Johns Hopkins UniversityEST. 1876
America’s First Research University
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Title: On Backwards uniqueness for singular mean curvature flows.Abstract: Mean curvature flow, the gradient flow of the area functional, is the most natural geometric heat flow for embedded hypersurfaces. Being non linear, the flow develops singularities, at which it stops being smooth. One fundamental, often delicate, question for such non linear flows is that of […] |
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Title: Semisimplifying categorical Heisenberg actions, diagrammatics, and periodic equivalences Abstract: Semisimplification functors on tensor categories underlie many powerful constructions in representation theory, including the Frobenius functor in modular representation theory and the Duflo-Serganova functor from Lie superalgebras. I will introduce a systematic approach to applying semisimplification functors to categories defined over positive characteristic, with the most […] |
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Title: Regularity theory for fractional elliptic equations in nondivergence form Abstract: We present recent advances in the regularity theory for solutions to fractional nonlocal equations driven by fractional powers of nondivergence form elliptic operators in bounded domains, where sharp regularity on the coefficients is assumed. The results include Harnack inequality, H”older regularity of solutions and Schauder […] |
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Title: Gauss — an agentic formalization of the Prime Number TheoremAbstract: In this talk we'll highlight some recent formalization advances using a new agent, Gauss. In particular, with Gauss we obtained a Lean proof of the Prime Number Theorem in strong form, completing a challenge set in January 2024 by Alex Kontorovich and Terence Tao. We hope Gauss will help assist working […] |
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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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