Why do we study local fields?
|분야Field||2018 Math Colloquim|
|날짜Date||2018-06-01||시간Time||15:50 ~ 18:00|
|장소Place||Math. Bldg. 404||초청자Host|
|TOPIC||Why do we study local fields?|
|소개 및 안내사항Content||Part I
Title: Why do we study local fields?
Abstract: In this talk, I will explain motivation of studying a p-adic local field from various local-global principles. Basic properties, Hensel's lemma, and local class field theory (if time permits) would be discussed. I will explain them as easy as possible, so undergraduate students are welcome to join.
Title: Linking between intersection numbers and modular forms
Abstract: In this talk, I will start with 'modularity' which explains relations among L-functions, geometric objects (elliptic curves), and analytic objects (modular forms). For instances of applications, it yields Fermat's last theorem and BSD conjecture (in low rank case).
I will then explain how linking between intersection numbers and modular forms can be understood in the context of modularity. If time permits, then I will introduce an ongoing project.
A main goal of this talk is to introduce the subject to non-number theorists, by minimizing use of technical terminologies.
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