Seminar

Title: The sandwich conjecture of random regular graphs and more

Abstract:

The sandwich conjecture formulated in [Kim, Vu, Advances in Math., 2004] states that if d >> log n, then the random d-regular graph on n vertices R(n, d) can asymptotically almost surely be ”sandwiched” between G(n, p₁) and G(n, p₂) where probabilities p₁ and p₂ are both (1 + o(1))d/n.

Title: Some results concerning frozen homomorphisms

Abstract:

A colouring is frozen if you cannot change any vertices colour and remain a proper colouring.

Title: The distribution of tree parameters via the martingale CLT

Abstract:

Tree parameters, like pattern or symmetry counts, have been extensively studied in the literature for various random models.

Title: A Fixed-Point Approach to Stable Matchings

Abstract:

We describe a xed-point based approach to the theory of bipartite stable matchings.

Title: The 600-cell as a Cayley graph

Abstract:

I will discuss some of the things we can learn about the 600-cell by viewing it as a Cayley graph for the group SL(2,5) (once I've discussed the basic properties of this group).

Title: Partial progress on enumerating K₅ descendants

Abstract:

We call a particular operation on a graph which converts one triangle into two triangles a double triangle expansion, and call all those graphs which can be obtained from repeated double triangle expansions of a fixed graph the double triangle descendants of the graph.

Title: Spanning cycles in Hypergraphs

*Please note the room change from the previous week

Abstract:

A long time ago, Lehel asked whether the vertex set of every complete graph, whose edges have been coloured red and blue, can be partitioned into a red and a blue cycle.

Title: Stochastic optimization methods beyond stochastic gradient descent

Abstract:

We will present a very general framework for unconstrained stochastic optimization which encompasses standard frameworks such as line search and trust region using random models.

Title: Stable Matching Overview

Abstract:

This semester, the CombOpt Reading Group studies Stable Matching. In this talk we will introduce the basic concepts in stable matching, provide an overview of the planned papers to be discussed this semester, and mention interesting open questions along the way.

Title: The Erdős-Pósa property for A-paths

Abstract:

Let A be a set of vertices in a graph G. An A-path is a path whose ends are in A. Gallai proved, for any integer k, that there are either k disjoint A-paths or there is a set of at most 2k vertices that hit all A-paths.