조회 수 459 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
Extra Form
일정시작 2021-10-09
일정종료 2021-10-09
배경색상 #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

Title:  Tight universal quadratic forms

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.

 

 

 

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
25 [Series of lectures 2/21, 2/23, 2/28] An introduction to geometric representation theory and 3d mirror symmetry qsms 2023.02.02 26
24 QSMS Workshop on symplectic geometry and related topics (2023 Winter) file qsms 2023.01.06 340
23 QSMS 2023 Winter workshop on number theory and representation theory file qsms 2023.01.06 335
22 서울대학교 수리과학부 Rookies Workshop 2022 file qsms 2022.10.30 240
21 2022 Summer School on Number Theory file qsms 2022.07.21 489
20 QSMS 2022 summer workshop on representation theory file qsms 2022.07.04 778
19 Mini-workshop on deformed W-algebras and q-characters II qsms 2022.06.03 521
18 Mini-workshop on deformed W-algebras and q-characters I qsms 2022.05.15 555
17 SYMPLECTIC GEOMETRY AND BEYOND (PART I) file qsms 2022.01.27 637
16 QSMS winter school on symplectic geometry and mirror symmetry qsms 2022.01.07 598
15 [QSMS 2022 Winter School] Workshop on Representation Theory file qsms 2022.01.07 751
14 2021 Winter School on Number Theory qsms 2021.12.13 634
» One Day Workshop on the Arithmetic Theory of Quadratic Forms qsms 2021.10.05 459
12 QUANTUM GROUPS AND CLUSTER ALGEBRAS qsms 2021.10.04 876
11 CONFERENCE ON ALGEBRAIC REPRESENTATION THEORY 2021 qsms 2021.10.04 716
10 QSMS 2021 위상기하 가을 워크숍 프로그램 qsms 2021.09.28 773
9 QSMS 2021 Summer Workshop on Representation theory (Week2) qsms 2021.08.02 568
8 QSMS 2021 Summer Workshop on Representation theory (Week1) file qsms 2021.08.02 632
7 Cluster algebras and related topics qsms 2021.05.07 2113
6 QSMS 20/21 Winter School on Representation Theory qsms 2021.01.13 1123
Board Pagination Prev 1 2 Next
/ 2