Events

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: 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: A Fixed-Point Approach to Stable Matchings

Abstract:

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

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: Some results concerning frozen homomorphisms

Abstract:

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

Title: Free Groups

Abstract:

(The "free" in the title is an adjective, not a verb.) I will discuss free groups from a combinatorial perspective, focusing on the connections to fundamental groups and covers of graphs.

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: Wronskians of polynomials

Abstract:

The Mukhin-Tarasov-Varchenko (MTV) theorem is the following statement in real algebraic geometry. If the wronskian of a set of complex polynomials has only real roots, then the vector space spanned by these polynomials is real.

Title: A Fixed-Point Approach to Stable Matchings

Abstract:

This talk will be independent of the previous reading group talk. Three classical results in stable matching are the correctness of Gale Shapley’s deferred acceptance algorithm, the result of Conway that Stable Matchings form a distributive lattice, and Vande Vate and later Rothblum’s result that the convex hull of stable matchings has a polynomial-sized linear description.