- Cart-seminar - snurep.crystalline.site

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

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(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

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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

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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

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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

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(Reminder) CART Seminar announcement (Hong Chen, Nov 27 (Thu), 10:30AM)
by 이신명 25 Nov '25

25 Nov '25

Dear all, This is a gentle reminder of the CART seminar by Hong Chen (Rutgers University) 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: "Hong Chen" <hc813(a)math.rutgers.edu> 보낸날짜: 2025-11-20 09:33:56 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Hong Chen, Nov 27 (Thu), 10:30AM) Dear all, The next CART seminar is scheduled for Nov 27th (Thu), 10:30 - 11:30 (Korea time). Speaker: Hong Chen (Rutgers University) Title: Partial orders on partitions and positivity on symmetric functions Abstract: Among partitions, three natural partial orders frequently arise: containment, dominance, and weak dominance. Interpreted on Young diagrams, these correspond respectively to removing boxes, lowering boxes, or allowing both operations. Symmetric functions exhibit two fundamental types of positivity: evaluation positivity and expansion positivity. Work of Cuttler–Greene–Skandera, Sra, and Khare–Tao established a duality between (weak) dominance and evaluation positivity for Schur polynomials. In recent work, we proved an analogous duality between the containment order and expansion positivity for Schur polynomials. Moreover, this result extends to the setting of Jack polynomials, and we further conjectured (and proved several cases of) the natural Jack generalization corresponding to the dominance order. This is joint work with Siddhartha Sahi and Apoorva Khare. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/89964724793?pwd=kq1faVNOZbtSO1Gyt8osJHmzAoKUsQ.1 Meeting ID: 899 6472 4793 Password: 076577 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

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CART Seminar announcement (Hong Chen, Nov 27 (Thu), 10:30AM)
by 이신명 20 Nov '25

20 Nov '25

Dear all, The next CART seminar is scheduled for Nov 27th (Thu), 10:30 - 11:30 (Korea time). Speaker: Hong Chen (Rutgers University) Title: Partial orders on partitions and positivity on symmetric functions Abstract: Among partitions, three natural partial orders frequently arise: containment, dominance, and weak dominance. Interpreted on Young diagrams, these correspond respectively to removing boxes, lowering boxes, or allowing both operations. Symmetric functions exhibit two fundamental types of positivity: evaluation positivity and expansion positivity. Work of Cuttler–Greene–Skandera, Sra, and Khare–Tao established a duality between (weak) dominance and evaluation positivity for Schur polynomials. In recent work, we proved an analogous duality between the containment order and expansion positivity for Schur polynomials. Moreover, this result extends to the setting of Jack polynomials, and we further conjectured (and proved several cases of) the natural Jack generalization corresponding to the dominance order. This is joint work with Siddhartha Sahi and Apoorva Khare. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/89964724793?pwd=kq1faVNOZbtSO1Gyt8osJHmzAoKUsQ.1 Meeting ID: 899 6472 4793 Password: 076577 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

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Joint VISGAT/CART seminar (Dr Veronica Kelsey, Manchester)
by Nyberg Brodda CarlFredrik 19 Oct '25

19 Oct '25

Dear visgat & CART subscribers, We are happy to announce that we will be holding a joint visgat/CART seminar on Oct 22nd, 2025 (Wed), 11:00 am - 12:00pm virtually and via Zoom. The seminar will be given by Veronica Kelsey (University of Manchester). The details are below: --- Date: Oct 22nd, 2025 (Wed) Time: 11:00am - 12:00pm Location: KIAS 1424 Zoom hybrid : https://kimsh.kr/vz Title: Irredundant bases of permutation groups Abstract: A base of a group $G \leq \mathrm{Sym}(Omega)$ is a sequence $\Lambda$ of points in $\Omega$ such that the identity is the only element of $G$ fixing $\Lambda$ pointwise. The size of the smallest base is denoted $\mathrm{b}(G, \Omega)$. The study of bases dates back to the 19th century but perhaps their most important use has been in computational group theory. There is a large computational saving when $|\Lambda|<<|\Omega|$, and so we’d ideally like to know $\mathrm{b}(G, \Omega)$. Sadly there is no known efficient algorithm for finding these minimal bases, and Blaha showed in 1992 that determining $\mathrm{b}(G,\Omega) \leq c$ for a given constant $c$ is NP-complete. Instead we consider irredundant bases which can be thought of as the “best worst case”. In this talk I will introduce all these concepts along with examples and discuss some of the recent work in this area. --- After the seminar, we will head for lunch together. We would appreciate your interest! Best wishes, Carl-Fredrik Nyberg-Brodda

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(Reminder) CART Seminar announcement (Hunter Spink, Sep 11 (Thu), 10:30AM)
by 이신명 10 Sep '25

10 Sep '25

Dear all, This is a gentle reminder of the CART seminar by Hunter Spink (University of Toronto) on 10:30 - 11:30 am 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> 보낸날짜: 2025-09-03 21:47:12 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Hunter Spink, Sep 11 (Thu), 10:30AM) Dear all, The CART seminar is coming back, with the first talk scheduled for Sep 11th (Thu), 10:30 - 11:30 (Korea time). [Note: this fall we plan to organize most of our seminars on Thursdays!] We will welcome Hunter Spink from University of Toronto, who will tell us about: Title: The Coxeter flag variety: A toric complex on noncrossing partitions paved by clusters Abstract: (Joint with Nantel Bergeron, Lucas Gagnon, and Vasu Tewari) In this talk I will introduce a new toric complex we call the "Coxeter flag variety" in G/B, defined as the vanishing of Plucker coordinates away from the subset of the Weyl group called the "c-noncrossing partitions" for c a standard Coxeter element. The combinatorics of this variety encodes the geometry of certain Richardson varieties R_{w,wc}, each of which has a distinguished affine chart whose characters correspond to positive clusters. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82283035487?pwd=r25KFTmr0hhVNKjvqUjHPvyTL6mVaN.1 ID: 822 8303 5487 password: 395575 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

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CART Seminar announcement (Hunter Spink, Sep 11 (Thu), 10:30AM)
by 이신명 03 Sep '25

03 Sep '25

Dear all, The CART seminar is coming back, with the first talk scheduled for Sep 11th (Thu), 10:30 - 11:30 (Korea time). [Note: this fall we plan to organize most of our seminars on Thursdays!] We will welcome Hunter Spink from University of Toronto, who will tell us about: Title: The Coxeter flag variety: A toric complex on noncrossing partitions paved by clusters Abstract: (Joint with Nantel Bergeron, Lucas Gagnon, and Vasu Tewari) In this talk I will introduce a new toric complex we call the "Coxeter flag variety" in G/B, defined as the vanishing of Plucker coordinates away from the subset of the Weyl group called the "c-noncrossing partitions" for c a standard Coxeter element. The combinatorics of this variety encodes the geometry of certain Richardson varieties R_{w,wc}, each of which has a distinguished affine chart whose characters correspond to positive clusters. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82283035487?pwd=r25KFTmr0hhVNKjvqUjHPvyTL6mVaN.1 ID: 822 8303 5487 password: 395575 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

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