April 2025 - Cart-seminar - snurep.crystalline.site

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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