- Cart-seminar - snurep.crystalline.site

CART seminar announcement (Andrew Hardt, Sep 18 (Fri), 10:00AM)
by 이신명 17 Sep '26

17 Sep '26

Dear all, The next CART seminar is scheduled for Sep. 18 (Fri), 10:00-11:00 in Korea time (9:00-10:00 in Beijing). Speaker: Andrew Hardt (Towson University, USA) Title: GL-multiplicities of type A quiver loci Abstract: The space of representations of a quiver admits an orbit structure via change of basis. When the quiver is type A, the orbit closures are described by rank conditions. These varieties generalize classical degeneracy loci. Their equations are understood through work of Zelevinsky and Kinser–Rajchgot, and their cohomology classes and K-polynomials have been computed by many authors, including Buch–Fulton, Knutson–Miller–Shimozono, Buch–Rimányi and Kinser–Knutson–Rajchgot. The coordinate ring of a quiver orbit closure is a rational representation of a product of general linear groups. In the special case of varieties of complexes, its irreducible decomposition is implicit in work of De Concini and Strickland. In joint work with Ian Cavey and Alexander Yong, we give a positive combinatorial rule for this decomposition, valid for all type A orbit closures in every orientation. Our rule is in terms of nonnegative integer matrices satisfying admissibility conditions corresponding to the rank conditions of the orbit closure. We put a crystal structure on these matrices, using the combinatorics of Stembridge's rational tableaux, and the irreducible multiplicities are counted by the highest weight admissible matrices. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/86352829715?pwd=KBrb6UvVv1myhwDmE7Xm59UUGsyKia… Meeting ID: 863 5282 9715 Password: 264696 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 (Rui Xiong, Sep 11 (Fri), 10:00AM)
by 이신명 10 Sep '26

10 Sep '26

Dear all, This is a gentle reminder of the CART seminar by Rui Xiong (University of Michigan) tomorrow at 10:00-11:00 in Korea time (9:00 - 10:00 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: rxion043(a)uOttawa.ca 보낸날짜: 2026-09-06 20:38:47 GMT +0900 (Asia/Seoul)제목: CART seminar announcement (Rui Xiong, Sep 11 (Fri), 10:00AM) Dear all, We resume our CART seminar, whose first talk is scheduled for Sep. 11 (Fri), 10:00-11:00 in Korea time (9:00-10:00 in Beijing). Speaker: Rui Xiong (University of Michigan, USA) Title: A Proof of Butler's Positivity Conjecture Abstract: In this talk, I will present our recent proof of Butler's Schur positivity conjecture for Macdonald intersection polynomials (arXiv: 2608.11543). The proof uses the geometry of the Hilbert scheme of points in the affine plane. This is joint work with Peter Guo and Mingyang Kang. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/83006661943?pwd=0ZeKWRUD2KnGdjROgueVh2hqzXZjAk… Meeting ID: 830 0666 1943 Password: 603397 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 (Rui Xiong, Sep 11 (Fri), 10:00AM)
by 이신명 06 Sep '26

06 Sep '26

Dear all, We resume our CART seminar, whose first talk is scheduled for Sep. 11 (Fri), 10:00-11:00 in Korea time (9:00-10:00 in Beijing). Speaker: Rui Xiong (University of Michigan, USA) Title: A Proof of Butler's Positivity Conjecture Abstract: In this talk, I will present our recent proof of Butler's Schur positivity conjecture for Macdonald intersection polynomials (arXiv: 2608.11543). The proof uses the geometry of the Hilbert scheme of points in the affine plane. This is joint work with Peter Guo and Mingyang Kang. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/83006661943?pwd=0ZeKWRUD2KnGdjROgueVh2hqzXZjAk… Meeting ID: 830 0666 1943 Password: 603397 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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(Program updated) Workshop: Diagrammatics for Combinatorics, Algebra, and Topology (Jul 20-24, SKKU)
by 이신명 24 Jun '26

24 Jun '26

Dear colleagues, Hello, it is Sin-Myung Lee from KIAS. This is the second announcement of the upcoming workshop "Diagrammatics for Combinatorics, Algebra, and Topology" on July 20-24, held at Sungkyunkwan University, Suwon. The workshop is intended to provide an open, accessible space to learn and discuss diagrammatic methods in combinatorics, algebra and topology, welcoming everyone from students to working mathematicians. To this end, the workshop will begin with three lecture series (3 hours each plus exercise sessions) covering the following keywords: Ben Elias (University of Oregon) : Soergel bimodules and their diagrammatics Matthew Hogancamp (Northeastern University)* : link invariants, categorification of braid groups Linhui Shen (Michigan State University)* : braid varieties, cluster structures via weaves, connections with Legendrian knots and representations (*:subject to change, title and abstract will be updated on the website shortly) and then conclude with six research talks for more recent developments, delivered by 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). whose titles and abstracts can be found from our website: https://sites.google.com/view/dcat2026/home If you are interested, kindly register from https://sites.google.com/view/dcat2026/registration before June ends to stay updated and help us prepare the workshop smoothly. Please feel free to forward this announcement to anyone who might be interested, especially to students. We are looking forward to your participation! Best regards, Sin-Myung Lee Jaeseong Oh

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(Reminder) CART seminar announcement (Grigori Olshanski, Jun 12 (Fri), 16:30PM)
by 이신명 11 Jun '26

11 Jun '26

Dear all, This is a gentle reminder of the CART seminar by Grigori Olshanski (HSE University) tomorrow at 16:30 - 17:30 in Korea time (15:30 - 16:30 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: "Grigori Olshanski" <olsh2007(a)gmail.com>, "Cesar Cuenca" <cesar.a.cuenk(a)gmail.com> 보낸날짜: 2026-06-07 20:59:54 GMT +0900 (Asia/Seoul)제목: CART seminar announcement (Grigori Olshanski, Jun 12 (Fri), 16:30PM) Dear all, The last CART seminar of this semester is scheduled for June 12th (Fri), at the unusual time 16:30 - 17:30 in Korea time (15:30 - 16:30 in Beijing). Speaker: Grigori Olshanski (HSE University) Title: Infinite-dimensional groups over finite fields and a related positivity problem in symmetric function theory Abstract: Sergei Kerov and Anatoly Vershik discovered a remarkable family of infinite-dimensional matrix groups over finite fields. These groups are locally compact, totally disconnected and bear some resemblance with reductive p-adic groups. The study of these infinite-dimensional groups and their representations is in the beginning stages. However, there are a number of promising results and a lot of intriguing open problems, some of which admit a reformulation in the language of symmetric functions. I will present an introduction to this area. The talk is based on joint work with Cesar Cuenca. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/82020074666?pwd=zTWOBlcmPxFYpcRfObhMqXPfCai7Xm… ID: 820 2007 4666 password: 764471 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 (Grigori Olshanski, Jun 12 (Fri), 16:30PM)
by 이신명 07 Jun '26

07 Jun '26

Dear all, The last CART seminar of this semester is scheduled for June 12th (Fri), at the unusual time 16:30 - 17:30 in Korea time (15:30 - 16:30 in Beijing). Speaker: Grigori Olshanski (HSE University) Title: Infinite-dimensional groups over finite fields and a related positivity problem in symmetric function theory Abstract: Sergei Kerov and Anatoly Vershik discovered a remarkable family of infinite-dimensional matrix groups over finite fields. These groups are locally compact, totally disconnected and bear some resemblance with reductive p-adic groups. The study of these infinite-dimensional groups and their representations is in the beginning stages. However, there are a number of promising results and a lot of intriguing open problems, some of which admit a reformulation in the language of symmetric functions. I will present an introduction to this area. The talk is based on joint work with Cesar Cuenca. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/82020074666?pwd=zTWOBlcmPxFYpcRfObhMqXPfCai7Xm… ID: 820 2007 4666 password: 764471 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 (Soyeon Kim, Jun 5 (Fri), 10:30AM)
by 이신명 03 Jun '26

03 Jun '26

Dear all, This is a gentle reminder of the CART seminar by Soyeon Kim (UC Davis) 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: syxkim(a)math.ucdavis.edu 보낸날짜: 2026-05-26 22:59:38 GMT +0900 (Asia/Seoul) 제목: CART seminar announcement (Soyeon Kim, Jun 5 (Fri), 10:30AM) Dear all, The next CART seminar is scheduled for June 5th (Fri), 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Speaker: Soyeon Kim (UC Davis) Title: Unexpected toric Richardson varieties Abstract: In this talk, we introduce a new class of toric Richardson varieties, which we call unexpected toric Richardson varieties. These Richardson varieties are toric varieties with respect to the action of a torus of higher dimension (compared to the standard torus case), whose torus action was previously completely unexplored. The standard torus action on Richardson varieties and a characterization of (expected) toric Richardsons with respect to the standard torus were well understood. The existence of such unexpected toric Richardsons were implied by our characterization result for all toric Richardson varieties: the open Richardson variety $R_{v,w}$ in the complete flag variety is a torus $\mathbb{T}$ if and only if the closed Richardson variety $\overline{R}_{v,w}$ is a toric variety with respect to $\mathbb{T}$. Equivalently, this can be said that when the Bruhat interval $[ v , w ] $ is a lattice. Moreover, we prove that similar to the standard torus case, the moment polytopes for all toric Richardson varieties have a nice combinatorial description in terms of Bruhat interval. This is based on my joint work with Eugene Gorsky and Melissa Sherman-Bennett. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/86733679216?pwd=K7Nm3op6PSzkL4PRDtyKiKSavdIayw… ID: 867 3367 9216 password: 067888 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 (Soyeon Kim, Jun 5 (Fri), 10:30AM)
by 이신명 29 May '26

29 May '26

Dear all, The next CART seminar is scheduled for June 5th (Fri), 10:30 - 11:30 in Korea time (9:30 - 10:30 in Beijing). Speaker: Soyeon Kim (UC Davis) Title: Unexpected toric Richardson varieties Abstract: In this talk, we introduce a new class of toric Richardson varieties, which we call unexpected toric Richardson varieties. These Richardson varieties are toric varieties with respect to the action of a torus of higher dimension (compared to the standard torus case), whose torus action was previously completely unexplored. The standard torus action on Richardson varieties and a characterization of (expected) toric Richardsons with respect to the standard torus were well understood. The existence of such unexpected toric Richardsons were implied by our characterization result for all toric Richardson varieties: the open Richardson variety $R_{v,w}$ in the complete flag variety is a torus $\mathbb{T}$ if and only if the closed Richardson variety $\overline{R}_{v,w}$ is a toric variety with respect to $\mathbb{T}$. Equivalently, this can be said that when the Bruhat interval $[ v , w ] $ is a lattice. Moreover, we prove that similar to the standard torus case, the moment polytopes for all toric Richardson varieties have a nice combinatorial description in terms of Bruhat interval. This is based on my joint work with Eugene Gorsky and Melissa Sherman-Bennett. You can join the seminar via the following Zoom link: https://kias-re-kr.zoom.us/j/86733679216?pwd=K7Nm3op6PSzkL4PRDtyKiKSavdIayw… ID: 867 3367 9216 password: 067888 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 (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

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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

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