Seminar
Studying isogeny-based cryptography using lattice geometry
Mixed-platonic 3-manifolds: at the interface of algebra, combinatorics, and (hyperbolic) geometry
I'll introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type. For reasons I'll give in the talk, we are interested in such manifolds that are complements of knots in the three-sphere. One such "knot complement" has been known for some time to fit this description; whether there are any more is an open question.
Ugur Abdulla - Kolmogorov Problem and Wiener-type Criteria for the Removability of the Fundamental Singularity for the Elliptic and Parabolic PDEs
Liding Yao - The Cauchy-Riemann problem via extension operators
Γ-Convergence and Asymptotic Analyses for a Diffuse Domain Problem with Transmission-Type Boundary Conditions
Diffuse domain methods (DDMs) have attracted significant attention for approximating solutions to partial differential equations on complex geometries in two and three dimensions. These methods implicitly represent the geometry by replacing the sharp boundary interface with a diffuse layer of thickness $\epsilon$. We will define and consider both one-sided and two-sided versions of the problem. For the one-sided case, this approach reformulates the original equations on an extended, regular domain (for example, a hyper-cuboid).
Partially Symmetric Macdonald Theory
Introduction to arithmetic topology
Critical Probability of Multi-State Bootstrap Percolation on Random Graphs, Part 3
Motivic Classes of Varieties and Stacks with Applications to Higgs Bundles Part II
Abstract: We will continue talking about motivic classes. We will first review the motivic classes of varieties. Then we will focus on the motivic classes of stacks. In particular, we will give the explicit formulas for the motivic classes of moduli of Higgs bundles and bundles with connections.