The Combinatorics Seminar

SPRING 2018

Organizers: Laura Anderson, Michael Dobbins, and 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: Shellability is NP-Complete
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, February 13
Speaker: Ting Su (Binghamton)
Title: A Classification of Stringent Hyperfields
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, February 20
Speaker: Florian Frick (Cornell)
Title: Intersections of Finite Sets: Geometry and Topology
Time: 1:15 - 2:15
Room: WH-100E
Thursday, February 22 (in the Geometry/Topology Seminar; note special day and times)
Speaker: Olakunle Abawonse (Binghamton)
Title: Topology of the Grünbaum–Hadwiger–Ramos Hyperplane Mass Partition Problem
Time: 2:50 - 3:50
Title: Hyperplane Mass Partitions Via Relative Equivariant Obstruction Theory
Time: 4:15 - 515
Room: WH-100E
Tuesday, February 27
Speaker: Benjamin Blum-Smith (NYU)
Title: 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 Algebra Seminar)
Speaker: Victor Reiner (Minnesota)
Title: Finite General Linear Groups and Symmetric Groups
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, March 20
Speaker: Thomas Zaslavsky (Binghamton)
Title: Circle Problems in Signed Graphs
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, March 27 (joint with the Algebra Seminar)
Speaker: Farbod Shokrieh (Cornell)
Title: Effective Divisor Classes on Graphs
Time: 1:15 - 2:15
Room: WH-100E
Monday, April 2
Speaker: Stefan van Zwam (Louisiana State)
Title: A Stroll through Partial Fields
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, April 10
Speaker: Jacob Matherne (U. Mass. Amherst)
Title: Singular Hodge Theory of Matroids
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, April 17
Speaker: Richard Behr
Title: 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 Geometry/Topology Seminar)
Speaker: Robert Connelly (Cornell)
Title: Tensegrities: Geometric Structures Suspended in Midair
Time: 1:15 - 2:15
Room: WH-100E
Tuesday, May 1 (joint with the Geometry/Topology Seminar)
Speaker: Boris Bukh (Carnegie Mellon)
Title: 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: 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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