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2:00pm, Wednesday 4th June

Abstract

The study of combinatorial designs and graph decompositions 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 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. Last year, Delcourt and Postle introduced the novel method of “refined absorption”, providing another combinatorial proof of the Existence Conjecture and proving many outstanding results in similar settings. This talk will present an overview of the refined absorption methodology, its novelty and strength, and how we use it to prove long-standing conjectures in graph decompositions. In particular, we will focus on an application combining questions by Erdős and Nash-Williams. This talk amalgamates joint works with Delcourt, Henderson and Postle.