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Thursday, March 21, 2024 2:00 pm - 3:00 pm EDT (GMT -04:00)

Algebraic and Enumerative Combinatorics - Nathan Pagliaroli

Title: Colored unstable map enumeration from random noncommutative geometries

Speaker: Nathan Pagliaroli
Affiliation: Western University
Location: MC 5479

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.

Abstract: The enumeration of maps originates from a series of works by Tutte in the 1960’s. This work later went on to find uses in physics in the enumeration of Feynman diagrammatic expansions of matrix integrals.

In this talk I will discuss how maps with colored edges glued from 2-cells with one or two boundaries arise in recent work in the construction of path integrals over finite dimensional noncommutative spaces. Explicit formulae for the enumeration of such planar maps can be found by solving generalizations of Tutte’s equations. The generating functions of higher genus maps can also be computed from planar map generating functions using a process called Topological Recursion. This talk is based on joint work with Hamed Hessam and Masoud Khalkhali.

Friday, March 22, 2024 12:00 pm - 1:30 pm EDT (GMT -04:00)

C&O Reading Group - Vihan Shah

Title: An Optimal Algorithm for Online Bipartite Matching 

Speaker: Vihan Shah
Affiliation: University of Waterloo
Location: MC 6029

Abstract: We consider the bipartite matching problem in the online setting where vertices on the left arrive in an arbitrary order along with all their edges. Once a vertex arrives, the algorithm has to match the vertex (or can choose to not match it) and this decision cannot be changed later. Karp, Vazirani, and Vazirani give an algorithm for this problem with a competitive ratio of 1-1/e and also show it is optimal.

Friday, March 22, 2024 3:30 pm - 4:30 pm EDT (GMT -04:00)

Tutte Colloquium - Luke Postle

Title: Refined Absorption: A New Proof of the Existence Conjecture

Speaker: Luke Postle
Affiliation: University of Waterloo
Location: MC 5501

Abstract: The study of combinatorial designs has a rich history spanning nearly two centuries.  In a recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating back to the 1800s was proved in full by Keevash via the method of randomized algebraic constructions. Subsequently Glock, Kühn, Lo, and Osthus provided an alternate purely combinatorial proof of the Existence Conjecture via the method of iterative absorption.  We introduce a novel method of “refined absorption” for designs; in this talk, as our first application of the method we provide a new alternate proof of the Existence Conjecture. Joint work with Michelle Delcourt.

Wednesday, July 17, 2024 12:00 am - Friday, July 19, 2024 11:59 pm EDT (GMT -04:00)

Fulkerson 100

Delbert Ray Fulkerson

Fulkerson 100 is a workshop organized by the Dept. of Combinatorics & Optimization (C&O) from July 17-19, 2024 at the University of Waterloo, to celebrate Fulkerson's legacy and impact in discrete mathematics, especially in the fields of graph theory, optimization, and operations research. Fulkerson 100 will feature invited talks in graph theory, combinatorics, optimization, and theoretical computer science, given by some of the foremost researchers in these areas, as well as lightning talks and a poster session devoted to students and postdocs. By bringing together various leading researchers in discrete mathematics with junior researchers and students, the workshop aims to boost research in the areas pioneered by Fulkerson, while commemorating his vision and contributions.