?

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 37094
40 [QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links qsms 2022.05.27 17459
39 [QSMS Monthly Seminar] Symmetric functions and super duality qsms 2021.05.28 18518
38 [QSMS Monthly Seminar] Smoothing of Fano varieties and mutations qsms 2021.09.23 18159
37 [QSMS Monthly Seminar] Recoverable lattices qsms 2021.05.07 18312
36 [QSMS Monthly Seminar] Quantum entanglement entropy in abelian arithmetic Chern-Simons theory qsms 2021.10.29 17923
35 [QSMS Monthly Seminar] Quantization of integrable differential difference equations qsms 2022.04.22 17647
34 [QSMS Monthly Seminar] Peterson conjecture via Lagrangian correspondences and wonderful compactifications qsms 2020.11.18 35742
33 [QSMS Monthly Seminar] Introduction to finite-dimensional representations of quantum affine algebras qsms 2021.12.03 17669
» [QSMS Monthly Seminar] Introduction to cluster algebras (and monoidal categorification) qsms 2020.11.18 21022
31 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 18447
30 [QSMS Monthly Seminar] Canonical basis qsms 2020.11.18 21729
29 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 18630
28 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 17837
27 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 17963
26 [QSMS Monthly Seminar 2024-10-18] Braid group actions on Grassmannians and extended crystals of type A / Modules of degenerate quantum groups for $P$-partition generating functions qsms 2024.10.18 80
25 [QSMS Monthly Seminar 2024-09-20] Braid varieties and cluster algebras / Symplectic geometry of Markov-type Diophantine equations qsms 2024.09.20 158
24 [QSMS Monthly Seminar 2024-05-24] Cuspidal subgroups and rational torsion subgroups / Free subgroups generated by Dehn twists and its categorification qsms 2024.05.24 14474
23 [QSMS Monthly Seminar 2024-04-12] Local systems and finite group symmetry in Floer theory / Calabi-Yau structures on Rabinowitz Fukaya categories qsms 2024.04.12 14009
22 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 13814
21 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 14958
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8