2021.10.05 13:05

One Day Workshop on the Arithmetic Theory of Quadratic Forms

Views 403 Votes 0 Comment 0
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
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

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.

 Subject+ContentSubjectContentCommentUser NameNick NameUser IDTag
List of Articles
No. Subject Author Date Views
22 weekplan_672_2020 2020.11.18 0
21 [집중강연 2021.02.01~05] Auslander-Reiten translation and $\tau$-tilting theory 2020.11.18 2465
20 QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 1) 2021.01.13 14157
19 QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 2) 2021.01.13 1004
18 QSMS mini-workshop on number theory and representation theory 2021.01.13 7119
17 QSMS 20/21 Winter School on Representation Theory 2021.01.13 1061
16 Cluster algebras and related topics 2021.05.07 2071
15 QSMS 2021 Summer Workshop on Representation theory (Week1) 2021.08.02 565
14 QSMS 2021 Summer Workshop on Representation theory (Week2) 2021.08.02 512
13 QSMS 2021 위상기하 가을 워크숍 프로그램 2021.09.28 698
12 CONFERENCE ON ALGEBRAIC REPRESENTATION THEORY 2021 2021.10.04 660
11 QUANTUM GROUPS AND CLUSTER ALGEBRAS 2021.10.04 826
» One Day Workshop on the Arithmetic Theory of Quadratic Forms 2021.10.05 403
9 2021 Winter School on Number Theory 2021.12.13 568
8 [QSMS 2022 Winter School] Workshop on Representation Theory 2022.01.07 683
7 QSMS winter school on symplectic geometry and mirror symmetry 2022.01.07 533
6 SYMPLECTIC GEOMETRY AND BEYOND (PART I) 2022.01.27 568
5 Mini-workshop on deformed W-algebras and q-characters I 2022.05.15 502
4 Mini-workshop on deformed W-algebras and q-characters II 2022.06.03 475
3 QSMS 2022 summer workshop on representation theory 2022.07.04 695
Board Pagination Prev 1 2 Next
/ 2