Applied Math Seminar-Ming Yan, Michigan State
3:45PM, Tue May 2 2017, Math 250
Brandon Seward, Courant Institute
Positive entropy actions of countable groups factor onto Bernoulli shifts
4:00PM, Wed May 3 2017, Math 250
I will show that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well known Sinai factor theorem from classical entropy theory. A consequence of this theorem is that every positive-entropy free ergodic action of a non-amenable group satisfies the measurable von Neumann conjecture.
Sam Taylor (Yale)
4:00PM, Fri May 5 2017, Math 122
Algebra Seminar- Matt Douglass (NSF & University of North Texas)
Schur-Weyl duality and the free Lie algebra
4:00PM, Mon May 8 2017, Math 250
Schur-Weyl duality, which goes back to Schur's thesis in 1927, may be phrased as the pair of assertions that (1) any endomorphism of the vector space r-fold tensors of an n-dimensional vector space V that commutes with all permutations of the factors arises from the diagonal action of the algebra of linear transformations of V and dually (2) any endomorphism of the vector space r-fold tensors of V that commutes with the diagonal action of the algebra of linear transformations of V arises from the permutation action of the rth symmetric group on the factors. In this talk I'll discuss the natural analog of Schur-Weyl duality when the space of r-fold tensors is replaced by the subspace of homogeneous, degree r, Lie polynomials. In this setting the rth symmetric group is replaced by a "Hecke" algebra that arises in a surprisingly different context. Studying the structure of this new algebra leads to intriguing combinatorial questions (and a sequence that does not appear in the Online Encyclopedia of Integer Sequences!).
Applied Math Seminar- Kanika Bansal, University at Buffalo
3:45PM, Tue May 9 2017, Buffalo
Last Day of Classes
Friday, May 12, 2017