NUMBER THEORY
April 8, 2020 3:00 pmvia Zoom Video Conferencing: https://harvard.zoom.us/j/136830668 (joint w/ Arul Shankar) We discuss a new method to bound 5-torsion in class groups of quadratic fields using the refined BSD conjecture for elliptic curves. The most...
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NUMBER THEORY
April 1, 2020 3:00 pmvia Zoom Video Conferencing: https://harvard.zoom.us/j/136830668 In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings R->T to be an isomorphism of complete intersections. In...
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NUMBER THEORY
March 25, 2020 3:00 pmvia Zoom Video Conferencing: https://harvard.zoom.us/j/136830668 The Sato-Tate group of an abelian variety A of dimension g defined over a number field is a compact real Lie subgroup of the unitary...
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NUMBER THEORY
March 11, 2020 3:00 pmWe explain a new height gap result on holonomic power series with rational coefficients, and prove the Schinzel-Zassenhaus conjecture as its consequence: a monic irreducible non-cyclotomic integer polynomial of degree...
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NUMBER THEORY
March 4, 2020 3:00 pmWe give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on $\Gamma_0(N)$ in the case where $N$ is prime and equal to...
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NUMBER THEORY
February 26, 2020 3:00 pmOne of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical...
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NUMBER THEORY
February 19, 2020 3:00 pmWe consider the family of normal octic fields with Galois group $D_4$, ordered by their discriminant. In forthcoming joint work with Arul Shankar, we verify the strong form of Malle's conjecture for this family of...
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NUMBER THEORY
February 12, 2020 3:00 pmEvery Newton polygon satisfying the Kottwitz conditions occurs on Shimura varieties of PEL-type in positive characteristic (Viehmann/Wedhorn). In most cases, it is not known whether these Newton polygon strata contain...
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NUMBER THEORY
February 5, 2020 3:00 pmThere is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of...
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NUMBER THEORY
November 20, 2019 3:00 pmIn a recent joint work with Kisin and Shin, we compared the Grothendieck-Lefschetz trace formula for abelian-type Shimura varieties with the stable Arthur-Selberg trace formulas. In this talk I will...
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