seminars:comb:start
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seminars:comb:start [2025/10/26 14:42] zaslav [FALL 2025] |
seminars:comb:start [2025/11/16 15:28] (current) zaslav [FALL 2025] |
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| **Tuesday, 10/21**\\ | **Tuesday, 10/21**\\ | ||
| No seminar today. \\ | No seminar today. \\ | ||
| - | 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\\ | + | |
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| - | **Tuesday, 11/4**\\ | + | **Tuesday, 11/4** **Cancelled**\\ |
| Speaker: Brendon Rhoades (U.C. San Diego)\\ | Speaker: Brendon Rhoades (U.C. San Diego)\\ | ||
| - | Title: TBA\\ | + | Title: Matrix Loci and Shadow Play\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| + | 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: Tan Tran (Binghamton)\\ | Speaker: Tan Tran (Binghamton)\\ | ||
| - | Title: \\ | + | Title: Vine Copulas, MAT-Labeled Graphs, and Single-Peaked Domains: A Three-Way Correspondence\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| + | Last year, I discussed an unexpected link between vine copulas—graphical models used in statistics—and MAT-labeled graphs, which arise in algebraic graph theory through the study of free hyperplane arrangements. | ||
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| + | This year, I’ll add a third piece to the picture. With H. M. Tran and S. Tsujie, I recently found that these structures are also closely connected to single-peaked domains in voting theory. In particular, MAT-labeled complete graphs, regular vines, and maximal Arrow’s single-peaked domains turn out to be three different manifestations of the same underlying combinatorial framework. This connection brings together ideas from algebraic combinatorics, probabilistic modeling, and social choice. As a consequence of this correspondence, we obtain a complete combinatorial characterization of maximal Arrow’s single-peaked domains, resolving a recent open question in the economics community. | ||
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| - | **Tuesday, 11/18**\\ | + | **Tuesday, 11/18** (joint with the Arithmetic Seminar)\\ |
| - | Speaker: \\ | + | Speaker: Jaeho Shin (Seoul National University)\\ |
| - | Title: \\ | + | Title: Biconvex Polytopes and Tropical Linear Spaces\\ |
| - | Time: 1:30-2:30\\ | + | Time: **Special time** 4:00-5:00\\ |
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| + | Tropical geometry is geometry over exponents of algebraic expressions, using the "logarithmized" operations (min,+) or (max,+). In this setting, one can define tropical convexity and the related notion of biconvex polytopes, which are convex both classically and tropically. There is also a tropical analogue of linear spaces, called tropical linear spaces. Sturmfels conjectured that every biconvex polytope arises as a cell of a tropical linear space. In this talk, I will outline a proof of this conjecture. | ||
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| **Tuesday, 11/25**\\ | **Tuesday, 11/25**\\ | ||
| - | Speaker: \\ | + | Speaker: Xiyong Yan (Binghamton)\\ |
| - | Title: \\ | + | Title: Realization and Classification of Hamiltonian-Circle Multisigns\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E\\ | Location: WH 100E\\ | ||
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| + | We investigate the multisigns of Hamiltonian circles in the multisigned complete graph \(\Sigma_n := (K_n, \sigma, \mathbb{F}_2^m)\). For a fixed \(m\) and sufficiently large \(n\), I prove that the set of multisigns of Hamiltonian circles \(\{\sigma(H) : H \text{ is a Hamiltonian circle of } \Sigma_n\}\) forms either a subspace, an affine subspace, or the entire space \(\mathbb{F}_2^m\), except in certain exceptional cases. | ||
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| + | The main tools used are the \(C_4\) Necklace Lemma and triangular paths. | ||
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| **Tuesday, 12/2**\\ | **Tuesday, 12/2**\\ | ||
| - | Speaker: \\ | + | Another working holiday today.\\ |
| - | Title: \\ | + | |
| - | Time: 1:30-2:30\\ | + | |
| Location: WH 100E\\ | Location: WH 100E\\ | ||
| <HTML></li></HTML> | <HTML></li></HTML> | ||
seminars/comb/start.1761504149.txt · Last modified: 2025/10/26 14:42 by zaslav