Milano, Italy
Title: Negative K-theory and bounded t-structures on the category of perfect complexes.

Abstract: After a brief review of algebraic K-theory, the starting point of the talk will be a 2019 theorem by Antieau, Gepner and Heller. The theorem asserts that negative K-theory provides obstructions to the existence of bounded t-structures.

This remarkable theorem gave rise to several conjectures. We now know that three of them are false, and we will very quickly go through these. The fourth conjecture happens to be true, and the talk will focus on the idea of the proof.

The proof involves techniques quite different from the K-theoretic ones involved in the work of Antieau, Gepner and Heller. This raises two questions:

(1) Is there a proof more along the obstruction-theoretic approach of Antieau, Gepner and Heller?
(2) Are the techniques of the non-obstructive proof applicable in other contexts?

We will say a little about (1), and much more about (2).

4. Trần Vũ Khanh, International University - Vietnam National University HCM City

Title: Some Degenerate Elliptic Problems: Estimates and Regularity

Abstract: Degenerate elliptic problems arise naturally in partial differential equations when ellipticity is lost in certain directions. Depending on the geometry of the degeneracy, one may still obtain subelliptic estimates, as in Hörmander’s theory of sums of squares and Grushin-type operators, or enter a genuinely non-subelliptic regime. In this talk, we will discuss this transition and ask what regularity can survive beyond the subelliptic setting. We will focus on several problems arising in several complex variables and CR geometry, including the D-bar-Neumann problem, the Kohn-Laplacian, and the Bergman projection. Starting from L^2 estimates, we will discuss subelliptic and non-subelliptic estimates, regularity on domains of finite and infinite type, as well as some recent L^p and global/local regularity results. A recurring theme will be the interplay between the geometry of degeneracy, analytic estimates, and regularity.

5. Chi-Wang Shu, Division of Applied Mathematics, Brown University

Title: High order numerical methods for hyperbolic equations

Abstract: Hyperbolic equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities. In this talk we will survey several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference and finite volume methods, discontinuous Galerkin finite element methods, and spectral methods. We will discuss essential ingredients, properties and relative advantages of each method, and provide comparisons among these methods. Recent development and applications of these methods will also be discussed.