Date/Time : 10 Sep 2021 15:00
Venue : via Zoom
Speaker : Emile Takahiro Okada, University of Oxford

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https://nus-sg.zoom.us/j/82201157603?pwd=WktRRC9hbHFsaFR6VlF6amdGNk5tZz09

Meeting ID: 822 0115 7603
Passcode: 509310

Abstract:  The wavefront set is a powerful invariant which one can attach to representations of reductive groups over both global and local fields. Notably there is a non-trivial interplay between the wavefront set of an automorphic representation and that of its local factors. In this talk we will discuss recent results computing the wavefront set for all spherical Arthur representations in the p-adic case and the new techniques used in the computation.

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Date/Time : 01 Sep 2021 14:00
Venue : via Zoom
Speaker : Yongqi Feng, Shantou University

Join Zoom Meeting https://nus-sg.zoom.us/j/89953315552?pwd=bERiQUVLSEhPNlFsRWNIR21qWGZOQT09 Meeting ID: 899 5331 5552 Passcode: 911014 Let k be a non-archimedean local field, and let G be a connected reductive k-group which splits over an unramified extension of k. Hiraga, Ichino and Ikeda conjectured that the formal degree d(π) of a discrete series representation π of G(k) can be computed via the associated discrete (i.e. elliptic) local Langlands parameter (φπ, ρπ). The supercuspidal unipotent representations form a convenient class to test this conjecture, with known classification and formal degrees when G is simple and adjoint. We shall discuss, for supercuspidal unipotent representations of classical groups, the proof of the HII formal degree conjecture. This leads to a local Langlands correspondence for such representations, which agrees with the parametrization obtained by Morris and Lusztig when G is simple and adjoint. This is joint-work with Eric Opdam and Maarten Solleveld.

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Date/Time : 25 Aug 2021 14:00
Venue : via Zoom
Speaker : Korkeat Korkeathikhun, University of North Carolina, Chapel Hill

Join Zoom Meeting https://nus-sg.zoom.us/j/89816394951?pwd=OXRvc1pXY0kxSGhYRkloMnFkL0dSUT09 Meeting ID: 898 1639 4951 Passcode: 903999 Let $G$ be a simply-connected simple algebraic group, $\mathfrak{g}$ its Lie algebra. Let $\mathrm{Gr}_G$ be the affine Grassmannian of $G$, and $\mathrm{Gr}_0^-$ the opposite open Schubert cell in $\mathrm{Gr}_G$. Achar and Henderson defined a map $\pi:\mathrm{Gr}_0^- \to \mathfrak{g}$ and used it to exhibit the relation between Schubert varieties in $\mathrm{Gr}_G$ and nilpotent cone in $\mathfrak{g}$. In our work, we consider a twisted analouge. We relate the geometry of Schubert varieties in twisted affine Grassmannian and the nilpotent varieties in symmetric spaces. This extends some results of Achar-Henderson in the twisted setting. We also get some applications for the geometry and topology of the order 2 nilpotent varieties in certain classical symmetric spaces.

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Date/Time : 18 Aug 2021 14:00
Venue : via Zoom
Speaker : Jinfeng Song, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/82727387952?pwd=WEo0M0lsd0tETHdhZWZIRGJUaEhEUT09 Meeting ID: 827 2738 7952 Passcode: 557651 Any variety over a field of characteristic p>0 possesses a Frobenius endomorphism F, which fixes all the points and raises the function to p-th power. A variety X is called Frobenius split if the p-th power map splits as a morphism of sheaves of modules. The most important class of examples of varieties which are Frobenius split are flag varieties. This is firstly proved by Mehta and Ramanathan using geometric methods. Later, Kumar and Littelmann construct an alternative proof using the methods of quantum groups. In this talk, I plan to introduce Kumar and Littelmann’s method, and explain its potential generalisation to quantum symmetric pairs.

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Date/Time : 21 Apr 2021 14:00
Venue : via Zoom
Speaker : Ming-Lun Hsieh, Academia Sinica

Join Zoom Meeting https://nus-sg.zoom.us/j/82234939628?pwd=TVRlLzBmS1VsaXhVZ3k5OWtXVlZYdz09 Meeting ID: 822 3493 9628 Password: 838848 Abstract: Darmon, Dasgupta and Pollack in 2011 applied the Eisenstein congruence for Hilbert modular forms to prove the rank one Gross conjecture for Deligne-Ribet p-adic L-functions under some technical assumptions. These assumptions were later lifted by Ventullo. In this talk, we will explain how to apply their ideas in the setting of CM congruence and compute the first derivative of the Katz p-adic L-functions associated with ring class characters of imaginary quadratic fields at the triviall zero. We will present a precise first derivate formula of the Katz p-adic L-functions in terms of certain Gross p-adic regulator and p-adic logarithms of elliptic units. This proves a formula proposed in a recent work of Betina and Dimitrov. This talk is based on a joint work with Masataka Chida.

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Date/Time : 07 Apr 2021 14:00
Venue : via Zoom
Speaker : Shu-Yen Pan, National Tsing Hua University

Join Zoom Meeting hhttps://nus-sg.zoom.us/j/82917531325?pwd=QzVzVVdNbUZhOHlwc09MRG5nWldudz09 Meeting ID: 829 1753 1325 Password: 555209 Let $(G,G’)$ be a reductive dual pair inside a finite symplectic group. By restricting the Weil representation to the dual pair, there exists a relation (called the finite Howe correspondence) between the irreducible representations of the two groups $G,G’$. In this talk, we would like to discuss some progress on the understanding of the correspondence by using Lusztig’s classification on the representations of finite classical groups. In particular, we will focus on the following three subjects: 1. the decomposition of the uniform projection of the Weil character. 2. the commutativity between the Howe correspondence and the Lusztig correspondence. 3. the description of the Howe correspondence on unipotent characters in terms of the symbols by Lusztig.

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Date/Time : 01 Apr 2021 09:00
Venue : via Zoom
Speaker : Jayce Getz, Duke University

Join Zoom Meeting https://nus-sg.zoom.us/j/87075061185?pwd=QnNmQzNQMGxudFZ0aEIwalFTV0ZCdz09 Meeting ID: 870 7506 1185 Password: 568903 Braverman and Kazhdan proposed a conjecture, later refined by Ngo and partially set in the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varieties admit Schwartz spaces, Fourier transforms, and Poisson summation formulae. In this talk I will describe explicit formulae for the Fourier transform on Braverman-Kazhdan spaces (also known as pre-flag varieties) and for certain spherical varieties that are built out of triples of quadratic spaces. Though my primary motivation comes from automorphic representation theory, these formulae should be of interest more broadly. In particular, they allow for many techniques of analytic number theory to be brought from the setting of vector spaces to the setting of spherical varieties.

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Date/Time : 23 Mar 2021 16:30
Venue : via Zoom
Speaker : Jack Thorne, University of Cambridge

Join Zoom Meeting https://nus-sg.zoom.us/j/85360804573?pwd=WUZCVlQ5NU5kTW5TbWdMRmtWb09YZz09 Meeting ID: 853 6080 4573 Password: 645892 Abstract: Langlands functoriality predicts the transfer of automorphic representations along maps of L-groups. In particular, the symmetric power representation Symm^{n-1} of GL(2) should give rise to a lifting from automorphic representations of GL(2) to automorphic representations of GL(n). I will discuss joint work with James Newton proving the existence of all symmetric power lifts for those automorphic representations of GL(2, A_Q) associated to holomorphic modular forms.

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Date/Time : 17 Mar 2021 15:00
Venue : via Zoom
Speaker : Gaetan Chenevier, Université Paris-Sud

Join Zoom Meeting https://nus-sg.zoom.us/j/89926187213?pwd=eGZ5M2gybnMvZWhCVGJHdnRSYWJqUT09 Meeting ID: 899 2618 7213 Password: 003341 Abstract: I will explain a method allowing to classify the isometry classes of unimodular integral lattices in all dimensions <= 28. This method has computational aspects, but also theoretical ones, involving automorphic representations of orthogonal groups. The talk should (hopefully) be accessible to a general number theorists audience.

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