Quadratic Euler Characteristics of Singular and Non-commutative Varieties

Explore an advanced mathematics seminar where Dr. Simon Pepin lehalleur from Universiteit van Amsterdam delves into the complexities of quadratic Euler characteristics in algebraic geometry. Learn about the refinement of topological Euler characteristics through symmetric bilinear forms and their arithmetic implications for non-algebraically closed fields. Discover recent developments in concrete computations for Hilbert schemes and symmetric powers of algebraic surfaces, as well as conductor formulas for hypersurface singularities. Gain insights into non-commutative techniques involving dg-categories of matrix factorizations and hermitian K-theory, presented as part of the New Equivariant Methods in Algebraic and Differential Geometry program at the Isaac Newton Institute.