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Events happening on October 28, 2014

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Oct. 28, 2014 11am (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules
Oct. 28, 2014 11am (MATH 350)	PDE/Analysis Magdalena Czubak (SUNY Binghamton) X We review Liouville theorems for the Navier-Stokes equation on the Euclidean space. In particular, the problem for the stationary Navier-Stokes equation in 3D under finite Dirichlet norm is open. In this talk we answer the analogous question on the 3D hyperbolic space. This is joint work with Chi Hin Chan. Liouville theorems for the Navier-Stokes equation on the hyperbolic space Sponsored by the Meyer Fund
Oct. 28, 2014 11am (MATH 350)	Number Theory Valentijn Karemaker (Utrecht University) X Let G denote a linear algebraic group over Q and K and L two number fields. Assume that there is a group isomorphism of points on G over the adeles of K and L, respectively. We establish conditions on the group G, related to the structure of its Borel groups, under which K and L have isomorphic adele rings. Under these conditions, if K or L is a Galois extension of Q and G(A_K) and G(A_L) are isomorphic, then K and L are isomorphic as fields. As a corollary, we show that an isomorphism of Hecke algebras for GL(n) (for fixed n > 1), which is an isometry in the L^1 norm over two number fields K and L that are Galois over Q, implies that the fields K and L are isomorphic. This can be viewed as an analogue in the theory of automorphic representations of the theorem of Neukirch that the absolute Galois group of a number field determines the field if it is Galois over Q. Hecke algebra isomorphisms and adelic points on algebraic groups
Oct. 28, 2014 12:10pm (MATH …	Kempner Daniel Stroock (MIT) X More or less at the same time, in 1896 Hadamard and de la Vall ?ee proved that lim ?(n)logn=1 n?? n where ?(n) denotes the number of prime numbers p ? n, a famous result known as the prime number theorem. Their proofs were magnificent examples of the power of analytic function theory to solve problems in number theory, and to understand their proofs one has to have the mastery of complex analysis that they had. Over the course of time, their proofs were simplified and other proofs were given. However, the first proof that could be called “elementary” was given by D.J. Newman in a MAA article that appeared in 1980. Newman’s proof requires only that one know that the Riemann zeta function has no zeroes in the half space {z ? C : R(z) ? 1}, and the way that he gets away with so little information is that he applies a novel Tauberian theorem, one that he invented himself. Newmans argument was further refined by D. Zagier on the 100th birthday of the prime number theory, and it Zagier’s article on which my lecture is based. Unfortunately, elementary as Newman’s proof is, it cannot be given in 40 minutes. Thus, in this lecture, I will concentrate on his Tauberian theorem and will only sketch the rest of the argument. The prime number theorem
Oct. 28, 2014 2pm (MATH 350)	Lie Theory Amanda Schaeffer Fry (Metro State) X The so-called “local-global” conjectures in the representation theory of finite groups relate the representation theory of G to that of certain proper subgroups, such as Sylow normalizers. Since the relationship often involves comparing the number of representations satisfying certain properties, many of these are nicknamed “counting conjectures”. I will introduce some of the conjectures and discuss recent results (by many authors) regarding them. Some “Counting” Conjectures in the Representation Theory of Finite Groups Sponsored by the Meyer Fund
Oct. 28, 2014 2pm (Math 220)	Functional Analysis Elizabeth Gillaspy X In this talk I will sketch a proof of the isomorphism between the universal C-algebra and the groupoid C-algebra associated to a directed graph E. Time permitting, I will also discuss more examples of graph C-algebras. Graph C-algebras, part 2 Sponsored by the Meyer Fund

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