NTSGrad Fall 2022/Abstracts: Difference between revisions
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | ''' | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park''' | ||
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| bgcolor="#BCD2EE" align="center" | '' | | bgcolor="#BCD2EE" align="center" | ''2-Selmer groups and Markov Chains'' | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | This is a survey talk on Klagsbrun, Mazur, and Rubin’s approach on utilizing Markov chains to compute the upper bound of the distribution of ranks of quadratic twist families of elliptic curves over number fields. Though we won’t be able to go through all the details, we will try to first identify how one can use 2-Selmer groups to bound the rank of certain families of elliptic curves, and why Markov chains are relevant for understanding the distribution of 2-Selmer groups. | ||
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Revision as of 22:13, 24 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
| John Yin |
| Some Examples in Etale Cohomology |
| I will motivate, define, and give explicit examples of etale cohomology. In addition, I will compute the Galois action on etale cohomology in certain cases. |
10/25
| Sun Woo Park |
| 2-Selmer groups and Markov Chains |
| This is a survey talk on Klagsbrun, Mazur, and Rubin’s approach on utilizing Markov chains to compute the upper bound of the distribution of ranks of quadratic twist families of elliptic curves over number fields. Though we won’t be able to go through all the details, we will try to first identify how one can use 2-Selmer groups to bound the rank of certain families of elliptic curves, and why Markov chains are relevant for understanding the distribution of 2-Selmer groups. |
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 |