====== The Combinatorics Seminar ====== ===== SPRING 2018 ===== [[http://www.anybrowser.org/campaign/|Best Viewed With Any Browser]] Organizers: [[http://www2.math.binghamton.edu/p/people/laura|Laura Anderson]], [[http://www2.math.binghamton.edu/p/people/dobbins/|Michael Dobbins]], and [[http://www2.math.binghamton.edu/p/people/zaslav/|Thomas Zaslavsky]].

**Tuesday, January 16**\\ No meeting planned at present.
**Tuesday, January 23**\\ //Speaker//: Steven Simon (Bard) **Cancelled**\\ //Title//: Hyperplane Equipartitions Plus Constraints\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, January 30**\\ No seminar today.
**Tuesday, February 6**\\ //Speaker//: Michael Dobbins (Binghamton)\\ //Title//: [[abstract.201802dob|Shellability is NP-Complete]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, February 13**\\ //Speaker//: Ting Su (Binghamton)\\ //Title//: [[abstract.201802su|A Classification of Stringent Hyperfields]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, February 20**\\ //Speaker//: Florian Frick (Cornell)\\ //Title//: [[abstract.201802fri|Intersections of Finite Sets: Geometry and Topology]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Thursday, February 22 (in the [[http://www2.math.binghamton.edu/p/seminars/topsem|Geometry/Topology Seminar]]; note special day and times)**\\ //Speaker//: Olakunle Abawonse (Binghamton)\\ //Title//: [[http://www2.math.binghamton.edu/p/seminars/topsem|Topology of the Grünbaum–Hadwiger–Ramos Hyperplane Mass Partition Problem]]\\ //Time//: 2:50 - 3:50\\ //Title//: [[http://www2.math.binghamton.edu/p/seminars/topsem|Hyperplane Mass Partitions Via Relative Equivariant Obstruction Theory]]\\ //Time//: 4:15 - 515\\ //Room//: WH-100E
**Tuesday, February 27**\\ //Speaker//: Benjamin Blum-Smith (NYU)\\ //Title//: [[abstract.201802blu|When Do Integer Permutation Invariants Form a Free Module Over the Symmetric Polynomials? An Application of Combinatorics to Invariant Theory]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, March 13 (joint with the [[http://www2.math.binghamton.edu/p/seminars/alge|Algebra Seminar]])**\\ //Speaker//: Victor Reiner (Minnesota)\\ //Title//: [[abstract.201803rei|Finite General Linear Groups and Symmetric Groups]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, March 20**\\ //Speaker//: Thomas Zaslavsky (Binghamton)\\ //Title//: [[abstract.201803zas|Circle Problems in Signed Graphs]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, March 27 (joint with the [[http://www2.math.binghamton.edu/p/seminars/alge|Algebra Seminar]])**\\ //Speaker//: Farbod Shokrieh (Cornell)\\ //Title//: [[abstract.201803sho|Effective Divisor Classes on Graphs]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Monday, April 2**\\ //Speaker//: Stefan van Zwam (Louisiana State)\\ //Title//: [[abstract.201804zwa|A Stroll through Partial Fields]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, April 10**\\ //Speaker//: Jacob Matherne (U. Mass. Amherst)\\ //Title//: [[abstract.201804mat|Singular Hodge Theory of Matroids]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, April 17**\\ //Speaker//: Richard Behr\\ //Title//: [[abstract.201804beh|Edge Coloring and Special Edges of Signed Graphs]]\\ //Time//: 12:00 - 1:00 and 1:15 - 2:15\\ //Room//: OR-100D and WH-100E (respectively)
**Tuesday, April 24 (joint with the [[http://www2.math.binghamton.edu/p/seminars/topsem|Geometry/Topology Seminar]])**\\ //Speaker//: Robert Connelly (Cornell)\\ //Title//: [[abstract.201804con|Tensegrities: Geometric Structures Suspended in Midair]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E
**Tuesday, May 1 (joint with the [[http://www2.math.binghamton.edu/p/seminars/topsem|Geometry/Topology Seminar]])**\\ //Speaker//: Boris Bukh (Carnegie Mellon)\\ //Title//: [[abstract.201805buk|Topological Version of Pach's Overlap Theorem]]\\ //Time//: 1:15 - 2:15\\ //Room//: WH-100E

Consider the collection of all the simplices spanned by some n-point set in **R**^d. There are several results showing that simplices defined in this way must overlap very much. In this talk I focus on the generalization of these results to 'curvy' simplices.

Specifically, Pach showed that every d+1 sets of points, Q₁, ..., Q_d+1, in **R**^d contain linearly-sized subsets P_i in Q_i such that all the transversal simplices that they span intersect. In joint work with Alfredo Hubard, we show, by means of an example, that a topological extension of Pach's theorem does not hold with subsets of size C(log n)^1/(d-1). We show that this is tight in dimension 2, for all surfaces other than S². Surprisingly, the optimal bound for S² is (log n)^1/2. This improves upon results of Barany, Meshulam, Nevo, Tancer.
**Tuesday, May 8**\\ //Speaker//: Jim Lawrence (George Mason)\\ //Title//: [[abstract.201805law|Interval Posets, Parity Representations, Binary Partitions, and Antiprisms]]\\ //Time//: 3:00 - 4:00 **(Note special time.)**\\ //Room//: WH-100E

Given a poset (a partially ordered set), one obtains another poset by considering the collection of intervals of the first, partially ordered by inclusion. (There are various possibilities, depending, for instance, upon whether one considers the empty set as being an "interval.") This construction has found use in the study of convex polytopes and other places. I describe a new method of representation of posets by utilizing certain geometric complexes in **R**^d having vertices in **Z**^d. The striking feature of this method of representation is that taking the interval poset corresponds to dilation by a factor of 2 of the geometric complex. I explore connections with the integer partitions of powers of 2 into powers of 2.

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