Title: Diagonal coefficients of Kirchhoff polynomials of 2k-regular graphs and the proof of the c_2 completion conjectureSpeaker: Karen Yeats Affiliation: University of Waterloo and Perimeter Institute Location: Please contact Sabrina Lato for Zoom link
Abstract: I have for many years been interested in graph invariants with the same symmetries as the Feynman period. Recently Erik Panzer found a new such invariant coming from a particular coefficient of the Martin polynomial. Together we used this to prove an over 10 year old conjecture on an arithmetic graph invariant known as the c_2 invariant, and came to understand that diagonal coefficients of Kirchhoff polynomials tie together many of the known graph invariants with the symmetries of Feynman periods and unlock previously inaccessible proofs.
Joint work with Erik Panzer.
Title: A Primal-Dual Extension of the Goemans--Williamson Algorithm for the Weighted Fractional Cut Covering Problem, Part IISpeaker: Nathan Benedetto Proenca Affiliation: University of Waterloo Location: MC 6029
Abstract: A cut in a graph \(G = (V, E)\) is a set of edges which has precisely one endpoint in \(S\), for a given subset \(S\) of \(V\). The fractional cut-covering number is the optimal value of a linear programming relaxation for the problem of covering each edge by a set of cuts. We define a semidefinite programming relaxation of fractional cut covering whose approximate optimal solutions may be rounded into a fractional cut cover via a randomized algorithm.
Title: Restricted Intersections and the Sunflower ProblemSpeaker: Jeremy Chizewer Affiliation: University of Waterloo Location: MC 5479
Abstract: A sunflower with $r$ petals is a collection of $r$ sets over a ground set $X$ such that every element in $X$ is in no set, every set, or exactly one set. Erdos and Rado showed that a family of sets of size $n$ contains a sunflower if there are more than $n!(r-1)^n$ sets in the family. Alweiss et al. and subsequently Rao improved this bound to $(O(r \log(rn))^n$.