NTSGrad Fall 2022/Abstracts: Difference between revisions
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| bgcolor="#BCD2EE" | We'll understand some key properties of elliptic curves (Weil Pairing, eigenvalues of Frobenius, and poles of j-invariants) and try to see how these properties are closely tied in with understanding certain properties of rank 2 local systems over an open subset of the projective line $\mathbb{P}^1$.This is a preparation talk for the NTS talk on Thursday. | | bgcolor="#BCD2EE" | We'll understand some key properties of elliptic curves (Weil Pairing, eigenvalues of Frobenius, and poles of j-invariants) and try to see how these properties are closely tied in with understanding certain properties of rank 2 local systems over an open subset of the projective line $\mathbb{P}^1$.This is a preparation talk for the NTS talk on Thursday. | ||
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Revision as of 17:15, 17 October 2022
This page contains the titles and abstracts for talks scheduled in the Spring 2022 semester. To go back to the main GNTS page, click here.
9/13
| Ivan Aidun |
| A Case Study in the Analogy Between Z and F_q[t] |
| An influential concept in modern number theory is the idea that the integers Z and the ring of polynomials over a finite field F_q[t] share many traits. In this talk, I will discuss some particular examples of how this analogy can work, focusing on zeta functions and counting problems. No prior familiarity will be required! |
9/20
| Jiaqi Hou |
| Poincare series and Petersson trace formula |
| I will talk about the Poincare series, which are basic examples of modular forms, and the Petersson trace formula for SL(2,Z). Then I will discuss some applications of Petersson's formula. |
9/27
| No speaker |
10/4
| Eiki Norizuki |
| p-adic L-functions |
| In this talk, I will look at how p-adic L-functions are constructed as first demonstrated by Kubota and Leopoldt. These are p-adic analogues of the Dirichlet L-functions and the main idea of the construction comes from interpolating the negative integer values of the classical L-functions. This talk should be accessible to everyone. |
10/11
| Sun Woo Park |
| Rank 2 local systems and Elliptic Curves |
| We'll understand some key properties of elliptic curves (Weil Pairing, eigenvalues of Frobenius, and poles of j-invariants) and try to see how these properties are closely tied in with understanding certain properties of rank 2 local systems over an open subset of the projective line $\mathbb{P}^1$.This is a preparation talk for the NTS talk on Thursday. |
10/18
| TBA |
| TBA |
10/25
| TBA |
| TBA |
11/1
| TBA |
| TBA |
11/8
| TBA |
| TBA |
11/15
| TBA |
| TBA |
11/22
| TBA |
| TBA |
11/29
| TBA |
| TBA |
12/6
| TBA |
| TBA |
12/13
| TBA |
| TBA |