- Cart-seminar - snurep.crystalline.site

(Reminder) CART seminar announcement (Reuven Hodges, May 22 (Fri), 10:30AM)
by 이신명 21 May '26

21 May '26

Dear all, This is a gentle reminder of the CART seminar by Reuven Hodges (University of Kansas) tomorrow at 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Hope to see you at the seminar! Best regards, Sin-Myung Lee -----------------------원본 메세지----------------------- 보낸사람: "이신명"<sinmyunglee(a)kias.re.kr> 받는사람: "Mathematics Members(mathall)" <mathall(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 참조: "Hodges,Reuven Moses" <rmhodges(a)ku.edu> 보낸날짜: 2026-05-13 18:29:19 GMT +0900 (Asia/Seoul) 제목: CART seminar announcement (Reuven Hodges, May 22 (Fri), 10:30AM) Dear all, The next CART seminar is scheduled for May 22nd (Fri), 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Speaker: Reuven Hodges (University of Kansas) Title: Orbits structures and complexity in Schubert and Richardson varieties Abstract: The study of orbits and orbit closures in the flag variety has a long and storied history with deep connections to algebraic combinatorics, Lie theory, and representation theory. The orbits of Borel subgroups and their Zariski closures, the Schubert varieties, have been of particular import. A central notion in this area is the complexity of a reductive group action on a variety, which equals the minimum codimension of a Borel subgroup orbit. In this talk we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety by developing the notion of algebraic dimensions of Bruhat intervals. Then, when a Levi subgroup acts on a Schubert variety, we exhibit a codimension preserving bijection between the Levi-Borel subgroup orbits in the big open cell of that Schubert variety and the torus orbits in the big open cell of a distinguished Schubert subvariety. This allows us to give a type-uniform formula for the Levi-Borel complexity of that Schubert variety. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/82665363913?pwd=7PO3Wck3khxsA6asEIHalVcjYDQDKV… Meeting ID: 826 6536 3913 Password: 236303 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

CART seminar announcement (Reuven Hodges, May 22 (Fri), 10:30AM)
by 이신명 15 May '26

15 May '26

Dear all, The next CART seminar is scheduled for May 22nd (Fri), 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Speaker: Reuven Hodges (University of Kansas) Title: Orbits structures and complexity in Schubert and Richardson varieties Abstract: The study of orbits and orbit closures in the flag variety has a long and storied history with deep connections to algebraic combinatorics, Lie theory, and representation theory. The orbits of Borel subgroups and their Zariski closures, the Schubert varieties, have been of particular import. A central notion in this area is the complexity of a reductive group action on a variety, which equals the minimum codimension of a Borel subgroup orbit. In this talk we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety by developing the notion of algebraic dimensions of Bruhat intervals. Then, when a Levi subgroup acts on a Schubert variety, we exhibit a codimension preserving bijection between the Levi-Borel subgroup orbits in the big open cell of that Schubert variety and the torus orbits in the big open cell of a distinguished Schubert subvariety. This allows us to give a type-uniform formula for the Levi-Borel complexity of that Schubert variety. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/82665363913?pwd=7PO3Wck3khxsA6asEIHalVcjYDQDKV… Meeting ID: 826 6536 3913 Password: 236303 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

CART Seminar announcement (Aritra Bhattacharya, Apr 17 (Fri), 10:30AM)
by 이신명 16 Apr '26

16 Apr '26

Dear all, The next CART seminar is scheduled for Apr 17th (Fri), 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Speaker: Aritra Bhattacharya (Beijing International Center for Mathematical Research) Title: On factorization of matrix of Kazhdan-Lusztig polynomials Abstract: The famous Kazhdan-Lusztig positivity states that the transition matrix between the canonical basis and the standard basis of the Hecke algebra (of a Weyl group) is a matrix with polynomial entries with non-negative integer coefficients. In this talk we will describe a factorization of this positivity via certain intermediate bases called the hybrid bases. We will also present a reformulation of the statements in terms of a natural restriction map on Hecke algebras. This framework also subsumes the positivity of parabolic Kazhdan-Lusztig polynomials corresponding to the sign representations. This is joint work with Ashish Mishra and Shraddha Srivastava. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/89659176224?pwd=TLxuQ7yKEqgGCnnBb6NxDE8z20J6lM… Meeting ID: 896 5917 6224 Password: 947850 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 1

Workshop announcement: Diagrammatics for Combinatorics, Algebra, and Topology (Jul 20-24, SKKU)
by 이신명 06 Apr '26

06 Apr '26

Dear colleagues, This is Sin-Myung Lee at KIAS. I hope this email finds you well. Jaeseong and I are very happy to announce the upcoming workshop "Diagrammatics for combinatorics, algebra and topology", which will be held at Sungkyunkwan university (Natural Sciences campus), Suwon, from this July 20(Mon) to 24(Fri). The central theme of the workshop is diagrammatic calculus and its applications in combinatorics, algebra, and topology. In particular, we aim to foster informal exchanges beyond the lectures, creating a space for participants to actively explore these growing fields, from basics to practical applications. Here is the list of invited speakers: Lecture series (3*1h) Ben Elias (University of Oregon) Matthew Hogancamp (Northeastern University) Linhui Shen (Michigan State University) Research talk Elise Catania (University of Minnesota - Twin Cities) Donghyun Kim (Ewha Womans University) Myungho Kim (Kyung Hee University) Hankyung Ko (Uppsala University) Mikhail Mazin (Kensas State University) Nathan Williams (University of Texas at Dallas) More information is (and will be) available on the workshop website: https://sites.google.com/view/dcat2026 If you plan on attending, please register by June 5 to stay updated and help us prepare the workshop smoothly. We would appreciate it if you could share this announcement with anyone who might be interested. We are looking forward to your participation! Best regards, Sin-Myung Lee Jaeseong Oh

1 0

(Reminder) CART seminar announcement (Heizo Sakamoto, Apr 3 (Fri), 10:30AM)
by 이신명 01 Apr '26

01 Apr '26

Dear all, This is a gentle reminder of the CART seminar by Heizo Sakamoto (The University of Tokyo) tomorrow at 10:30 - 11:30 (in Korea time). Hope to see you at the seminar! Best regards, Sin-Myung Lee -----------------------원본 메세지----------------------- 보낸사람: "이신명"<sinmyunglee(a)kias.re.kr> 받는사람: "Mathematics Members(mathall)" <mathall(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 보낸날짜: 2026-03-26 03:12:12 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Heizo Sakamoto, Apr 3 (Fri), 10:30AM) Dear all, The next CART seminar is scheduled for Apr 3rd (Fri), 10:30 - 11:30 (Korea time). Speaker: Heizo Sakamoto (The University of Tokyo) Title: Classification of real and imaginary modules of quantum affine algebras in monoidal categorifications of affine cluster algebras Abstract: A finite-dimensional module $L$ over an affine quantum group is called real if the tensor product $L \otimes L$ is irreducible. It is known that for an appropriately chosen subcategory $\mathcal{C}$ of the category of finite-dimensional representations, the Grothendieck ring $K(\mathcal{C})$ has a cluster algebra structure in which cluster monomials correspond to irreducible modules (categorification of cluster algebras).In such a category $\mathcal{C}$, Hernandez-Leclerc conjectured that an irreducible module corresponds to a cluster monomial if and only if it is a real module. This conjecture remains generally open, except for cases where the categorified cluster algebra is of finite type. In this talk, I will construct subcategories that categorify cluster algebras of affine type and explain that the conjecture holds within these categories. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/86178377083?pwd=znH3EbxqjXmDCiVnv4OTl3SgJHlxva… Meeting ID: 861 7837 7083 Password: 172764 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

CART Seminar announcement (Heizo Sakamoto, Apr 3 (Fri), 10:30AM)
by 이신명 26 Mar '26

26 Mar '26

Dear all, The next CART seminar is scheduled for Apr 3rd (Fri), 10:30 - 11:30 (Korea time). Speaker: Heizo Sakamoto (The University of Tokyo) Title: Classification of real and imaginary modules of quantum affine algebras in monoidal categorifications of affine cluster algebras Abstract: A finite-dimensional module $L$ over an affine quantum group is called real if the tensor product $L \otimes L$ is irreducible. It is known that for an appropriately chosen subcategory $\mathcal{C}$ of the category of finite-dimensional representations, the Grothendieck ring $K(\mathcal{C})$ has a cluster algebra structure in which cluster monomials correspond to irreducible modules (categorification of cluster algebras).In such a category $\mathcal{C}$, Hernandez-Leclerc conjectured that an irreducible module corresponds to a cluster monomial if and only if it is a real module. This conjecture remains generally open, except for cases where the categorified cluster algebra is of finite type. In this talk, I will construct subcategories that categorify cluster algebras of affine type and explain that the conjecture holds within these categories. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/86178377083?pwd=znH3EbxqjXmDCiVnv4OTl3SgJHlxva… Meeting ID: 861 7837 7083 Password: 172764 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

(Reminder) CART Seminar announcement (Jihyeug Jang, Mar 20 (Fri), 4:30PM)
by 이신명 18 Mar '26

18 Mar '26

Dear all, This is a gentle reminder of the CART seminar by Jihyeug Jang (University of Geneva) tomorrow at the unusual time 16:30 - 17:30 (in Korea time). Hope to see you at the seminar! Best regards, Sin-Myung Lee -----------------------원본 메세지----------------------- 보낸사람: "이신명"<sinmyunglee(a)kias.re.kr> 받는사람: "Mathematics Members(mathall)" <mathall(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 참조: jihyeugjang(a)gmail.com 보낸날짜: 2026-03-12 21:33:38 GMT +0900 (Asia/Seoul) 제목: CART Seminar announcement (Jihyeug Jang, Mar 20 (Fri), 4:30PM) Dear all, The next CART seminar is scheduled for Mar 20th (Fri), 16:30 - 17:30 (Korea time). Note the unusual time! Speaker: Jihyeug Jang (University of Geneva) Title: Grounded partitions Abstract: In this talk, I will discuss partition identities arising from affine Lie algebras. A classical example is provided by the Rogers--Ramanujan identities: Lepowsky and Wilson, building on earlier work of Lepowsky and Milne, gave a representation-theoretic proof of these identities. In particular, the product side arises from the principal specialisation of the Weyl--Kac character formula for highest weight modules of type A_1^{(1)} at level 3. I will then turn to grounded partitions, combinatorial objects introduced by Dousse and Konan, motivated by the theory of perfect crystals developed by Kang, Kashiwara, Misra, Miwa, Nakashima, and Nakayashiki. While grounded partitions were originally introduced from the crystal-theoretic viewpoint, we instead take the reverse perspective: we use grounded partitions to describe the structure of the affine crystal of type A_1^{(1)} at level 2. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/88942840816?pwd=45KKaHbQadH1wIjY8UI5WnYWbDz1po… Meeting ID: 889 4284 0816 Password: 123063 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

CART Seminar announcement (Jihyeug Jang, Mar 20 (Fri), 4:30PM)
by 이신명 12 Mar '26

12 Mar '26

Dear all, The next CART seminar is scheduled for Mar 20th (Fri), 16:30 - 17:30 (Korea time). Note the unusual time! Speaker: Jihyeug Jang (University of Geneva) Title: Grounded partitions Abstract: In this talk, I will discuss partition identities arising from affine Lie algebras. A classical example is provided by the Rogers--Ramanujan identities: Lepowsky and Wilson, building on earlier work of Lepowsky and Milne, gave a representation-theoretic proof of these identities. In particular, the product side arises from the principal specialisation of the Weyl--Kac character formula for highest weight modules of type A_1^{(1)} at level 3. I will then turn to grounded partitions, combinatorial objects introduced by Dousse and Konan, motivated by the theory of perfect crystals developed by Kang, Kashiwara, Misra, Miwa, Nakashima, and Nakayashiki. While grounded partitions were originally introduced from the crystal-theoretic viewpoint, we instead take the reverse perspective: we use grounded partitions to describe the structure of the affine crystal of type A_1^{(1)} at level 2. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/88942840816?pwd=45KKaHbQadH1wIjY8UI5WnYWbDz1po… Meeting ID: 889 4284 0816 Password: 123063 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

Re: CART Seminar announcement (Ole Warnaar, Mar 6 (Fri), 10:30AM)
by 이신명 05 Mar '26

05 Mar '26

Dear all, This is a gentle reminder of the CART seminar by Ole Warnaar (The University of Queensland) on 10:30 - 11:30 tomorrow (in Korea time). Hope to see you at the seminar! Best regards, Sin-Myung Lee -----------------------원본 메세지----------------------- 보낸사람: "이신명"<sinmyunglee(a)kias.re.kr> 받는사람: "이신명" <sinmyunglee(a)kias.re.kr> 참조: "Ole Warnaar" <o.warnaar(a)maths.uq.edu.au> 보낸날짜: 2026-02-26 17:04:31 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Ole Warnaar, Mar 6 (Fri), 10:30AM) Dear all, This semester's first CART seminar is scheduled for Mar 6th (Fri), 10:30 - 11:30 (Korea time). Speaker: Ole Warnaar (The University of Queensland) Title: Hall--Littlewood symmetric functions and the Rogers--Ramanujan identities Abstract: Thanks to the groundbreaking work of Lepowsky, Milne and Primc in the late 1970s and early 1980s it is well understood that the celebrated Rogers--Ramanujan identities are related to the level-$3$ standard modules of the affine Lie algebra $\mathrm{A}_1^{(1)}$. This poses the natural question if Rogers--Ramanujan-type identities exist for arbitrary standard modules of affine Lie algebras. In this talk I will explain how ideas from symmetric function theory may shed some light on this question, which is very open despite recent advances. No prior knowledge of the representation theory of affine Lie algebras will be assumed in this talk. You can join the seminar via the following Zoom link: https://skku-edu.zoom.us/j/83228018171?pwd=03VlbsfaHsxD5jJLpKDbNS3Mb6QQVg.1 Meeting ID: 832 2801 8171 Password: 336194 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0

CART Seminar announcement (Ole Warnaar, Mar 6 (Fri), 10:30AM)
by 이신명 26 Feb '26

26 Feb '26

Dear all, This semester's first CART seminar is scheduled for Mar 6th (Fri), 10:30 - 11:30 (Korea time). Speaker: Ole Warnaar (The University of Queensland) Title: Hall--Littlewood symmetric functions and the Rogers--Ramanujan identities Abstract: Thanks to the groundbreaking work of Lepowsky, Milne and Primc in the late 1970s and early 1980s it is well understood that the celebrated Rogers--Ramanujan identities are related to the level-$3$ standard modules of the affine Lie algebra $\mathrm{A}_1^{(1)}$. This poses the natural question if Rogers--Ramanujan-type identities exist for arbitrary standard modules of affine Lie algebras. In this talk I will explain how ideas from symmetric function theory may shed some light on this question, which is very open despite recent advances. No prior knowledge of the representation theory of affine Lie algebras will be assumed in this talk. You can join the seminar via the following Zoom link: https://skku-edu.zoom.us/j/83228018171?pwd=03VlbsfaHsxD5jJLpKDbNS3Mb6QQVg.1 Meeting ID: 832 2801 8171 Password: 336194 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

1 0