2021.10.05 13:05

# One Day Workshop on the Arithmetic Theory of Quadratic Forms

조회 수 79 추천 수 0 댓글 0
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
일정시작 2021-10-09 2021-10-09 #FF5733

One Day Workshop on the Arithmetic Theory of Quadratic Forms

Date:  10월 9일 (토)   10:00 ~ 11:50,   14:00 ~ 15:50,   16:00 ~ 17:50

Place:  129-406 (SNU)

Talk 1:   10:00 ~ 11:50

Title:  Universal sums of generalized polygonal numbers

Speaker:  Jangwon Ju (Ulsan University)

Abstract:

The sum of generalized polygonal numbers is said to be universal if it represents all nonnegative integers. In this talk, we introduce some arithmetic method on studying representations of sums of generalized polygonal numbers. We provide effective criteria on the universalities of sums of generalized polygonal numbers with sime small order. These might be considered as a generalization of the "15-Theorem" of Conway and Schneeberger.

Talk 2:  14:00 ~ 15:50

Title: The use of modular form theory in studying quadratic forms

Speaker:  Kyoungmin Kim (Hannam University)

Abstract:

In this talk, we introduce some modular form theory used in studying the number of representations of integers by quadratic forms.

Talk 3:  16:00 ~ 17:50

Speaker:  Mingyu Kim (Sungkyunkwan University)

Abstract:

For a positive integer $n$, let $\mathcal{T}(n)$ be the set of all integers greater than or equal to $n$. An integral quadratic form $f$ is called tight $\mathcal{T}(n)$-universal if the set of nonzero integers that are represented by $f$ is exactly $\mathcal{T}(n)$. The smallest possible rank over all tight $\mathcal{T}(n)$-universal quadratic forms is denoted by $t(n)$. In this talk, we prove that $t(n) \in \Omega(\log_2(n)) \cap \mathcal{O}(\sqrt{n})$. Explicit lower and upper bounds for $t(n)$ will be provided for some small integer $n$. We also consider the classification of all tight $\mathcal{T}(n)$-universal diagonal quadratic forms.

This is a joint work with Byeong-Kweon Oh.

 제목+내용제목내용댓글이름닉네임아이디태그
List of Articles
번호 제목 글쓴이 날짜 조회 수
» One Day Workshop on the Arithmetic Theory of Quadratic Forms 2021.10.05 79
12 QUANTUM GROUPS AND CLUSTER ALGEBRAS 2021.10.04 125
11 CONFERENCE ON ALGEBRAIC REPRESENTATION THEORY 2021 2021.10.04 297
10 QSMS 2021 위상기하 가을 워크숍 프로그램 2021.09.28 254
9 QSMS 2021 Summer Workshop on Representation theory (Week2) 2021.08.02 197
8 QSMS 2021 Summer Workshop on Representation theory (Week1) 2021.08.02 260
7 Cluster algebras and related topics 2021.05.07 1751
6 QSMS 20/21 Winter School on Representation Theory 2021.01.13 769
5 QSMS mini-workshop on number theory and representation theory 2021.01.13 6696
4 QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 2) 2021.01.13 653
3 QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 1) 2021.01.13 13793
2 [집중강연 2021.02.01~05] Auslander-Reiten translation and $\tau$-tilting theory 2020.11.18 2057
1 weekplan_672_2020 2020.11.18 0
Board Pagination Prev 1 Next
/ 1