NTSGrad Fall2023/Abstracts: Difference between revisions
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Caroline Nunn''' | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" | Motivating class field theory | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | In this talk, I will give an outline of the main ideas of class field theory. I will begin by investigating the structure of the Galois group of an abelian extension of number fields using local information at unramified primes. I will then show how, in the case of cyclotomic fields, this local information can be pieced together to recover the full Galois group. This will lead us to the main results of class field theory. I will end with a number theoretic application to the problem of representing primes in the form x^2+ny^2. | ||
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Revision as of 13:54, 2 October 2023
This page contains the titles and abstracts for talks scheduled in the Fall 2023 semester. To go back to the main GNTS page for the semester, click here.
9/12
| Joey Yu Luo |
| Geometric proof of Hurwitz class number relation |
| In this talk I will introduce the Hurwitz class number relation, and give a geometric proof using the modular curves over complex number. The main ingredients are different perspective of elliptic curves. First year graduate students who are interested in number theory are welcome. |
9/19
9/26
| Eiki Norizuki |
| Mass Formula |
| I will talk about a nice result by Serre which can be seen as counting the totally ramified extensions of a local field by an appropriate weight. By easy computations, one can arrive at analogous mass formulas for other extensions from Serre's mass formula. I will mention how it relates to other problems in number theory. |
10/3
| Caroline Nunn |
| Motivating class field theory |
| In this talk, I will give an outline of the main ideas of class field theory. I will begin by investigating the structure of the Galois group of an abelian extension of number fields using local information at unramified primes. I will then show how, in the case of cyclotomic fields, this local information can be pieced together to recover the full Galois group. This will lead us to the main results of class field theory. I will end with a number theoretic application to the problem of representing primes in the form x^2+ny^2. |
10/10
10/17
10/24
10/31
11/7
| TBA |
| TBA |
11/14
11/21
11/28
12/5
12/12