Dates: 11 September, 2026
Venue: The University of Hong Kong (Run Run Shaw Building Room 210)
Invited Speakers:
Rui Chen (John Hopkins University)
Dan Ciubotaru (University of Oxford)
Jing-Song Huang (CUHK-Shenzhen)
Chuijia Wang (HKU)
Daniel Kayue Wong (CUHK-Shenzehn)
Schedule: TBA
Titles and Abstracts:
Speaker: Rui Chen (John Hopkins University)
Title: Spherical functions on spherical varieties for unramified groups
Abstract: Let X = H\G be a homogeneous a!ne spherical variety for an unramified reductive group G over the integers o of a p-adic field k, and K = G(o) a hyperspherical maximal compact subgroup of G = G(k). We compute eigenfunctions (“spherical functions”) on X = X(k) under the action of the unramified (or spherical) Hecke algebra of G, generalizing the work of Sakellaridis from split groups to unramified groups.
Speaker: Dan Ciubotaru (University of Oxford)
Title: A classification of Arthur nilpotent pairs
Abstract: Motivated by the construction of microlocal Arthur packets for reductive p-adic groups, following the foundational work of Adams, Barbasch, and Vogan, it is important to study the homomorphisms $SL(2) \times SL(2) \to G^\vee$ for which the diagonal restriction is conjugate to a fixed homomorphism $\phi: SL(2) \to G^\vee$; here $G^\vee$ is the Langlands complex dual group. I'll refer to such homomorphisms as Arthur pairs. We prove that the Arthur partner of a graded nilpotent orbit, when it exists, is unique and is determined by Piasetski duality, and classify all conjugacy classes of Arthur pairs when $\phi$ comes from an even nilpotent orbit. This classification has particularly nice consequences for the decomposition and parametrisation of the weak Arthur packets introduced in joint work with Lucas Mason-Brown and Emile Okada.
Speaker: Jing-Song Huang (CUHK-Shenzhen)
Title: Principal elements and Fourier operators
Abstract: Let g be a complex semisimple Lie algebra. Let G be the adjoint group of g. The principal element of G is related to the Coxeter element of the Weyl group, while the Fourier element is related to the longest element. We define the associated Fourier operators of a real form G（R） and show that they act on unitary representation of G（R） similar to the classical Fourier transforms on the oscillator representations of the symplectic groups. The Fourier operator extends to the orthosymplectic supergroups and it acts as the hybrid Fourier transforms on oscillator representations on the superspace.
Speaker: Chuijia Wang (HKU)
Title: TBA
Speaker: Daniel Kayue Wong (CUHK-Shenzhen)
Title: TBA
Organizer & Contact: Kei Yuen Chan (kychan1 [AT] hku.hk)