Current students

Title: Graph Reconstruction

Abstract: The graph reconstruction conjecture by Kelly and Ulam states that all graphs on at least three vertices are determined by their one-vertex deleted subgraphs, up to isomorphism.

Title: Finding Independent Transversals Efficiently

Abstract: Let G be a graph whose vertex set is partitioned into classes V₁,..., V_m. An independent transversal of G with respect to (V_1,...,V_m) is an independent set {v_1,...,v_m} in G such that v_i is in V_i for each i.

Title: The number theory of equiangular lines

Abstract:

It is easy to prove that there can exist at most d² equiangular complex lines in C^d. Configurations saturating this bound are known by other names: maximal equiangular tight frames, minimal complex projective 2-designs and symmetric informationally complete positive operator-valued measures (SIC-POVMs).

Title: The Combinatorial Nullstellensatz 

Abstract: I will survey Alon's survey of the combinatorial nullstellensatz.

Title: Representability of Matroids

Abstract: I will go over some negative results regarding characterizations for the class of representable

Title: Asymptotic Distribution of Parameters in Random Maps

Abstract: A rooted map is a connected graph

Title: The Number 6 Hash Function Collision

Abstract: If V is a vector space of dimension d over the eld GF(q), we have all sorts of families of

Title: Large matroids: asymptotic enumeration

Abstract:

How many matroids are there on a ground set of a given size? Although the question is a very basic one, we only know the answer up to a constant factor in the exponent.

Title: Coloring Graphs of Bounded Maximum Degree with Small Clique Number

Abstract: Greedy coloring yields an upper bound on the chromatic number $\chi$ of $\Delta+1$ for graphs of maximum degree at most $\Delta$, which is tight for cliques. 

Title: LWE part 3: The relation with BDD

Abstract: The last piece of the puzzling reduction