NUMBER THEORY
October 21, 2020 3:00 pmIn this talk, we will discuss a geometric construction of p-adic analogues of Maass--Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is,...
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NUMBER THEORY
October 21, 2020 3:00 pmIn this talk, we will discuss a geometric construction of p-adic analogues of Maass--Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is,...
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NUMBER THEORY
October 14, 2020 3:00 pmThe Bloch--Kato conjecture predicts that the dimension of the Selmer group of a global Galois representation is equal to the order of vanishing of its L-function. In this talk, I...
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NUMBER THEORY
October 7, 2020 3:00 pmMazur conjectured, after Faltings’s proof of the Mordell conjecture, that the number of rational points on a curve of genus g at least 2 defined over a number field of...
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NUMBER THEORY
September 30, 2020 3:00 pm$\ell$-torsion conjecture states that $\ell$-torsion of the class group $|\text{Cl}_K[\ell]|$ for every number field $K$ is bounded by $\text{Disc}(K)^{\epsilon}$. It follows from a classical result of Brauer-Siegel, or even earlier...
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NUMBER THEORY
September 23, 2020 10:00 amA few years ago Maksym Radziwill and I showed that the average of a multiplicative function in almost all very short intervals $[x, x+h]$ is close to its average on...
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NUMBER THEORY
September 16, 2020 3:00 pmThe Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of...
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NUMBER THEORY
September 9, 2020 3:00 pmWe apply methods from geometric representation theory toward the mod p Langlands program. More specifically, we explain a mod p version of the geometric Satake isomorphism, which gives a sheaf-theoretic...
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NUMBER THEORY
May 13, 2020 3:00 pmI would like to explain a classification result for p-divisible groups, which unifies many of the existing results in the literature. The main tool is the theory of prisms and...
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NUMBER THEORY
May 6, 2020 3:00 pm Langlands functoriality predicts the transfer of automorphic representations along maps of L-groups. In particular, the symmetric power representation Symm^{n-1} of GL(2) should give rise to a lifting from automorphic representations...
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