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. […]
Rather than a seminar talk, this week we will meet to brainstorm on the relation between Euler systems and harmonic analysis.
Topic: Formalizing ∞-category theory in Lean
Title: Existence of 5 minimal tori in 3-spheres of positive Ricci curvatureAbstract: In 1989, Brian White conjectured that every Riemannian 3-sphere contains at least five embedded minimal tori. The number five is optimal, corresponding to the Lyusternik-Schnirelmann category of the space of Clifford tori. I will present recent joint work with Adrian Chu, where we […]
Title: Linear Chern-Hopf-Thurston conjectureAbstract: The Chern-Hopf-Thurston conjecture asserts that for a closed, aspherical manifold X of dimension 2d, the Euler characteristics satisfies $(-1)^dchi(X)geq 0$. In this talk, we present a proof of the conjecture for projective manifolds whose fundamental groups admit an almost faithful linear representation. Moreover, we establish a stronger result: all perverse sheaves on X […]