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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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(Remind) CART Seminar announcement (Serena An and Katherine Tung, Apr 3 (Thu), 10:30AM)
by 오재성 02 Apr '25

02 Apr '25

Dear all, This is a gentle reminder of the CART seminar by Serena An (Massachusetts Institute of Technology) and Katherine Tung (Harvard University) on 10:30 - 11:30 am tomorrow (in Korea time). Hope to see you at the seminar! Best regards, Jaeseong Oh -----------------------원본 메세지----------------------- 보낸사람: "오재성"<jsoh(a)kias.re.kr> 받는사람: "All Members(all)" <all(a)kias.re.kr> 참조: cart-seminar(a)snurep.crystalline.site, anser(a)mit.edu, katherinetung(a)college.harvard.edu 보낸날짜: 2025-03-27 21:53:47 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Serena An and Katherine Tung, Apr 3 (Thu), 10:30AM) Dear all, The upcoming CART seminar is scheduled for April 3rd (Thursday), 10:30 - 11:30 (Korea time). Speaker: Serena An (Massachusetts Institute of Technology, USA) and Katherine Tung (Harvard University, USA) Title: Postnikov–Stanley polynomials are Lorentzian Abstract: The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, Mészáros, and St. Dizier in 2022. We give an alternative, elementary proof of this result, explicitly characterize the Newton polytopes of dual Schubert polynomials, and provide a polynomial-time algorithm for determining if a dual Schubert polynomial coefficient vanishes. We furthermore generalize the M-convexity result by showing that Postnikov–Stanley polynomials, also called skew dual Schubert polynomials, are Lorentzian. This work is joint with Yuchong Zhang and is contained in papers arXiv:2411.16654 and arXiv:2412.02051. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/86248755466?pwd=J0AVcWEKab1siO8KQ4yeXQgFkKJyqo.1 Meeting ID: 862 4875 5466 Password: 673602 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 (Serena An and Katherine Tung, Apr 3 (Thu), 10:30AM)
by 오재성 27 Mar '25

27 Mar '25

Dear all, The upcoming CART seminar is scheduled for April 3rd (Thursday), 10:30 - 11:30 (Korea time). Speaker: Serena An (Massachusetts Institute of Technology, USA) and Katherine Tung (Harvard University, USA) Title: Postnikov–Stanley polynomials are Lorentzian Abstract: The M-convexity of dual Schubert polynomials was first proven by Huh, Matherne, Mészáros, and St. Dizier in 2022. We give an alternative, elementary proof of this result, explicitly characterize the Newton polytopes of dual Schubert polynomials, and provide a polynomial-time algorithm for determining if a dual Schubert polynomial coefficient vanishes. We furthermore generalize the M-convexity result by showing that Postnikov–Stanley polynomials, also called skew dual Schubert polynomials, are Lorentzian. This work is joint with Yuchong Zhang and is contained in papers arXiv:2411.16654 and arXiv:2412.02051. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/86248755466?pwd=J0AVcWEKab1siO8KQ4yeXQgFkKJyqo.1 Meeting ID: 862 4875 5466 Password: 673602 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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(Remind) CART Seminar announcement (Kang Lu, Mar 28 (Fri), 10:00AM)
by 이신명 27 Mar '25

27 Mar '25

Dear all, This is a gentle reminder of the CART seminar by Kang Lu (University of Virginia) on 10:00 - 11:00 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: "Mathematics Members(mathall)" <mathall(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 참조: "Lu,Kang (wbt4qn)" <kang.lu(a)virginia.edu> 보낸날짜: 2025-03-21 23:36:39 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Kang Lu, Mar 28 (Fri), 10:00AM) Dear all, The upcoming CART seminar is scheduled for March 28th (Friday), 10:00 - 11:00 (Korea time). Speaker: Kang Lu (University of Virginia, USA) Title: A Drinfeld presentation of twisted Yangians and applications Abstract: Twisted Yangians were first introduced in R-matrix presentation by Olshanski in 1990 in connections with classical Lie algebras and more generally by Molev-Ragoucy and Guay-Regelskis associated with symmetric pairs of classical type. A Drinfeld type current presentation of (quasi-)split twisted Yangians has been recently obtained in two different approaches, and in this talk we will explain the Gauss decomposition approach. Then we shall outline ongoing work on generalizations and applications of the Drinfeld presentation. This is based on joint work of Weiqiang Wang, Weinan Zhang and collaborators. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/87862623868?pwd=9Loka6Gl9GUjIulSk3o287ctcWmGba.1 Meeting ID: 878 6262 3868 Password: 753940 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 (Kang Lu, Mar 28 (Fri), 10:00AM)
by 이신명 21 Mar '25

21 Mar '25

Dear all, The upcoming CART seminar is scheduled for March 28th (Friday), 10:00 - 11:00 (Korea time). Speaker: Kang Lu (University of Virginia, USA) Title: A Drinfeld presentation of twisted Yangians and applications Abstract: Twisted Yangians were first introduced in R-matrix presentation by Olshanski in 1990 in connections with classical Lie algebras and more generally by Molev-Ragoucy and Guay-Regelskis associated with symmetric pairs of classical type. A Drinfeld type current presentation of (quasi-)split twisted Yangians has been recently obtained in two different approaches, and in this talk we will explain the Gauss decomposition approach. Then we shall outline ongoing work on generalizations and applications of the Drinfeld presentation. This is based on joint work of Weiqiang Wang, Weinan Zhang and collaborators. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/87862623868?pwd=9Loka6Gl9GUjIulSk3o287ctcWmGba.1 Meeting ID: 878 6262 3868 Password: 753940 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 (Christian Gaetz, Mar 14 (Fri), 10:30AM)
by 오재성 13 Mar '25

13 Mar '25

Dear all, This is a gentle reminder of the CART seminar by Christian Gaets (University of California, Berkeley), on 10:30 - 11:30 am tomorrow. Hope to see you at the seminar! Best regards, Jaeseong Oh ---------------------------------------------- Dear all, The upcoming CART seminar is scheduled on March 14th (Friday), 10:30 - 11:30 (Korea time). Speaker: Christian Gaets (University of California, Berkeley) Title: Hypercube decompositions and combinatorial invariance for Kazhdan-Lusztig polynomials Abstract: Kazhdan-Lusztig polynomials are of foundational importance in geometric representation theory. Yet the Combinatorial Invariance Conjecture, due to Lusztig and to Dyer, suggests that they only depend on the combinatorics of Bruhat order. I'll describe joint work with Grant Barkley in which we adapt the hypercube decompositions introduced by Blundell-Buesing-Davies-Veličković-Williamson to prove this conjecture for Kazhdan-Lusztig R-polynomials in the case of elementary intervals in the symmetric group. This significantly generalizes the main previously known case of the conjecture, that of lower intervals. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/83754139506?pwd=zzWTu3fgXbInC8EYagJzQfUaPo3J9n.1 Meeting ID: 837 5413 9506 Passcode: 800099 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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