UNIVERSITY OF CALIFORNIA, RIVERSIDE Department of Mathematics

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1 , Department of Mathematics Calendar of Events For the Week of November 10 th 14 th, 2014 MONDAY, 10 th 12:10-1:00PM, SURGE 268 2:10-3:00PM, SURGE 268 3:10-4:30PM, SURGE 268 TUESDAY, 11 th VETERANS DAY 9:40-11:00AM, SURGE :10-11:00AM, SURGE :10AM-12:00PM, SURGE 268 1:00-2:00PM, SURGE 284 WEDNESDAY, 12 th 11:10AM-12:00PM, SURGE :10AM-12:00PM, SURGE :10-1:00PM, SURGE :10-1:00PM, SURGE 268 1:10-2:00PM, SURGE 268 2:10-3:00PM, SURGE 268 3:40-5:00PM, SURGE 284 THURSDAY, 13 th 11:10-12:30PM, SURGE 268 1:00-2:00PM, SURGE 284 3:40-5:00PM, SURGE 268 4:10-5:00PM, SURGE 284 FRIDAY, 14 th 11:10AM-12:00PM, SURGE :10-1:00PM, SURGE 268 2:10-3:00PM, SURGE 268 3:10-4:00PM, SURGE 284 TOPICS IN HOMOLOGICAL ALGEBRA Dr. Wee Liang Gan TOPICS IN LIE THEORY Dr. Vyjayanthi Chari NETWORK THEORY Dr. John Baez ALGEGBRAIC GEOMETRY Dr. Ziv Ran OPERATOR ALGEBRAS & RELATED TOPICS Dr. Feng Xu TOPOLOGY Dr. Julie Bergner LIE THEORY Dr. Vyjayanthi Chari COMBINATORIAL NUMBER THEORY Dr. Mei-Chu Chang GRADUATE STUDENT SEMINAR Matthew Barber, UC Riverside Introduction to Operads FLUIDS Dr. Jim Kelliher TOPICS IN HOMOLOGICAL ALGEBRA Dr. Wee Liang Gan PDE & APPLIED MATHEMATICS Taylor Baldwin, UC Riverside Asymptotic behavior of a Vlasov-Fokker-Planck/compressible Navier- Stokes system TOPICS IN LIE THEORY Dr. Vyjayanthi Chari COLLOQUIUM Dr. Li-Sheng Tseng, UC Irvine A New Product for Differential Forms on Symplectic Manifolds FRACTAL RESEARCH GROUP Edward Voskanian, UC Riverside TBA LIE THEORY Dr. Daniel Juteau, Université de Caen, France, and MSRI Modular Generalized Springer Correspondence MATHEMATICAL PHYSICS & DYNAMICAL SYSTEMS Lauren Ruth, UCR Understanding the Class Number of a Quadratic Extension (Part 1) MATH CLUB Dr. Kevin Costello, UC Riverside Graduate School Q&A Session DIFFERENTIAL GEOMETRY Dr. Fred Wilhelm TOPICS IN HOMOLOGICAL ALGEBRA Dr. Wee Liang Gan TOPICS IN LIE THEORY Dr. Vyjayanthi Chari COMMUTATIVE ALGEBRA Dr. David Rush

2 Graduate Student Seminar Matthew Barber UC Riverside Introduction to Operads The term operad (or multicategory) was originally coined by Peter May to study infinite loop spaces. Consider a pointed space X, then the loop space of X is something you would want to think of as a topological monoid because you are able to compose paths. However, such composition is only associative up to homotopy. But we do have a canonical equivalence up to homotopy. We want a good way to hide all of these homotopies. So an operad will be something like a collection of operations together with some way to compose them. Then many common algebraic structures will become algebras over some operad. Wednesday, November 12 th, 2014 Surge :10 a.m. - 12:00 noon

3 Partial Differential Equations & Applied Math Taylor Baldwin UC Riverside Asymptotic behavior of a Vlasov-Fokker- Planck/compressible Navier-Stokes system The evolution of dispersed particles in a fluid may be modeled by a system coupling the Navier-Stokes equations with the Vlasov-Fokker- Planck equation. I will discuss the behavior of a particular Vlasov- Fokker-Planck/Navier-Stokes asymptotic regime. Using entropy methods, I will show that weak solutions of the asymptotic regime converge to weak solutions of a multi-fluid system. Wednesday, November 12 th, 2014 Surge 268 1:10-2:00 p.m.

4 COLLOQUIUM Dr. Li-Sheng Tseng UC Irvine A New Product for Differential Forms on Symplectic Manifolds Many geometrical invariants of manifolds can be expressed in terms of the differential forms on them. As such, it is important to understand the types of algebra that differential forms may have on a manifold. In this talk, I will describe how differential forms on symplectic manifolds have novel characteristics. In particular, I will present a new product operation for forms on symplectic manifolds that is different from the standard wedge product. This new product interestingly involves derivatives and is nonassociative. Of consequence, it leads to an A-infinity algebra structure for forms and a ring structure for the cohomologies on symplectic manifolds. Wednesday, November 12 th, 2014 Surge 284 Tea Time 3:40 p.m. Talk Begins 4:10 p.m.

5 Lie Theory Dr. Daniel Juteau Université de Caen, France, and MSRI Modular Generalized Springer Correspondence For a reductive group G, the Springer correspondence is an injection from irreducible representations of the Weyl group W to the simple G-equivariant perverse sheaves on the nilpotent cone of the Lie algebra (or the unipotent variety of the group). However, in general not all simple perverse sheaves arise in this way. This led Lusztig to define a generalized Springer correspondence, involving the process of inducing cuspidal perverse sheaves from Levi subgroups. The classical correspondence is the part coming from a maximal torus. In the case of the general linear group, though, nothing new arises in this way. In my thesis I studied a modular Springer correspondence, where one takes modular representations of the Weyl group and perverse sheaves with positive characteristic coefficients. In this talk I will explain the modular version of the generalized Springer correspondence, focusing on the case of the general linear group. In the modular case there is something new, namely there is a cuspidal perverse sheaf supported by the regular nilpotent orbit when the rank is a power of the characteristic. I will also mention the most striking phenomena concerning groups of other types. This is joint work with Pramod Achar, Anthony Henderson and Simon Riche. Thursday, November 13 th, 2014 Surge 284 1:00-2:00 p.m.

6 Mathematical Physics & Dynamical Systems Lauren Ruth UC Riverside Understanding the Class Number of a Quadratic Extension (Part 1) Focusing on examples from quadratic field extensions of the rational numbers, we will examine as much of the following material as time permits, covering the remaining material in Part 2 on December 11: unique prime factorization of ideals (not elements!); fractional ideals and (finiteness of) the class group; the field discriminant and the Minkowski bound; the ideal norm and the Dedekind zeta function; Dirichlet L-functions, Hecke L-functions, Shintani L-functions, Eisenstein series, and their role in a proof of Dirichlet's class number formula; quadratic reciprocity; Gauss's conjectures on quadratic fields with class number one and the Stark-Heegner theorem. (References: Haruzo Hida's "Elementary Theory of L-functions and Eisenstein Series," Serge Lang's "Algebraic Number Theory," and Keith Conrad's handouts.) Thursday, November 13 th, 2014 Surge 268 3:40 5:00 p.m.

7 Math Club University Of California Riverside Mathematics 11/13/14 4PM SURGE 284 ð Undergraduate math majors! If you are thinking of going to graduate school come to this information panel! Organizing Faculty: Dr. Vyjayanthi Chari Dr. Kevin Costello ð Graduate Student Mentors: Donna Blanton Kaylee Hamann Matthew O Dell Parker Williams And selected others.