NTSGrad Spring 2025/Abstracts: Difference between revisions
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(Created page with "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 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" |- | bgcolor="#F0A0A0" align="center" style="font-size:125%" |Joey Yu Luo |- | bgcolor="#BCD2EE" align="center" |Mahler integral and L-function |- | bgcolor="#BCD2EE" |...") |
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | | | bgcolor="#F0A0A0" align="center" style="font-size:125%" |Joey Yu Luo | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" |Jacquet-Rallis Fundamental Lemma | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" |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. | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | | | bgcolor="#F0A0A0" align="center" style="font-size:125%" |Eiki Norizuki | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" |Arithmetic Statistics of Curves in Positive Characteristic | ||
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| bgcolor="#BCD2EE" | | | 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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Revision as of 21:10, 14 March 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. |