# Homological conjectures

Thursday, November 29, 2012 - 3:30pm - 4:30pm

Bryna Kra (Northwestern University)

The interaction between combinatorics and dynamics is a classical subject and an illustration of this interaction arises in the combinatorics of words. The Morse-Hedlund Theorem states that an infinite word in a finite alphabet is periodic if and only if there is exists a positive integer n such that the complexity (the number of words of length n) is bounded by n. A natural approach to this theorem is via analyzing the dynamics of the Z-action associated to the word.

Wednesday, February 1, 2012 - 9:00am - 10:00am

Parimala Raman (Emory University)

The Milnor conjectures relating the graded Witt ring and the mod-2 Galois cohomology ring of a field have been a driving force in the algebraic theory of quadratic forms. The degree 2 norm

residue isomorphism, due to Merkurjev, established the first case of the Milnor conjectures and ushered in a new era in the theory of quadratic forms. We shall explain some of the consequences of the

Milnor conjectures, with particular reference to invariants of fields associated to quadratic forms.

residue isomorphism, due to Merkurjev, established the first case of the Milnor conjectures and ushered in a new era in the theory of quadratic forms. We shall explain some of the consequences of the

Milnor conjectures, with particular reference to invariants of fields associated to quadratic forms.