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鉁掞笍TITLE / TITRE听

Symmetry and Graph Coloring: Algebraic and Combinatorial Mysteries

馃搫 ABSTRACT /听R脡SUM脡听

The study of proper colorings of graphs is a longstanding and important area in mathematics. The Four Color theorem for planar graphs is one famous success, and this simple problem in cartography launched a vast theory leading to many concrete applications, as well as to the algebraic study of chromatic polynomials and symmetric functions, which also arise in the geometry of Hessenberg varieties.

In 2024, Hikita announced a proof of the Stanley-Stembridge Conjecture on e-positivity of certain chromatic symmetric functions, which had been open for 32 years. This breakthrough leaves open, and gives rise to, many followup mysteries. We will discuss the significance of the symmetric functions arising in graph colorings, and give an overview of some of the important open problems in the area. This discussion will include joint work with Joseph Pappe and Kyle Salois, towards the question, "When is the chromatic quasisymmetric function symmetric?"

馃搷 PLACE /听LIEU听
Hybride - UQAM, Salle / Room PK-5115, Pavillon Pr茅sident-Kennedy

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