Department of Mathematics

Title: Existence, Non-existence, and Regularity of Minimizers in Weighted Fractional Cluster ProblemsAbstract: Recently, fractional partitioning problems have attracted significant attention: given a domain Omega, how should it be divided to minimize a weighted fractional perimeter? These problems arise naturally as sharp-interface limits of fractional vectorial Allen-Cahn equations. Unlike the classical setting, where the weights correspond […]

Title: Type B websAbstract: This talk is about joint work in preparation with Elias—Rose on webs for Spin(2n+1) fundamental representations. Our approach is similar to Cautis—Kamnitzer—Morrison’s skew Howe duality approach to type A webs. We use ingredients from: Wenzl’s quantum spin Howe duality, Iorgov—Klimyk’s work on representation theory of iquantum groups, and our previous work […]

Title: Bounding the singular locus of the moduli of curves on a hypersurfaceAbstract: The space of rational curves on a Fano variety X serves as a powerful tool for probing the geometry of X. Even for hypersurfaces, characterizing these spaces is difficult; however, work by Riedl–Yang established they are irreducible and have the expected dimension. In this talk, […]

Title: Counting number fields of fixed degree by their smallest defining polynomial Abstract: When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of GL(2)xGL(1) on the space of polynomials of degree n so that for any two polynomials f and g in the same orbit, the […]

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Title: Stability in the Free Boundary Curve Shortening Flow.Abstract: The free boundary curve shortening flow is natural Neumann analogue of the usual curve shortening flow; a geometric flow which arrises as the negative L^{2} gradient flow of arc-length. If the boundary curve is convex, Stahl in his PhD thesis established the convergence of convex initial […]