seminars:comb:start
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seminars:comb:start [2025/09/30 23:46] zaslav [FALL 2025] |
seminars:comb:start [2025/10/30 00:28] (current) zaslav [FALL 2025] |
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| - | Anticipated speakers: Daniel Slilaty (Wright State), Lee Kennard (Syracuse), Marwa Mosallam (Binghamton), Margaret Readdy (Kentucky), Richard Ehrenborg (Kentucky), Rigoberto Florez (The Citadel), Ernesto Estrada (Campus Universitat Illes Balears), Aida Abaid (Amsterdam) | + | Anticipated speakers: Daniel Slilaty (Wright State), Margaret Readdy (Kentucky), Richard Ehrenborg (Kentucky), Rigoberto Florez (The Citadel), Ernesto Estrada (Campus Universitat Illes Balears), Aida Abaid (Amsterdam) |
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| **Tuesday, 10/7**\\ | **Tuesday, 10/7**\\ | ||
| - | Speaker: \\ | + | There will be no seminar today. \\ |
| - | Title: \\ | + | |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| - | **Tuesday, 10/14**\\ | + | **Tuesday, 10/14** (jointly with the Geometry/Topology Seminar)\\ |
| Speaker: Lee Kennard (Syracuse)\\ | Speaker: Lee Kennard (Syracuse)\\ | ||
| - | Title: \\ | + | Title: Regular Matroids and Torus Representations\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
| + | Recent work with Michael Wiemeler and Burkhard Wilking presents a link between arbitrary finite graphs and torus representations all of whose isotropy groups are connected. The link is via combinatorial objects called regular matroids, which were classified in 1980 by Paul Seymour. We then apply Seymour’s deep result to classify and to compute geometric invariants of this class of torus representations. | ||
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| + | The applications to geometry are significant. A highlight of our analysis of these representations is the first proof of Hopf’s 1930s Euler Characteristic Positivity Conjecture for metrics invariant under a torus action where the torus rank is independent of the manifold dimension. | ||
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| **Tuesday, 10/21**\\ | **Tuesday, 10/21**\\ | ||
| - | Speaker: Tan Tran (Binghamton)\\ | + | No seminar today. \\ |
| - | Title: \\ | + | |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| **Tuesday, 10/28**\\ | **Tuesday, 10/28**\\ | ||
| - | Speaker: \\ | + | The seminar takes a holiday today.\\ |
| - | Title: \\ | + | |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| **Tuesday, 11/4**\\ | **Tuesday, 11/4**\\ | ||
| - | Speaker: \\ | + | Speaker: Brendon Rhoades (U.C. San Diego)\\ |
| - | Title: \\ | + | Title: Matrix Loci and Shadow Play\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
| + | |||
| + | Let lis$(w)$ be the length of the longest increasing subsequence of a permutation $w$ in $S_n$. I describe a graded quotient $R_n$ of the polynomial ring over an $n$-by-$n$ matrix of variables whose Hilbert series is the generating function of lis, up to reversal. The Gröbner theory of $R_n$ is governed by the Viennot shadow avatar of the Schensted correspondence. The ring $R_n$ is constructed via the orbit harmonics technique of deformation theory. | ||
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| + | I will give some related results and open problems. | ||
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| + | Joint with Jasper Liu, Yichen Ma, Jaeseong Oh, and Hai Zhu. | ||
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| **Tuesday, 11/11**\\ | **Tuesday, 11/11**\\ | ||
| - | Speaker: \\ | + | Speaker: Tan Tran (Binghamton)\\ |
| Title: \\ | Title: \\ | ||
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
seminars/comb/start.1759290381.txt · Last modified: 2025/09/30 23:46 by zaslav