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.
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