NTSGrad Spring 2025/Abstracts: Difference between revisions
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| bgcolor="#BCD2EE" |For a curve in positive characteristic, one can study the a-number, p-ranks and other arithmetic invariants of its Jacobian. A natural question to ask is what the proportion of curves with a given arithmetic invariant in your chosen family of curves is. I will give a flavor of some of the heuristics predicted by Cais, Ellenberg, Zureick-Brown and survey some known results. | | bgcolor="#BCD2EE" |For a curve in positive characteristic, one can study the a-number, p-ranks and other arithmetic invariants of its Jacobian. A natural question to ask is what the proportion of curves with a given arithmetic invariant in your chosen family of curves is. I will give a flavor of some of the heuristics predicted by Cais, Ellenberg, Zureick-Brown and survey some known results. | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" |Jiaqi Hou | |||
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| bgcolor="#BCD2EE" align="center" |Maass forms on arithmetic hyperbolic surfaces | |||
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| bgcolor="#BCD2EE" |Besides holomorphic modular forms, Maass forms are another important class of automorphic forms. I will talk about the definitions and basic properties of Maass forms on hyperbolic surfaces. Then, I will discuss the analytic problem of how to bound Maass forms and present a sup-norm bound by Iwaniec and Sarnak and their proof. | |||
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Revision as of 01:47, 7 April 2025
This page contains the titles and abstracts for talks scheduled in the Spring 2025 semester. To go back to the main GNTS page for the semester, click here.
1/28
| Joey Yu Luo |
| Mahler integral and L-function |
| I will define Mahler integrals and L-funciton of elliptic curves, and discuss some conjectural identities between them. They are secretly prediected by the Beilinson-Bloch conjecture, but I will not dig into it. |
2/18
| Joey Yu Luo |
| Jacquet-Rallis Fundamental Lemma |
| Jacquet-Rallis Fundamental Lemma is some mysterious lattice counting equality in the p-adic field. In this talk, I will present the statement of the FL, relate them with orbit integrals, and if time permits, discuss the relating smooth transfer conjecfture(theorem) and arithmetic variants. |
3/18
| Eiki Norizuki |
| Arithmetic Statistics of Curves in Positive Characteristic |
| For a curve in positive characteristic, one can study the a-number, p-ranks and other arithmetic invariants of its Jacobian. A natural question to ask is what the proportion of curves with a given arithmetic invariant in your chosen family of curves is. I will give a flavor of some of the heuristics predicted by Cais, Ellenberg, Zureick-Brown and survey some known results. |
4/8
| Jiaqi Hou |
| Maass forms on arithmetic hyperbolic surfaces |
| Besides holomorphic modular forms, Maass forms are another important class of automorphic forms. I will talk about the definitions and basic properties of Maass forms on hyperbolic surfaces. Then, I will discuss the analytic problem of how to bound Maass forms and present a sup-norm bound by Iwaniec and Sarnak and their proof. |