Tuesday, October 13, 2020

2020-10-14 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 학과 세미나: 4차산업혁명과 수학

by 유희열 (전 과학기술부 차관)(KCRC)

이 강연에서는 4차산업혁명에 있어서 수학이 얼마나 중요한 역할을 하는 지 살펴 본다. 먼저 과학발전의 역사를 살펴보고 4차산업혁명시대의 도래에 대하여 논한다. 4차산업혁명의 기초이론을 살펴보고 4차산업혁명의 가장 핵심인 인공지능과 생명공학기술을 논한 다음 수학산업의 경쟁력 제고 방안을 논한다. (Zoom link: https://kaist.zoom.us/j/86300617369?pwd=WlkyNkJYY0RZR2lNZHRHazBZcU5sUT09)

2020-10-14 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Varieties parameterizing Galois extensions: Arithmetic and local analogues of essential dimension

by 쾨니히 요아힘(한국교원대학교)

The essential dimension quantifies the algebraic-geometric complexity of a class of algebraic objects (such as, but not necessarily, the class of Galois extensions with a given group): roughly speaking, it is the minimal number of parameters required to describe all objects in this class (over all fields containing a given field K). We introduce and discuss arithmetic-geometric and local analogues of this notion. These are supposed to quantify the difference in complexity between the local and global Galois theory of a given group over a given number field K. In particular, we show that the "local dimension" of a finite group is bounded by 2 - whereas arithmetic dimension remains mysterious in general. We give an application concerning solution of Grunwald problems.

2020-10-13 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 정수론:

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In this talk, we introduce an idea of producing rational torsion points on J_0(N), which is well-known. Conjecturally, the points constructed in this way exhaust all the rational torsion points on J_0(N). So, we briefly explain how to compute the orders of such points, and prove the conjecture up to finitely many primes. (If you would like to join this online seminar, please contact Bo-Hae Im to get the Zoom link.)

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