?

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
Extra Form
일정시작 2020-09-25
배경색상 #036eb7

Date: 9월25일 금요일 12일 오후2시
Place: 27동 220호

Speaker: 김명호

Title: Introduction to cluster algebras (and monoidal categorification)

 

Abstract:

Cluster algebra는 Q(x_1,x_2,...,x_m)  (변수가 m개인  유리함수들의 ring)의 subring으로서 "cluster variable"이라고 불리는 특별한 원소들이 생성하는 것으로 정의합니다. 이 때 변수들의 집합 {x_1,x_2,...x_m}은 "initial cluster", 그리고 x_i 들은 "initial cluster variable"이라고 각각 불립니다.  Cluster variable은 이 initial cluster에서 시작하여, 한번에 하나의 variable을 다른 것으로 바꾸는 "mutation"이라는 특별한 과정으로 얻어지는 원소를 말합니다.  따라서 이 mutation이 무엇인지 이해하면 cluster algebra의 정의를 이해할 수 있습니다. 편의상 Fomin-Zeleveinsky의 분류에서는 "skew-symmetric cluster algebra of geometric type"에 해당하는 경우만을 다루도록 하겠습니다. 이 경우에는 mutation이 "quiver mutation"이라는 조합적인 방법으로 주어집니다. Finite type classification, Laurent phenomenon등을 설명드리고, 그리고 나서도 시간이 있다면, cluster algebra의 monoidal categorification을 간략히 소개하겠습니다.

 

 

Date: 9월25일 금요일 12일 오후4시
Speaker: 조윤형

Title: Cluster structures in mirror symmetry


Abstact:

In this talk, I will explain "mutations" on various objects; mutations of (1) Laurent polynomials, (2) polytopes, (3) Lagrangian tori

in symplectic manifolds. I will also explain how those concepts are "expected" to fit together in the context of SYZ mirror symmetry. 

If time permits, I will provide examples of flag varieties in which every mutation appeared are turned out to coincide with the mutations in cluster theory.

 


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 4785
145 [2021 KMS Annual Meeting] Related talks qsms 2021.10.05 1841
144 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 5475
143 [2022 Global KMS International Conference 10/19 ~ 10/21] Related talks qsms 2023.01.05 1225
142 [2022 KMS Spring Meeting] Related talks qsms 2022.04.28 1671
141 [BK21-QSMS Toric Geometry Seminar] Moment Polytope qsms 2022.01.03 1741
140 [BK21-QSMS Toric Geometry Seminar] The Fredholm regularity of discs qsms 2022.03.14 1509
139 [KMS Specical Conference with 2022 Fields Medalists] Related talks qsms 2023.10.11 1054
138 [QSMS Geometry Seminar 2022-05-12] Tropical Lagrangian multi-sections and tropical locally free sheaves qsms 2022.05.07 1539
137 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications qsms 2022.05.09 1621
136 [QSMS Geometry Seminar 20221230] Morphism spaces between coisotropic A-branes qsms 2022.12.27 1162
135 [QSMS Geometry seminar 2023-05-25] Symplectic field theory and codimension-2 stable Hamiltonian submanifolds qsms 2023.05.25 1158
134 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 1491
133 [QSMS Monthly Seminar 2022-09-30] Monotone Lagrangians via toric degenerations: algebraic approach qsms 2022.09.30 1356
132 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 1238
131 [QSMS Monthly Seminar 2022-12-02] Extended crystal structures of Hernandez-Leclerc categories qsms 2022.12.02 1268
130 [QSMS Monthly Seminar 2023-03-24] Rational points on abelian varieties qsms 2023.03.24 1174
129 [QSMS Monthly Seminar 2023-04-21] Lagrangian submanifolds and their Legendrian lifts qsms 2023.04.21 1146
128 [QSMS Monthly Seminar 2023-05-26] Lagrangian submanifolds and their Legendrian lifts qsms 2023.05.26 1132
127 [QSMS Monthly Seminar 2023-10-13] Quantum Grothendieck rings of Hernandez-Leclerc categories / Regular Schur labeled skew shape posets and their 0-Hecke modules qsms 2023.10.13 972
126 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 1070
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8