Matias von Bell - Doctoral Defense
Date:
-
Location:
POT 745
Event Series:
DISCRETE CATS SEMINAR
Discrete CATS Seminar
Speaker: Cyrus Hettle, Georgia Tech
Title: Mathematically Quantifying Gerrymandering in
Georgia’s Congressional Redistricting
Abstract:
While gerrymandering has been widely suspected in Georgia for years,
it has been difficult to quantify. We generate a large ensemble of
randomly generated non-partisan maps that are sampled from a
probability distribution which respects the geographical constraints
of the redistricting process. Using a Markov chain Monte Carlo process
and techniques involving spanning trees, we can quickly generate a
robust set of plans.
Based on historical voting data, we compare the Georgia congressional
redistricting plan enacted in 2021 with the non-partisan maps. We find
that the 2021 plan will likely be highly non-responsive to changing
opinions of the electorate, unlike the plans in the ensemble. Using
additional spatial analysis, we highlight areas where the map has been
redrawn to weaken the influence of Democratic voters.
This talk is based on joint work with Swati Gupta, Gregory Herschlag,
Jonathan Mattingly, Dana Randall, and Zhanzhan Zhao.
Date:
Location:
POT 745
Event Series:
Derek Hanely - Doctoral Defense
Date:
-
Location:
POT 745
Event Series:
Discrete CATS Seminar
Discrete CATS Seminar
Speaker: Richard Ehrenborg, University of Kentucky
Title: Sharing Pizza in n Dimensions
Monday, February 7th 2022
2 pm POT 745
Abstract:
We introduce and prove the n-dimensional Pizza Theorem. Let ℋ be a real n-dimensional hyperplane arrangement. If K is a convex set of finite volume, the pizza quantity of K is the alternating sum of the volumes of the regions obtained by intersecting K with the arrangement ℋ. We prove that if ℋ is a Coxeter arrangement different from A_1^n such that the group of isometries W generated by the reflections in the hyperplanes of ℋ contains the negative of the identity map, and if K is a translate of a convex set that is stable under W and contains the origin, then the pizza quantity of K is equal to zero. Our main tool is an induction formula for the pizza quantity involving a subarrangement of the restricted arrangement on hyperplanes of H that we call the even restricted arrangement. We get stronger results in the case of balls. We prove that the pizza quantity of a ball containing the origin vanishes for a Coxeter arrangement ℋ with |ℋ|-n an even positive integer.
This is joint work with Sophie Morel and Margaret Readdy.
Date:
Location:
POT 745
Event Series:
Discrete CATS Seminar
Discrete CATS Seminar
Note special day and time!
Speaker: JiYoon Jung, Marshall University
Title: Lattice path matroid polytopes
Abstract: A lattice path matroid is a transversal matroid
corresponding to a pair of lattice paths on the plane. A matroid base
polytope is the polytope whose vertices are the incidence vectors of
the bases of the given matroid. In this talk, we study the facial
structures of matroid base polytopes corresponding to lattice path
matroids. In the case of a border strip, we show that all faces of a
lattice path matroid polytope can be described by certain subsets of
deletions, contractions, and direct sums. In particular, we express
them in terms of the lattice path obtained from the border
strip. Subsequently, the facial structures of a lattice path matroid
polytope for a general case are explained in terms of certain tilings
of skew shapes inside the given region.
Zoom meeting number: 868 0578 9053
Date:
Location:
Zoom meeting number: 868 0578 9053
Event Series:
Discrete CATS Seminar
Speaker: Ben Reese
University of Kentucky
Title: Pipe Dream Complexes and Root Polytopes
Qualifying Exam
Committee: M Readdy (Chair), R Ehrenborg, M Yip, Derek Young
Date:
Location:
Zoom
Event Series:
Discrete Group Open House
Date:
-
Location:
Zoom
Event Series:
discrete CATS seminar
Title: Lattice minors and Eulerian posets
Abstract: We define a notion of deletion and contraction for lattices. The result of a sequence of deletions and contractions is called a minor of the original lattice. The name minors is justified by the fact that the minors of the lattice of flats of a graph correspond to the simple minors of the graph when the vertices are labeled (and the edges unlabeled). For each finite lattice we define a poset of minors and show it is Eulerian and a PL sphere. We also obtain some inequalities for the cd-indices of these posets of minors.
Date:
Location:
Zoom
Event Series:
discrete CATS seminar
Title: Coloring (P5, gem)-free graphs with ∆ − 1 colors.
Abstract: The Borodin–Kostochka Conjecture states that for a graph G, if ∆(G) ≥ 9 and ω(G) ≤ ∆(G)−1, then χ(G) ≤ ∆(G)−1. This conjecture is a strengthening of Brooks' Theorem and while known for certain graph classes it remains open for general graphs. In this talk we prove the Borodin– Kostochka Conjecture for (P5,gem)-free graphs, i.e. graphs with no induced P5 and no induced K1 ∨ P4.
Date:
Location:
Zoom
Event Series:
discrete CATS seminar
Title: Characterizing quotients of positroids
Abstract: We characterize quotients of specific families of positroids. Positroids are a special class of representable matroids introduced by Postnikov in the study of the nonnegative part of the Grassmannian. Postnikov defined several combinatorial objects that index positroids. In this talk, we make use of one of these objects called a decorated permutation to combinatorially characterize when certain positroids form quotients. Furthermore, we conjecture a general rule for quotients among arbitrary positroids on the same ground set. This is joint work with Carolina Benedetti and Daniel Tamayo.
Date:
Location:
Zoom
Event Series: