ABSTRACT
- Pierre-Henri Chaudouard
- Ngo Bao Chau
Title: On finite dimensional models of singularities of arc spaces
Abstract: I will present an amplified version of the Grinberg-Kazhdan-Drinfeld theorem on singularities of arc spaces.
- Wee Teck Gan
Title: Restriction problem for nontempered representations of classical groups
Abstract: In this somewhat speculative talk, we describe our joint work with Gross and Prasad on extending the Gross-Prasad conjecture to the setting of nontempered A-packets.
- Jayce Getz
Title: A summation formula for triples of quadratic spaces
Abstract: Let V_1,V_2,V_3 be a triple of vector spaces each equipped with a nondegenerate quadratic form Q_i. Motivated by ideas of Braverman, Kazhdan, and Ngo on generalized Poisson summation formulae we prove a version of the Poisson summation formula for the closed subscheme of V_1 \oplus V_2 \oplus V_3 consisting of vectors v_1,v_2,v_3 such that
Q_1(v_1)=Q_2(v_2)=Q_3(v_3).
- Phung Ho Hai
Title: On affine group schemes over a DVR and applications
Abstract: We study some properties of affine group schemes (of possibly infinite type) over a DVR. We start by providing a structure theorem representing such a group scheme as the limit of a special pro-system. This involves the process of iteratively taking Neron blow-ups. We then address the question on the projectivity of the coordinate ring and introduce the notion of prudent group schemes to solve the question in case the base ring is complete. Applications toward the relative fundamental group scheme of a smooth, proper scheme over a DVR are discussed.
- Heekyoung Hahn
Title: Langlands beyond endoscopy proposal and detection of classical groups
Abstract: Langlands' beyond endoscopy proposal for establishing functoriality motivates the study of irreducible subgroups of $\mathrm{GL}_n$ that stabilize a line in a given representation of $\mathrm{GL}_n$. Such subgroups are said to be detected by the representation. In this talk we present a family of results describing the case when the subgroup is a classical group in the important special case where the representation of $\mathrm{GL}_n$ is a subrepresentation of the triple tensor product representation $\otimes^3$.
- Tamutso Ikeda
Title: On the Gross-Keating invariant of a quadratic form and its application to Siegel series.
Abstract: The Siegel series of a quadratic form over a local non-archimedean local field of characteristic zero appears as a local factor of the Fourier coefficient of the Siegel Eisenstein series.
But the calculation of the Siegel series was very complicated in the case of dyadic field.
In this talk, we develop the theory of the Gross-Keating invariant of a quadratic form, and give an explicit formula of the Siegel series which is expressed in terms of Gross-Keating invariants in a uniform way.
This is a joint work with H. Katsurada.
- Gerard Laumon
Title: Exotic Fourier transformations over finite fields
Gérard Laumon (CNRS and Université Paris-Sud)
Abstract: Independently, Braverman-Kazdhan (2003) and Lafforgue (2013) introduced a new approach to Langlands's functoriality involving Fourier transformations associated to Langlands transfert morphisms.
The Langlands functoriality has an analog over finite fields, which has been proved in full generality by Lusztig. So the Fourier transformation part of the above approach makes sense in that context.
In the talk, I will present some examples that we have recently studied with Emmanuel Letellier.
- Wen-Wei Li
Title: A survey of basic functions
Abstract: The basic function defined through inverse Satake transform is an outstanding feature of the Braverman-Kazhdan program. These functions and the Schwartz spaces to which they belong are expected to yield analytic properties of L-functions. I will give an overview of the related questions and techniques, and try to present both the old and new results in this direction.
P.S. I will use slides. Hopefully there won't be too much overlap with the other speakers' talks.
- Arvind Nair
Title: Mixed (Tate) motives in the cohomology of A_g
Abstract: I will discuss the appearance of unramified mixed Tate motives in the cohomology of the Siegel modular variety of level 1 and in its natural compactifications, using methods of automorphic forms. Some results on more complicated motives appearing in A_g will also be discussed.
- Yiannis Sakellaridis
Title: Examples of relative functoriality.
Abstract: The relative functoriality conjecture, generalizing Langlands' functoriality from groups to spherical varieties, predicts, according to the ``Beyond Endoscopy'' program, comparisons between the (stable) relative trace formulas of different spaces for every map between their $L$-groups. In this talk, I will present examples of this phenomenon, most of which have appeared in the literature in one form or the other, and which can be used to investigate the nature of ``transfer operators'' between different relative trace formulas. I will also discuss the behavior of these operators under degenerations.
- Dao Van Thinh
Title: Average size of 2-Selmer groups of Jacobians of hyperelliptic curves over function fields.
Abstract: Over rational field, M. Bhargava and A. Shankar proved that the average size of 2-Selmer groups of elliptic curves is equal to 3 by using the geometry of number. After that, by employing the geometric setting inspired by the proof of the fundamental lemma, Q.P. Ho, V.B. Le Hung, and B.C. Ngo was able to estimate the average size of 2-Selmer groups of elliptic curves over function fields. Their results are consistent with the results of M. Bhargava and A. Shankar in rational field case. For hyperelliptic curves over rational field, by using similar method as in elliptic curves case, M. Bhargava and B. H. Gross showed that the average size of 2-Selmer groups of Jacobians of hyperelliptic curves equals 3.
In this talk, I will try to compute the average size of 2-Selmer groups of hyperelliptic curves over function fields by adopting the method of Q.P. Ho et al.
- Chengbo Zhu
Title: Unipotent representations of real classical groups
Abstract: Let \bfG be a complex orthogonal or complex symplectic group, and G be a real form of \bfG, namely G is a real orthogonal group, a real symplectic group, a quaternionic orthogonal group, or a quaternionic symplectic group. Write Ğ for the metaplectic cover of G if G is a real symplectic group, and Ğ=G otherwise. I will discuss a notion of Ğ representations being unipotent, and explain a construction of all such representations. This is a joint work with Jiajun Ma and Binyong Sun.