NTSGrad Fall 2019/Abstracts: Difference between revisions
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It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. | It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. | ||
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== Oct 1 == | |||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He''' | |||
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| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem'' | |||
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In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. | |||
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Revision as of 18:14, 1 October 2019
This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click here.
Sept 10
| Brandon Boggess |
| Law and Orders in Quadratic Imaginary Fields |
|
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers. |
Sept 17
| Solly Parenti |
| The Siegel-Weil Formula |
|
Theta functions, Eisenstein series, and Adeles, Oh my! |
Sept 24
| Dionel Jamie |
| On The Discrete Fuglede Conjecture |
|
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. |
Oct 1
| Qiao He |
| Modularity Theorem |
|
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. |