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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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(Reminder) [Cart-seminar, Hybrid] CART Seminar announcement (Donggun Lee, June 20 (Fri), 10:30AM)
by 오재성 19 Jun '25

19 Jun '25

Dear all, This is a gentle reminder of the CART seminar by Donggun Lee (Institute for Basic Science, CCG, Korea), on 10:30 - 11:30 am tomorrow. Hope to see you at the seminar! Best regards, Jaeseong Oh -----------------------원본 메세지----------------------- 보낸사람: "오재성"<jsoh(a)kias.re.kr> 받는사람: cart-seminar(a)snurep.crystalline.site, "All Members(all)" <all(a)kias.re.kr> 보낸날짜: 2025-06-03 11:46:35 GMT +0900 (Asia/Seoul)제목: [Cart-seminar, Hybrid] CART Seminar announcement (Donggun Lee, June 20 (Fri), 10:30AM) Dear all, The upcoming CART seminar is scheduled for June 20th (Fri), 10:30 - 11:30 (Korea time). Speaker: Donggun Lee (Institute for Basic Science, CCG, Korea) Venue: KIAS 1424 (hybrid, zoom link below) Title: Geometry of regular semisimple Lusztig varieties Abstract: Lusztig varieties were introduced in the study of character sheaves and related representation theory. They can be seen as variants of both Schubert varieties and Hessenberg varieties. For example, they admit a Weyl group action on their intersection cohomology through monodromy, and their singularities can be resolved via Bott-Samelson-type resolutions. I will present results on their geometry, including vanishing theorems for the cohomology of line bundles, their relations to Hessenberg varieties, and diffeomorphism types. Along the way, we also establish that their open cells are affine, and that the same is true for Deligne-Lusztig varieties, settling a question that has been open since the foundational paper of Deligne and Lusztig. Some of the results were motivated by our forthcoming study of the representations via a trace map of the Hecke algebra. Based on joint works with Patrick Brosnan and Jaehyun Hong. You can also join the seminar via the following Zoom link: https://us06web.zoom.us/j/81089968347?pwd=9eJFqalwC62aTBdEp4kVG305ifl0gH.1 Meeting ID: 810 8996 8347 Password: 799885 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, Jaeseong Oh

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(Reminder) CART Seminar announcement (Daniel Bump, May 23 (Fri), 9:00AM)
by 이신명 21 May '25

21 May '25

Dear all, This is a gentle reminder of the CART seminar by Daniel Bump (Stanford University) on 9:00 - 10:00 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: "All Members(all)" <all(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 보낸날짜: 2025-05-16 01:45:39 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Daniel Bump, May 23 (Fri), 9:00AM) Dear all, The upcoming CART seminar is scheduled for May 23rd (Fri), 9:00 - 10:00 (Korea time). Speaker: Daniel Bump (Stanford University, USA) Title: Solvable Lattice Models and Yang-Baxter Groupoids Abstract: We will review some applications of the Yang-Baxter equation to proving that certain partition functions represent functions of interest to combinatorialists such as Schur polynomials, Hall-Littlewood polynomials or Schubert polynomials. The underlying mechanism is the parametrized Yang-Baxter equation. Typically these are regarded as coming from quantum groups, and we will see how for the six-vertex model there is a contrast between the "free-fermionic" case relying on the quantum group U_q(sl(1|1)) and the non-free-fermionic case relying on U_q(sl(2)). A deeper look at the non-free-fermionic case leads to Naprienko's six-vertex groupoid. We will argue that groupoid parametrized Yang-Baxter equations may be common, and give another example of a groupoid parametrized Yang-Baxter equation in the five-vertex model. This talk will rely on joint work with Brubaker, Buciumas and Gustafsson, and with Naprienko. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82269442887?pwd=7DdbmNqDVY1SIjfoNzXBP3XBGarK5V.1 Meeting ID: 822 6944 2887 Password: 294582 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 (Daniel Bump, May 23 (Fri), 9:00AM)
by 이신명 16 May '25

16 May '25

Dear all, The upcoming CART seminar is scheduled for May 23rd (Fri), 9:00 - 10:00 (Korea time). Speaker: Daniel Bump (Stanford University, USA) Title: Solvable Lattice Models and Yang-Baxter Groupoids Abstract: We will review some applications of the Yang-Baxter equation to proving that certain partition functions represent functions of interest to combinatorialists such as Schur polynomials, Hall-Littlewood polynomials or Schubert polynomials. The underlying mechanism is the parametrized Yang-Baxter equation. Typically these are regarded as coming from quantum groups, and we will see how for the six-vertex model there is a contrast between the "free-fermionic" case relying on the quantum group U_q(sl(1|1)) and the non-free-fermionic case relying on U_q(sl(2)). A deeper look at the non-free-fermionic case leads to Naprienko's six-vertex groupoid. We will argue that groupoid parametrized Yang-Baxter equations may be common, and give another example of a groupoid parametrized Yang-Baxter equation in the five-vertex model. This talk will rely on joint work with Brubaker, Buciumas and Gustafsson, and with Naprienko. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82269442887?pwd=7DdbmNqDVY1SIjfoNzXBP3XBGarK5V.1 Meeting ID: 822 6944 2887 Password: 294582 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 (Soo-Hong Lee, May 2 (Fri), 10:30AM)
by 오재성 01 May '25

01 May '25

Dear all, The upcoming CART seminar is scheduled for May 2nd (Friday), 10:30 - 11:30 (Korea time). Speaker: Soo-Hong Lee (Seoul National University, Korea) Title: Infinite level Fock space, crystal bases, and tensor products of extremal weight modules of type A_+∞ Abstract: We construct an infinite-level Fock space that admits commuting actions of the quantized enveloping algebra of infinite affine type A_+∞ and the parabolic boson algebra associated with (gl_∞, gl_{∞\0}). This construction extends the classical Howe duality on higher-level Fock spaces. Its study revisits a subtle phenomenon in which the crystal base of a proper submodule coincides with that of the entire space — a behavior previously observed in level-zero representations of affine type by Kashiwara, Beck, and Nakajima. In the A+∞ type, we show that this combinatorial phenomenon is intricately tied to the socle filtration of ambient representations. Utilizing this connection, we construct a saturated crystal base through a limiting process and provide a comprehensive description of the socle filtration for extremal weight modules of type A+∞, recovering coefficients first obtained by Penkov and Styrkas. This is a joint work with Jae-Hoon Kwon. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/85728812852?pwd=mYaLjZSh5ZaPbNmXbExIuthHU4vFiW.1 Meeting ID: 857 2881 2852 Password: 537826 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, Jaeseong Oh

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CART Seminar announcement (Sean Griffin, Apr 18 (Fri), 04:00PM)
by 오재성 17 Apr '25

17 Apr '25

Dear all, The upcoming CART seminar is scheduled for April 18th (Friday), 16:00 - 17:00 (Korea time). Please notice the unusual time. Speaker: Sean Griffin (University of Vienna, Austria) Title: On Macdonald expansions of q-chromatic symmetric functions and the Stanley-Stembridge Conjecture Abstract: The Stanley-Stembridge conjecture asserts that the chromatic symmetric function of a (3+1)-free graph is e-positive, meaning that it expands positively in the elementary symmetric function basis. Motivated by a geometric construction of Kato, recently Hikita proved this conjecture by giving an explicit e-expansion of the Shareshian-Wachs q-chromatic refinement (or chromatic quasisymmetric function) for unit interval graphs. Using the A_{q,t} algebra of Carlsson and Mellit, we give an expansion of these q-chromatic symmetric functions into Macdonald polynomials. Upon setting t=1, we obtain another proof of the Stanley-Stembridge conjecture and rederive Hikita's formula. Upon setting t=0, we obtain an expansion into Hall-Littlewood symmetric functions. This is joint work with Mellit, Romero, Weigl, and Wen. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/81269364430?pwd=9vb0YlUq2fX31EFOV24YRGMoWlbQSa.1 Meeting ID: 812 6936 4430 Password: 159706 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, Jaeseong Oh

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