Department of Mathematics

Title: On singular points in the supercooled Stefan problemAbstract: The supercooled Stefan problem models how water, cooled below freezing, forms into ice. Experiments have shown that this process can exhibit nucleation (pieces of ice forming spontaneously) and that fractal-like patterns can emerge in the ice. This stands in sharp contrast with the melting problem, in which the […]

Title: Baily--Borel Compactifications of Period Images and the b-semiampleness Conjecture (following Bakker--Filipazzi--Mauri--Tsimerman)

Title: Spectral Fourier-Mukai transform and level-rank dualityAbstract: I will explain the construction of a Fourier-Mukai transform in the setting of spectral algebraic geometry of oriented elliptic curves, and discuss its fundamental properties. As an application, this yields a common refinement of three facets of the phenomenon known as "level–rank duality": positive-energy representations of LU(n)_k and LSU(k)_n […]

Title: A local sign decomposition for symplectic self-dual Galois representations of rank two Abstract: We present a new structure on the first Galois cohomology of families of symplectic self-dual p-adic representations of $G_Qp$ of rank two. This is a functorial decomposition into free rank one Lagrangian submodules encoding Bloch-Kato subgroups and epsilon factors, mirroring an […]