A Morning of Arithmetic of Algebraic Groups
November 26, 2025
Join us on November 26th for a morning of arithmetic of algebraic groups.
Organizer: Sujatha Ramdorai
SCHEDULE
| TIME | SPEAKER | TITLE & ABSTRACT |
| 10:30 AM - 11 AM | Mishty Ray | Geometric realizations of local Arthur packets for p-adic groups Local Arthur packets are sets of representations of p-adic groups that help us realize important classes of automorphic representations. Vogan’s geometric perspective on the local Langlands correspondence attaches to each enhanced Langlands parameter a perverse sheaf on an associated parameter space. In this context, Vogan suggested a geometric analogue to local Arthur packets for p-adic groups (following his work on real groups with Adams and Barbasch). Cunningham et al reformulated this proposal by using the vanishing cycles functor. In this talk, I will introduce the aforementioned geometric perspective and report on the status of Vogan’s conjecture. |
| 11:10 AM - 11:40 AM | Amin Soofiani |
A local–global approach to the norm principle over function fields In this talk, based on joint work with Sujatha Ramdorai, I will discuss new results on the norm principle for spinor |
| 11:50 AM - 12:20 PM | Nguyen Manh Linh | Duality theorems and arithmetics of homogeneous spaces over p-adic function fields Let K be the function field of a p-adic curve, a field of cohomological dimension 3. If X is a smooth geometrically integral K-variety, we are interested in the following arithmetic questions for X. 1. Local-global principle (LGP): If X has Kv-points for all closed points v on a smooth projective model of K, does X have K-points? 2. Weak approximation (WA): If X has K-points, is X(K) dense in the topological product of the X(Kv)’s? Generalizing the Brauer–Manin obstruction over number fields, we may use the group H3 nr(X, Q/Z(2)) of unramified degree 3 cohomology to detect the failure of LGP and WA (the “reciprocity obstruction”). It is natural to ask if this obstruction is the only one. Using global duality Poitou–Tate style duality theorems and parts of the Poitou-Tate sequences, Harari, Scheiderer, Szamuely, and Izquierdo gave an affirmative answer for tori. Tian established the same result for certain reductive groups. In this talk, we present similar results for classifying spaces of groups multiplicative type, obtained by the same technique. |
| 12:30 PM - 1 PM | Danny Ofek | Lower bounds on the essential dimension of reductive groups The essential dimension of an algebraic group G is an integer measuring the complexity of G and of its torsors. Often G-torsors classify a class of algebraic objects, in which case ed(G) is the minimal number of independent parameters needed to define a generic object of that type. For example, ed(PGLn) is the number of parameters needed to define a generic division algebra of degree n. We introduce a technique for proving lower bounds on the essential dimension of split reductive groups. As an application, we strengthen the best previously known lower bounds for various split simple algebraic groups, most notably for the exceptional group E8. In the case of the projective linear group PGLn, we recover A. Merkurjev’s celebrated lower bound with a simplified proof. Our technique relies on decompositions of loop torsors over valued fields due to P. Gille and A. Pianzola. |
Event Details
November 26, 2025
10:30am to 1:00pm
MATX 1102
, , CA