Johns Hopkins UniversityEST. 1876
America’s First Research University
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Title: Vibrodynamics of constrained mechanical systemsAbstract: We study the effect of rapid vibration of constraining surfaces of arbitrary codimension on a confined mechanical particle. The slow dynamics experience an effective potential force coming from the geometry of the vibrating surface, which can introduce new equilibria and change stability character of existing ones. A classical example […] |
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Title: Projectivity of the Moduli Space of Equidimensional BranchvarietiesAbstract: A branchvariety of a projective $k$-scheme $X$ is a geometrically reduced scheme $Y$ equipped with a finite map to $X$. Alexeev and Knutson showed the existence of a proper moduli space of branchvarieties with fixed numerical invariants, but the projectivity of this space remained an open question. In […]
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Title: On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularitiesAbstract: Kleinian singularities are quotients of C^2 by finite subgroups of SL_2(C). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities that are related […] |
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1 event,Title: Critical sets of harmonic functions and Almgren's frequency functionAbstract: Given a harmonic function on a nice domain in n-dimensional Euclidean space, its critical set (the set of points where its gradient vanishes) is known to have dimension at most n-2, with locally finite (n-2)-dimensional Hausdorff measure. For harmonic polynomials, the Hausdorff measure can be […] |
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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: Periods and skeletonsAbstract: Given a degeneration X of a complex algebraic variety over the punctured unit disk, one can associate to X, a non-archimedean analytic space called its analytification X^an. The analytification retains all the original information about X but in general can be very complicated. A beautiful aspect of the theory is that X^an contains a […]
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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: A conformally invariant energy for the Paneitz operator on cornered Riemannian manifolds Abstract: We construct conformally invariant boundary and corner operators associated to the Paneitz operator on a cornered Riemannian manifold. These operators give rise to a conformally invariant energy for the Paneitz operator on a cornered Riemannian manifold, and hence to formulations of […] |
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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: The Volume of K-semistable Fano ManifoldsAbstract: In 2015, K. Fujita showed that for any n-dimensional K-semistable Fano manifold, the anti-canonical volume is always less than or equal to that of complex projective space (CP^n). In this talk, I will discuss my recent joint work with Chi Li on characterizing the second-largest volume. We prove that for […] |
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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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