?

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 weekplan_672_2020 secret qsms 2020.11.18 0
144 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 407
143 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 666
142 [QSMS Representation theory seminar 2024-03-29] Quantum Grothendieck rings of Hernandez-Leclerc Categories qsms 2024.03.05 729
141 [QSMS Representation theory seminar 2024-01-31] Kostant’s problem for Whittaker modules over Lie superalgebras qsms 2024.01.18 849
140 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 907
139 [QSMS Representation theory seminar 2023-12-28] Generalized polynomial functors qsms 2023.12.15 923
138 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 968
137 [QSMS Symplectic geometry seminar 2023-10-17, 18] New approaches to discovering symplectic non-convexity / Banach-Mazur distances in symplectic and contact geometry qsms 2023.10.10 971
136 [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
135 [QSMS Representation theory seminar - 2023-10-17] A Data-Scientific Approach to Representation Theory: Case Study of Kronecker Coefficients qsms 2023.09.27 994
134 [KMS Specical Conference with 2022 Fields Medalists] Related talks qsms 2023.10.11 1054
133 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 1064
132 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 1068
131 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 1075
130 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 1094
129 [QSMS-BK21 Symplectic Seminar 9 June] Physical Aspects of the Calegaro System / Introduction to BV Formalism qsms 2023.06.26 1119
128 [QSMS Seminar 2023-05-17] Affinizations, R-matrices and reflection functors qsms 2023.05.04 1126
127 [QSMS Monthly Seminar 2023-05-26] Lagrangian submanifolds and their Legendrian lifts qsms 2023.05.26 1131
126 [QSMS-BK21 Symplectic Seminar 28 July] Nonexistence of Exact K(G,1) Lagrangians in Milnor Fibers of Weighted Homogeneous Polynomials / Associative Yang-Baxter Equation and Fukaya Categories qsms 2023.07.17 1133
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8