Future students

Title: Applications of the entropy method: Brégman's theorem

Abstract: Following Section 5 of Galvin's notes on Entropy and Counting,

Title:‘Coloring 3-colorable graphs with o(n^1⁄5) colors’ by Kawarabayashi and Thorup

Abstract: Much attention has been devoted to nding polynomial time algorithms for coloring three-
colorable graphs with the fewest possible colors.

Title: Permutation Problems, Chessboards, and Rook Equivalence

Abstract: We discuss the motivation and development of the theory around rook polynomials.

Title: Circle graphs are quadratically x-bounded

Abstract: A circle graph $G$ is an intersection graph of a set of chords on a circle.

Title: The rank of random matrices over finite fields

Abstract:

We determine the rank of a random matrix over a finite field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes.

Title: Eigenvalue bounds to the (co)clique and chromatic numbers

Abstract:

This is perhaps one of the oldest topics of interest in spectral graph theory, dating back to the works of Hoffman, Haemers, Delsarte and others, in the 70s.

Title: 2-approximation of chromatic number on graph classes excluding a minor

Abstract: In this talk we will see a 2-approximation of the chromatic number of graphs excluding a fixed minor.

Title: Fractional coloring with local demands

Abstract: In a fractional coloring, vertices of a graph are assigned subsets of the $[0, 1]$-interval such that adjacent vertices receive disjoint subsets. 

Title: Applications of the entropy method

Abstract: In the second talk of our reading group on entropy and counting.

Title: Quantum Walks on Oriented Graphs

Abstract: A quantum walk on a graph is defined based on a Hermitian matrix associated with the graph, such as the adjacency matrix.