Speaker: Pablo Castilla, University of Kentucky
Title: TBA
Date: April 21, 2025
Abstract:
This is a Masters Exam talk.
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Open date.
March 24
Memories of Adriano Garsia
We will show highlights of mathematical work of Adriano Garsia from a recent memorial ceremony.
Speaker: Einar Steingrímsson, University of Strathclyde
Title: Permutation statistics, patterns and moment sequences
Date: March 10, 2025 at 2 pm, 745 POT
Abstract:
Which combinatorial sequences correspond to moments of probability measures on the real line? We present two large classes of such sequences, where for one of the classes we prove these to be moment sequences, and conjecture it for the other class.
This is joint work with Natasha Blitvić and Slim Kammoun.
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DOUBLE FEATURE!!
TWO TALKS FROM: The Many Combinatorial Legacies of Richard P. Stanley: Immense Birthday Glory of the Epic Catalonian Rascal
Speaker: Jim Propp, U Mass Lowell
Title : The further adventures of Stanley's transfer map
Date: Monday, March 3, 2025 at 2 pm in 745 POT
Abstract:
In 1986 Stanley showed that the natural bijection between antichains and order ideals of a poset P gives rise
to a well-behaved continuous piecewise-linear map from the order polytope of P to a new polytope he called
the chain polytope of P. I’ll describe several directions in which this map has been generalized and also discuss
the role these newer maps have played in dynamical algebraic combinatorics.
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Speaker: Sara Billey, University of Washington
Title : Brewing Fubini-Bruhat partial orders with ASMs
Date: Monday, March 3, 2025 at 2:20 pm in 745 POT
Abstract:
Fubini words (also known as Cayley permutations, packed words, and surjective words) are generalized permutations, allowing for repeated letters, and they are in one-to-one correspondence with ordered set partitions. Brendan Pawlowski and Brendon Rhoades extended permutation matrices to pattern matrices for Fubini words. Under a lower triangular action, these pattern matrices produce cells in projective space, specifically (Pk−1)n. The containment of the cell closures in the Zariski topology gives rise to a poset which generalizes the Bruhat order for permutations. Unlike Bruhat order, containment is not equivalent to intersection of a cell with the closure of another cell. This allows for a refinement of the poset.
It is additionally possible to define a weaker order, giving rise to a subposet containing all the elements. We call these orders, in order of decreasing strength, the espresso, medium roast, and decaf Fubini-Bruhat orders. The espresso and medium roast orders are not ranked in general. The decaf order is ranked by codimension of the corresponding cells. In fact, the decaf order has rank generating function given by a well-known q-analog of the Stirling numbers of the second kind.
In this paper, we give increasingly smaller sets of equations describing the cell closures, which lead to several different combinatorial descriptions for the relations in all three orders. Studying these partial orders and their associated rank functions has lead to generalizations of Fulton’s essential set and alternating sign matrices.
This talk is based on joint work with Stark Ryan and Matjaˇz Konvalinka.
Speaker: Richard Ehrenborg, University of Kentucky
Title : The graph polytope of a cycle
Date: Monday, February 17, 2025, 2 pm in 745 POT
Abstract:
We present one of my favorite polytopes: the subset in the first
orthant such that the sum of two cyclically adjacent coordinates is
less than or equal to 1. We will discuss its volume, its Ehrhart
polynomial, the volume again and its face polynomial.
Speaker: Margaret Readdy, University of Kentucky
Title: Introduction to Schubert polynomials and pipe dream complexes
Monday, February 24, 2024, 2 pm, 745 POT
Abstract:
This is an introductory talk about Schubert polynomials and pipe dream complexes. We will mostly focus on the special case of the symmetric group. We will discuss different lines of study in this area including enumeration, inequalities, pattern avoidance and pipe dream complexes.
Rescheduled due to job candidates.
Speaker: Margaret A. Readdy, University of Kentucky
Title: The Pizza Theorem
Abstract:
The Pizza Theorem is a classical result in fair division: if one cuts a disk by an even number of equally-spaced lines through any point in the disk, where there are at least four lines, then the alternating sum of the areas of the slices equals zero. We extend the Pizza Theorem to translates of convex bodies in n dimensions that contain the origin and are stable under a given Coxeter group. We also give stronger results for the case of a ball in n dimensions. Using Herb’s theory of 2-structures, we derive a dissection proof and extensions to all intrinsic volumes.
This is joint work with Richard Ehrenborg and Sophie Morel.
