Speaker: Dr. Mihir Hasabnis

In the speaker's research at CMU with Prof. Alan Frieze we mainly studied several problems in random graphs. Random graphs are one of the biggest fields in Probabilistic combinatorics with applications to various fields in Mathematics and Computer Science. We will briefly look at a variety of problems in this area such as the Game Chromatic Number for Hypergraphs, Rainbow matching, Colorful Hamiltonian Cycles, and Random Graph Isomorphism. Extremal combinatorics studies how large or how small a collection of finite objects can be if it has to satisfy certain restrictions. We will look at a problem of saturation in bipartite graphs in that context.