Organizers: Harry Tamvakis, Tom Haines, Jeffrey Adams
When: Wednesdays @ 2pm
Where: Math 1311
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  • Organizational meeting

    Speaker: () -

    When: Wed, August 30, 2017 - 2:00pm
    Where: Kirwan Hall 1311
  • Characters of Finite Dimensional Representations

    Speaker: Jeffrey Adams (University of Maryland) -

    When: Wed, September 6, 2017 - 2:00pm
    Where: Kirwan Hall 1311

    View Abstract

    Abstract: The main objects of study of the Atlas of Lie Groups and
    Representations are infinite dimensional representations. However
    there are quite a few interesting open questions about finite
    dimensional representations. One is: what can one say about the
    signature of the invariant (Hermitian or bilinear) form on an
    irreducible finite dimensional representation? How does this depend on
    the real form of the group? Another one is: if g in G represents the
    Coxeter element of the Weyl group, its trace in any finite dimensional
    representation is 0,\pm 1 (Kostant). What do these values mean, and
    are there other conjugacy classes like this?

  • Real representation of finite simple groups

    Speaker: Ryan Vinroot (William and Mary ) -

    When: Mon, September 18, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: It has been conjectured that if G is a finite simple group, then every complex irreducible representation of G may be realized over the real numbers if and only if every element of G is the product of two involutions of G. This follows for most families of finite simple groups from work of various people over the past several decades, but not for the cases that G is either $p(2n,F_q) with q even or the simple orthogonal group Omega^{\pm}(4m,F_q) with q even. We will discuss the proof that this statement indeed holds for these symplectic groups, and what modifications must be made to the proof for the same method to apply to the simple orthogonal groups.
  • Unipotent Packets for Real Groups

    Speaker: Jonathan Fernandes (University of Maryland) -

    When: Wed, October 11, 2017 - 2:00pm
    Where: Kirwan Hall 1311
  • The pseudo-identity operator on the space of automorphic functions

    Speaker: Jonathan Wang (IAS) -

    When: Mon, October 16, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Let F be a global field and G a reductive group over F. We define a "strange" operator on the space of automorphic functions on G(A)/G(F). We discuss how this "pseudo-identity operator" relates to pseudo-Eisenstein series and inversion of the standard intertwining operator. We show that this operator is natural from the viewpoint of the geometric Langlands program via the functions-sheaves dictionary. The operator is also connected to Deligne-Lusztig duality and cohomological duality of representations over a local field.
  • Serre-Tate theory for Shimura varieties

    Speaker: Rong Zhou (IAS) -

    When: Mon, October 23, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We study the $\mu$ ordinary locus in the special fiber of Hodge-type Shimura varieties. This is the group theoretic analogue of the ordinary locus in the moduli space of abelian varieties. We show that each point on this locus has a canonical special point which lifts it and that the completed local ring at each point has a group-like structure, in analogy with classical Serre-Tate theory for ordinary abelian varieties. If we have time we will also talk about some generalizations and applications of these results. This is joint work with A. Shankar.
  • Relative Local Langlands Correspondence and Geometry of Parameter Spaces

    Speaker: Dipendra Prasad (Tata Institute and University of Maryland) -

    When: Wed, October 25, 2017 - 2:00pm
    Where: Kirwan Hall 1311
  • Supercuspidal L-packets

    Speaker: Tasho Kaletha (University of Michigan) -

    When: Wed, November 8, 2017 - 2:00pm
    Where: Kirwan Hall 1311

    View Abstract

    Abstract: Harish-Chandra has given a simple and explicit classification of the discrete series representations of reductive groups over the real numbers. We will describe a very similar classification that holds for a large proportion of the supercuspidal representations of reductive groups over non-archimedean local fields (which we may call regular). The analogy runs deeper: there is a remarkable parallel between the characters of regular supercuspidal representations and the characters of discrete series representations of real reductive groups. This leads to an explicit construction of the local Langlands correspondence for discrete Langlands parameters with trivial monodromy, under mild conditions on the residual characteristic.
  • Generalizations of Springer fibers associated to ad nilpotent ideals

    Speaker: Ke Xue (University of Maryland) -

    When: Wed, November 15, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We state that certain varieties arising as natural generalization of Springer fibers are paved by affines, i.e. possessing a cell decomposition into affine spaces. The proof will be presented in a sketch after introducing several motivations. The chief techniques of the proof are the Bala-Carter Theorem on nilpotent orbits and those employed in the 1988 paper by de Concini, Lusztig and Procesi concerning similar property of Springer fibers.
  • Transfer operators between relative trace formulas in rank one

    Speaker: Yiannis Sakellaridis (Rutgers Newark and IAS) -

    When: Mon, November 27, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: I will introduce a new paradigm for comparing relative trace formulas,
    in order to prove instances of (relative) functoriality and relations
    between periods of automorphic forms.

    More precisely, for a spherical variety X=H\G of rank one, I will prove
    that there is an explicit "transfer operator" which transforms the
    orbital integrals of the relative trace formula for X x X/G to the
    orbital integrals of the Kuznetsov formula for GL(2) or SL(2), equipped
    with suitable non-standard test functions. The operator is determined by
    the L-value associated to the square of the H-period integral, and the
    proof uses a deep theory of Friedrich Knop on the cotangent bundles of
    spherical varieties. This is part of an ongoing joint project with
    Daniel Johnstone and Rahul Krishna, who are proving instances of the
    fundamental lemma. Globally, this transfer will induce an identity of
    relative trace formulas and global relative characters, translating to
    an Ichino–Ikeda type formula that relates the square of the H-period to
    the said L-value.

    This can be viewed as part of the program of relative functoriality, a
    generalization of the Langlands functoriality conjecture, predicting
    relations between the automorphic spectra of two spherical varieties
    when there is a map between their dual groups. The case under
    consideration here is the simplest non-abelian case of this, when the
    dual groups are equal and of rank one. If time permits, I will discuss
    how the transfer operator here and in a few examples of higher rank
    where it is known is a "deformation" of an abelian transfer operator
    obtained by replacing the spherical variety by its asymptotic cone (or
    boundary degeneration).
  • Jeff Hakim - TBA

    Speaker: Jeff Hakim (American University) -

    When: Wed, December 6, 2017 - 2:00pm
    Where: Kirwan Hall 1311
  • Relative Local Langlands Correspondence II

    Speaker: Dipendra Prasad (Tata Institute) -

    When: Mon, December 11, 2017 - 2:00pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Weiqiang Wang (University of Virginia)

    When: Wed, February 14, 2018 - 2:00pm
    Where: Kiran Hall 1311