SEMINARS, NUMBER THEORY
March 9, 2022 3:00 pmFor a smooth projective curve $C/\mathbb{Q}$, how many field extensions of $\mathbb{Q}$ -- of given degree and bounded discriminant --- arise from adjoining a point of $C(\overline{\mathbb{Q}})$? Can we further count the number...
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SEMINARS, NUMBER THEORY
March 2, 2022 3:00 pmInspired by an analogy between torsion and preperiodic points, Zhang has proposed a dynamical generalization of the classical Manin-Mumford and Bogomolov conjectures. A special case of these conjectures, for `split' maps, has recently...
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SEMINARS, NUMBER THEORY
February 16, 2022 3:00 pmFor an elliptic curve E, Kolyvagin used Heegner points to construct special Galois cohomology classes valued in the torsion points of E. Under the conjecture that not all of these classes vanish,...
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SEMINARS, NUMBER THEORY
February 9, 2022 3:00 pmGrothendieck's Section Conjecture posits that the set of rational points on a smooth projective curve Y of genus at least two should be equal to a certain "section set" defined purely in...
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SEMINARS, NUMBER THEORY
February 2, 2022 3:00 pmConsider the set of Galois extensions L of Q whose Galois group is the quaternion group. For large X, Klüners counted extensions with |disc(L)| <= X. We discuss asymptotics when...
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NUMBER THEORY
December 1, 2021 3:00 pmThe study of mod p points on Shimura varieties was originally motivated by the study of the Hasse-Weil zeta function for Shimura varieties. It involves some rather subtle problems which...
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NUMBER THEORY
December 1, 2021 3:00 pmThe study of mod p points on Shimura varieties was originally motivated by the study of the Hasse-Weil zeta function for Shimura varieties. It involves some rather subtle problems which...
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NUMBER THEORY
November 17, 2021 3:00 pmThe integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms. Viewing this metrized line bundle as a class in the codimension one arithmetic...
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NUMBER THEORY
November 17, 2021 3:00 pmThe integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms. Viewing this metrized line bundle as a class in the codimension one arithmetic...
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NUMBER THEORY
November 10, 2021 3:00 pmA phenomenon underlying many remarkable results in number theory is the natural Galois action on the cohomology of symplectic groups of integers. In joint work with Soren Galatius and Akshay...
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