Title: The Nevo-Thangavelu spherical maximal function on two step nilpotent Lie groups.Consider R^d times R^m with the group structure of a 2-step Carnot Lie group and natural parabolic dilations. The maximal operator originally introduced by Nevo and Thangavelu in the setting of the Heisenberg groups is generated by (noncommutative) convolution associated with measures on […]
Title: Minimal Exponent of Local Complete Intersection Subvarieties.Abstract: Classification of singularities is an interesting problem in many areas of algebraic geometry, like the minimal model program. One classical approach is to assign to a singular subvariety a rational number, its log canonical threshold. For complex hypersurface singularities, this invariant has been refined by M. Saito to the […]
Topic: Formalizing ∞-Category Theory in Lean
Title: Asymptotic Enumerativity of Tevelev Degrees.Abstract: A Tevelev degree is a type of Gromov-Witten invariant where the domain curve is fixed in the moduli. After reviewing the basic definitions and previously known results, I will report on joint work with Lehmann, Lian, Riedl, Starr, and Tanimoto, where we improve the Lian-Pandharipande bound on asymptotic enumerativity of Tevelev […]
Title: On the Gan-Gross-Prasad conjecture for unitary groups Abstract: The Gan-Gross-Prasad conjecture stipulates the existence of relations between the central values of certain L-functions and some automorphic periods on classical groups. It can be seen as a higher rank generalization of a famous formula of Waldspurger for toric periods on GL(2). In this talk, I […]
Title and abstract TBA
Title: Transfer operators for the relative trace formula. (Cont.) Abstract: Last time I presented an explicit formula for transfer operators that relate test measures and characters between the double quotients HG/H, for any rank-one homogeneous space G/H and the Whittaker model of SL(2) or PGL(2). In this talk, I will give a possible explanation for […]
Formalizing cotensors in Lean.
Title: Optimal observability times for wave and Schrodinger equations on really simple domainsAbstract: Observability for evolution equations asks: if I take a partial measurement in a system, can it “see” some physical quantity, such as energy? In a series of papers with E. Stafford, Z. Lu, and S. Carpenter, we showed that energy for the […]
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Title: Shimura Varieties and Eigensheaves Abstract: The cohomology of Shimura varieties is a fundamental object of study in algebraic number theory by virtue of the fact that it is the only known geometric realization of the global Langlands correspondence over number fields. Usually, the cohomology is computed through very delicate techniques involving the trace formula. […]