Rutgers University at Newark


Format: This is mostly a learning seminar, with occasional invited talks. During the fall of 2011 we will be studying the theta correspondence and its applications to automorphic forms. 
Thursday 2 February, 1:002:20pm 


Thursday 9 February, 10:0011:20am 


Thursday 16 February, 1:002:20pm 


Thursday 23 February, 1:002:20pm 


Thursday 8 March, 1:002:20pm 


Thursday 29 March, 1:002:20pm 


Monday 16 April, 2:303:50pm 


Sunday 22 April, 2:003:20pm 


Monday 30 April, 2:303:50pm 


Thursday 3 May, 3:005:00pm 


Wednesday 28 September, 4:005:15pm 


Wednesday 5 October, 2:303:45pm 


Wednesday 2 November, 3:455:00pm 


Wednesday 30 November, 10:0011:20am 


Wednesday 7 December, 10:0011:20am 


Last Year's seminar 
Back to the Department of Mathematics & Computer Science. 
Feb. 2 and 9
Title: A result of GanGomez on the unitary spectrum of some spherical varieties.
Speaker: Yiannis Sakellaridis
Abstract:
A conjecture of Venkatesh and myself states that for a spherical variety X over a local field the space L^2(X) should have a Plancherel decomposition in terms of certain "Xdistinguished" Arthur parameters.
I will present a recent paper of Wee Teck Gan and Raul Gomez, where they use the theta correspondence to prove this conjecture for most varieties of rank one.
Feb. 16 and 23, Mar. 8 and 29
Title: Introduction to the conjectures of Stark.
Speaker: Robert Sczech
Abstract:
A fundamental problem of algebraic
number theory is the problem of constructing
all abelian extensions of a given algebraic
number field. That problem was solved by
Kronecker ("Jugendtraum") in the special case
of the rational number field and the case of
an imaginary quadratic field. The conjectures
of Stark (from the 1970's) represent a partial
answer to that problem for an infinite class
of base fields.
In my talk I will report on the most accessible
cases of that conjecture starting with the case
of the rational number field. The talk will be
elementary and therefore accessible to
interested graduate students.
Apr. 16
Title: Euler Systems from CM cycles for Unitary Shimura Varieties and the Gross—Prasad Conjectures
Speaker: Dimitar Jetchev (EPF Lausanne)
Abstract:
Euler systems have been invented by Kolyvagin as a tool to algebraically model Lfunctions and have been successfully used in proving various deep results towards the Birch and SwinnertonDyer conjecture, the Iwasawa main conjecture and various modularity theorems. Currently, there are only few constructions of Euler systems known in the literature: the Euler systems of cyclotomic units, Stickelberger elements, elliptic units, Siegel units (Kato's construction) and Heegner points (Kolyvagin's construction). It is an open question to understand more conceptually the construction of Euler systems and to place it in a more generalrepresentation theoretic context. In this talk, we discuss a novel, higherdimensional construction of an Euler system from CM 1cycles on certain Shimura varieties for the group U(2,1)xU(1,1) via the Gross—Prasad restriction problem for the Gelfand pair U(1,1) embedded diagonally in U(2,1)xU(1,1). This construction can be used to prove new results towards a generalization of the Birch and SwinnertonDyer conjecture closely related to a recent Gross—Zagier type formula studied by Zhang—Zhang—Yuan in the same case. In addition, it indicates a general strategy for constructing Euler systems out of restriction problems for automorphic representations in the context of general recent conjectures by Gan—Gross—Prasad. Part of this project is joint work in progress with Yiannis Sakellaridis.
Apr. 22
Title: Products of distinct Whittaker coefficients on the metaplectic
group and the relative trace formula.
Speaker: Cesar Valverde (RutgersNewark)
Abstract:
I will talk about a relative trace formula between the
metaplectic and the general linear group. As a consequence, one expects a
relation between a product of distinct Whittaker coefficients on the
metaplectic group and a nonsplit period on the general linear group.
Apr. 30
Title: Transfer relations in essentially tame local Langlands correspondence.
Speaker: Geo KamFai Tam (Toronto)
Abstract:
We first describe the essentially tame local Langlands
correspondence of GL_n constructed by Bushnell and Henniart. Then we
relate their results to endoscopic relations of Langlands and Shelstad
by comparing twisted characters of representations. Finally we
interpret the essentially tame correspondence using admissible
embeddings of Lgroups constructed by Langlands and Shelstad.
May 3
Title: Nonstandard comparison of relative trace formulas.
Speaker: Yiannis Sakellaridis
Abstract:
The standard paradigm of endoscopy involves an orbitbyorbit comparison of the geometric sides of two trace formulas. I will present a different way to compare trace formulas, using certain integral transforms between the pertinent spaces of orbital integrals. More precisely, I will compare the Kuznetsov trace formula to Jacquet's relative trace formula for torus periods on GL(2), obtaining a new proof of a wellknown result of Waldspurger (also proven by Jacquet). The global argument involves a Poisson summation formula for functions defined on a meager subset of the adeles!