Seminar

Title: Free subshifts and the Local Lemma

Abstract: The purpose of this talk is to demonstrate how combinatorial tools and techniques can be used to tackle problems in other areas of mathematics, specifically,

Title: Toward a Theory of Crossing-Critical Graphs

Abstract: 

The crossing number of a graph is defined as the minimum number of crossings of edges in a drawing of the graph in the plane. In his seminal 1970 paper Toward a Theory of Crossing Numbers, Tutte made a fundamental contribution by proving what is known today as the Hanani-Tutte Theorem.

Title: Difference-of-SOS and Difference-of-Convex-SOS Decomposition Techniques for Polynomials

Abstract:

We are interested in polynomial decomposition techniques for reformulating any multivariate polynomial into difference-of-sums-of-squares (DSOS) and difference-of-convex-sums-of-squares (DCSOS) polynomials.

Title: MAD and Local Versions of Reed's Conjecture

Abstract:

Graph coloring is a widely studied area of graph theory dating from the time of the Four Color Conjecture (now theorem).

Title: Fixed-parameter tractability with respect to tree-widt

Abstract: Courcelle’s Theorem says that a very general class of decision problems on graphs is FPT with

Title: Bounding Dedekind numbers with entropy

Abstract: The Dedekind numbers (sequence A000372 in the OEIS)

Title: Cyclic flat approach to matroid base polytopes

Abstract: Ardila, Benedetti and Doker realised matroid polytopes as generalized permutohedra, and using the work of Postnikov,

Title: Coloring 3-colorable graphs with o(n^1/5) colors

Abstract: This is the second part of the seminar on recent results obtained by Kawarabayashi and Thorup

Title: Quantum Walks, State Transfer, and Entanglement

Abstract: Quantum walks are the quantum analogues of classical random walks and can be used to model quantum computations.

Title: Applications of the entropy method: Counting proper colorings of a regular graph

Abstract: Following Section 6 of Galvin's notes on Entropy and Counting, we will explore Galvin and Tetali’s tight upper bound