2021.10.05 13:05

One Day Workshop on the Arithmetic Theory of Quadratic Forms

조회 수 501 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
32 East Asian Symplectic Conference 2023 2023.09.04 80
31 [Symplectic Geometry] QSMS SUMMER SCHOOL 2023 2023.07.17 287
30 The 3rd International Undergraduate Mathematics Summer School 2023.07.11 273
29 2023 Summer School on Number Theory 2023.07.11 173
28 QSMS 2023 Summer Workshop on Representation theory 2023.07.11 241
27 Cluster algebras and related topics in East Asia 2023.05.15 369
26 Combinatorics on flag varieties and related topics 2023 2023.02.13 163
25 [Series of lectures 2/21, 2/23, 2/28] An introduction to geometric representation theory and 3d mirror symmetry 2023.02.02 146
24 QSMS Workshop on symplectic geometry and related topics (2023 Winter) 2023.01.06 523
23 QSMS 2023 Winter workshop on number theory and representation theory 2023.01.06 442
22 서울대학교 수리과학부 Rookies Workshop 2022 2022.10.30 352
21 2022 Summer School on Number Theory 2022.07.21 548
20 QSMS 2022 summer workshop on representation theory 2022.07.04 868
19 Mini-workshop on deformed W-algebras and q-characters II 2022.06.03 555
18 Mini-workshop on deformed W-algebras and q-characters I 2022.05.15 592
17 SYMPLECTIC GEOMETRY AND BEYOND (PART I) 2022.01.27 689
16 QSMS winter school on symplectic geometry and mirror symmetry 2022.01.07 641
15 [QSMS 2022 Winter School] Workshop on Representation Theory 2022.01.07 849
14 2021 Winter School on Number Theory 2021.12.13 681
» One Day Workshop on the Arithmetic Theory of Quadratic Forms 2021.10.05 501
Board Pagination Prev 1 2 Next
/ 2