Seminar

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

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.