# The Hanna Neumann Conjecture, generalizations, and relations to several fields of mathematics.

SPEAKER: Igor Mineyev

TITLE: The Hanna Neumann Conjecture, generalizations, and relations to several fields of mathematics.

ABSTRACT: The Hanna Neumann Conjecture (HNC) is an easy-to-formulate question coming from group theory, it asserts a specific upper bound on the rank of intersections of finitely generated subgroups in free groups. HNC has been open since 1957. I will discuss several points of view on this conjecture, generalizations of its statement, submultiplicativity, relations of HNC to graph theory, geometry, topology, analysis, ring theory. Then I will present two recent proofs of HNC, one analytic (one-month-old) and another graph-theoretic (one-week-old), and pose some general questions. The two parts can be attended independently. Part I will concentrate on analysis, geometry and topology, and the first proof of HNC. Part II will be more about groups, graphs, some related questions in ring theory, and the second proof of HNC.