Johns Hopkins UniversityEST. 1876
America’s First Research University
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Title: Graphs embedded on surfaces and their delta-matroidsAbstract: By “cutting out” the edges and vertices of a graph cellularly embedded in a surface, we obtain a ribbon graph. A partial Petrial is obtained from a ribbon graph by selecting a subset of the ribbon edges and adding a half-twist to each. The resulting ribbon graph […] |
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Title: A degenerate one-phase free boundary problem arising from the Alt-Phillips equation for negative exponents Abstract: We study viscosity solutions for a degenerate one-phase free boundary problem of the form $Delta w = frac{h( abla w)}{w}$. We assume the existence of a star-shaped domain $D$ such that $h < 0$ in $D$, $h = 0$ on […] |
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Title: Profinite transfers in K(n)-local homotopy theoryAbstract: After K(1)-localization, the classical J-homomorphism can be interpreted as a profinite transfer map. More precisely, it is a transfer map Sigma^{-1}KO^wedge_2 to mathbb{S}_{K(1)} from the C_2-homotopy fixed points (with a twist) to the mathbb{Z}_2^times-homotopy fixed points of the 2-complete complex topological K-theory. In joint work in progress with […] |
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Title: Rigidity of critical points of hydrophobic capillary functionalsAbstract: We prove the rigidity, among sets of finite perimeter, of volume-preserving critical points of the capillary energy in the half space, in the case where the prescribed interior contact angle is between 90◦ and 120◦. No structural or regularity assumption is required on the finite perimeter […] |
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Title: Ricci Solitons and Hamiltonian DynamicsAbstract: In this talk, we will discuss a specific connection between a Kähler Gradient Ricci soliton (GRS) and Hamiltonian dynamics. The former is a singularity model of the Kahler version of Ricci flows and a generalization of Einstein metrics while the latter comes from classical mechanics. In particular, we show […] |
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Title: Poincaré Duality in abstract 6-functor formalismsAbstract: In this talk, I will discuss Poincaré Duality in the context of abstract 6-functor formalisms. Somewhat surprisingly, a 6-functor formalism satisfies an appropriate form of Poincaré Duality under a relatively weak set of extra assumptions. Most importantly, these assumptions are essentially independent of the ``coefficient'' categories D(X).This makes […] |
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