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일정시작 2021-10-21
일정종료 2021-10-21
배경색상 #77CC00

Invited Lecture

 

Speaker:  Myungho Kim (Kyung Hee University)

Date:   TBA

Title:  Cluster algebras and monoidal categories

Abstract:

Cluster algebras are special commutative rings introduced by Fomin and Zelevinsky in the early 2000s. Specifically, the cluster algebra refers to a subring generated by special elements called cluster variables in the field of rational functions, and the process of creating a new cluster variable from given cluster variables is called a mutation. Cluster algebra is being actively studied as it is observed that the mutation operation appears in various forms in various fields of mathematics.
A monoidal categorification of a given cluster algebra means that the Grothenieck ring is isomorphic to the cluster algebra and that special elements called cluster monomials correspond to simple objects. If there is such a monoidal categorification, then the given monoidal category and the cluster algebra are closely related and help understand each other's properties.
In this talk, I will explain that the category of finite-dimensional representations of quiver Hecke algebras and that of quantum affine algebras form monoidal categorifications of cluster algebras. This is based on several joint works with Seok-Jin Kang, Masaki Kashiwara, Se-jin Oh, and Euiyong Park.

 

 

 

Special Session

(SS-03) Representation Theory and Related Topics

 

Speaker:  Jethro van Ekeren (Universidade Federal Fluminense)

Schedule:  2021.10. 21.  AM 8:40~9:10

Title:  Chiral Homology and Classical Series Identities

Abstract:

I will discuss results of an ongoing project on the chiral homology of elliptic curves with coefficients in conformal vertex algebras. We find interesting links between this structure and classical number theoretic identities of Rogers-Ramanujan type (joint work with George Andrews and Reimundo Heluani).

 

 

Speaker:  Ryo Sato (Kyoto university)

Schedule:  2021.10.21.  AM 9:10~9:40

Title:  Feigin-Seikhatov duality in W-superalgebras

Abstract:

W-superalgebras are a large class of vertex superalgebras which generalize affine Lie superalgebras and the Virasoro algebras. It has been known that princial W-algebras satisfy a certain duality relation (Feigin-Frenkel duality) which can be regarded as a quantization of the geometric Langlands correspondence. Recently, D. Gaiotto and M. Rapčák found dualities between more general W-superalgebras in relation to certain four-dimensional supersymmetric gauge theories. A large part of thier conjecture is proved by T. Creutzig and A. Linshaw, and a more specific subclass (Feigin-Seikhatov duality) is done by T. Creutzig, N. Genra, and S. Nakatsuka in a different way. In this talk I will explain how to upgrade the latter case to the level of representation theory by using relative semi-infinite cohomology. This is based on a joint work with T. Creutzig, N. Genra, and S. Nakatsuka.

 

Speaker:  유필상 (칭화대학교)

Schedule:   2021.10.21.  AM 9:50~10:20

Title:  Representation Theory via Quantum Field Theory

Abstract:

It is known that some subjects in mathematics may be enriched by finding their context in physics. In this talk, we argue that representation theory is no exception. After explaining the physical context for representation theory of a finite group as the most basic example, we discuss a research program on how to use ideas of quantum field theory to study certain objects of interest in geometric representation theory.

 

 

Speaker:  George D. Nasr (University of Oregon)

Schedule:  2021.10.21.  AM 10:20~10:50

Title:  A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids and its connections to Representation Theory

Abstract:

In 2016, Elias, Proudfoot, and Wakefield introduced Kazhdan-Lusztig polynomials for a class of combinatorial objects called matroids. Later, they presented the equivariant (representation-theoretic) version of these polynomials. We will introduce both these topics and discuss results in the case of sparse paving matroids. For the ordinary Kazhdan-Lusztig polynomials, we present a combinatorial formula using skew Young tableaux for the coefficients of these polynomials for sparse paving matroids. In the case of uniform matroids (a special case of sparse paving matroids), this formula results in a nice combinatorial interpretation that arises in the equivariant version of these polynomials.

 

 

Speaker:  오재성 (고등과학원)

Schedule:  2021.10.21.  AM 11:00~11:30

Title:  A tugging symmetry conjecture for the modified Macdonald polynomials

Abstract:

In this talk, we propose a conjecture which is a symmetry relation for the modified Macdonald polynomials of stretched partitions, $\widetilde{H}_{k\mu}[X;q,q^k]=\widetilde{H}_{\mu^k}[X;q^k,q]$. Using the LLT-expansion of the modified Macdonald polynomials and linear relations of the LLT polynomials, we prove the conjecture for one column shape partition $\mu=(1^l)$. This is based on the joint work with Seung Jin Lee.

 

 

Speaker:  김영훈 (서울대학교, QSMS)

Schedule:   2021.10.21  AM 11:30~12:00

Title:  Extensions of 0-Hecke modules for dual immaculate quasisymmetric functions by simple modules

Abstract:

For each composition $\alpha$, Berg {\it et al.} introduced an indecomposable $0$-Hecke module $\mathcal{V}_\alpha$ with a dual immaculate quasisymmetric function as the quasisymmetric characteristic image. In this talk, we study extensions of $\mathcal{V}_\alpha$ by simple modules. To do this, we construct a minimal projective presentation of $\mathcal{V}_\alpha$ and calculate $\mathrm{Ext}^1$-group between $\mathcal{V}_\alpha$ and simple modules. Then we describe all non-split extensions of $\mathcal{V}_\alpha$ by simple modules in a combinatorial manner. As a corollary, it is shown that $\mathcal{V}_\alpha$ is rigid. This is joint work with S.-I. Choi, S.-Y. Nam, and Y.-T. Oh.

 

 

 

(SS-01) Trends in Arithmetic Geometry 
Speaker:  Chang-Yeon Chough (서울대학교, QSMS)

Schedule:  TBA

Title:  Brauer groups in derived/spectral algebraic geometry

Abstract:

Toën gave an affirmative answer to Grothendieck's question of comparing the Brauer group and the cohomological Brauer group of a scheme for all quasi-compact and quasi-separated (derived) schemes by introducing the notion of derived Azumaya algebras. I'll give a glimpse of the extension of this result to algebraic stacks in the setting of derived/spectral algebraic geometry. If time permits, my latest work on twisted derived equivalences in the derived/spectral setting, which is based on the aforementioned extension, will be presented.


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 112
58 [QSMS Seminar 14,16 Dec] A brief introduction to differential graded Lie algebras I, II qsms 2021.11.29 39
57 [SNU Number Theory Seminar 2021.12.03] Algebraization theorems in complex and non-archimedean geometry qsms 2021.11.19 62
56 [QSMS 위상기하 세미나 2021.11.25] Exotic families of Weinstein manifolds with Milnor fibers of ADE types qsms 2021.11.19 47
55 [SNU Number Theory Seminiar 2021.11.12] Moduli of Fontaine-Laffailles and mod-p local-global compatibility file qsms 2021.10.29 96
54 [QSMS Monthly Seminar] Quantum entanglement entropy in abelian arithmetic Chern-Simons theory qsms 2021.10.29 69
53 [SNU Number Theory Seminiar 2021.11.05] Bianchi modular symbols and p-adic L-functions qsms 2021.10.20 75
52 [QSMS Seminar 2021.10.26, 10.28] Feigin-Semikhatov duality in W-superalgebras qsms 2021.10.13 148
» [2021 KMS Annual Meeting] Related talks qsms 2021.10.05 163
50 [QSMS Monthly Seminar] Smoothing of Fano varieties and mutations qsms 2021.09.23 116
49 [QSMS Seminar 2021.10.12, 10.14] Vertex algebras and chiral homology I and II qsms 2021.09.23 198
48 [QSMS Seminar 2021.09.30] Schur-Weyl duality, old and new & Quantum symmetric pairs and Schur-type dualities qsms 2021.09.10 308
47 [SNU Number Theory Seminiar] 2021.10.15 qsms 2021.09.09 134
46 [QSMS 기하/위상 세미나 2021.09.06] The mirror P=W conjecture from homological mirror symmetry of Fano manifolds qsms 2021.09.03 224
45 [SNU Number Theory Seminiar] 2021.10.08 qsms 2021.08.23 20399
44 [QSMS Seminar 2021.08.23, 08.24] Affine PBW bases and affine MV polytopes qsms 2021.08.17 313
43 [정수론 집중강연 2021.08.03, 08.05] Geometric approaches to the local Langlands correspondence I-IV qsms 2021.07.29 603
42 [사교위상 초청강연 2021.07.16] Categorical entropy and symplectic geometry qsms 2021.07.05 478
41 [QSMS Seminar 2021.07.02] Lefschetz fibrations on cotangent bundles qsms 2021.06.29 44129
40 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 631
39 [Seminar 2021.06.11] The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma qsms 2021.05.28 584
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