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--- seminars:comb:start [2025/09/30 23:46]
zaslav [FALL 2025]
+++ seminars:comb:start [2025/11/16 15:28] (current)
zaslav [FALL 2025]
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 ===== FALL 2025 =====
-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**\\
-Speaker: \\
+There will be no seminar today. \\
-Title: \\
 Time: 1:30-2:30\\
 Location:  WH 100E\\
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-**Tuesday, 10/14**\\
+**Tuesday, 10/14** (jointly with the Geometry/Topology Seminar)\\
 Speaker: Lee Kennard (Syracuse)\\
-Title: \\
+Title: Regular Matroids and Torus Representations\\
 Time: 1:30-2:30\\
 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.
+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**\\
-Speaker: Tan Tran (Binghamton)\\
+No seminar today. \\
-Title: \\
-Time: 1:30-2:30\\
 Location:  WH 100E\\
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 **Tuesday, 10/28**\\
-Speaker: \\
+The seminar takes a holiday today.\\
-Title: \\
-Time: 1:30-2:30\\
 Location:  WH 100E\\
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-**Tuesday, 11/4**\\
+**Tuesday, 11/4**  **Cancelled**\\
-Speaker: \\
+Speaker: Brendon Rhoades (U.C. San Diego)\\
-Title: \\
+Title: Matrix Loci and Shadow Play\\
 Time: 1:30-2:30\\
 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.
+I will give some related results and open problems.
+Joint with Jasper Liu, Yichen Ma, Jaeseong Oh, and Hai Zhu.
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 **Tuesday, 11/11**\\
-Speaker: \\
+Speaker: Tan Tran (Binghamton)\\
-Title: \\
+Title: Vine Copulas, MAT-Labeled Graphs, and Single-Peaked Domains: A Three-Way Correspondence\\
 Time: 1:30-2:30\\
 Location:  WH 100E\\
+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.
+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\\
+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**\\
-Speaker: \\
+Speaker: Xiyong Yan (Binghamton)\\
-Title: \\
+Title: Realization and Classification of Hamiltonian-Circle Multisigns\\
 Time: 1:30-2:30\\
 Location:  WH 100E\\
+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.
+The main tools used are the \(C_4\) Necklace Lemma and triangular paths.
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 **Tuesday, 12/2**\\
-Speaker: \\
+Another working holiday today.\\
-Title: \\
-Time: 1:30-2:30\\
 Location:  WH 100E\\
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