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BIMSA-YMSC Tsinghua Number Theory Seminar
BIMSA-YMSC Tsinghua Number Theory Seminar
Desiderata and Uniqueness of Local Langlands correspondence
Desiderata and Uniqueness of Local Langlands correspondence
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Chi-Heng Lo
Time
Monday, May 18, 2026 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
Abstract
The local Langlands conjecture predicts a "canonical" bijection between the set of smooth irreducible representations of a p-adic reductive algebraic group G and the set of enhanced L-parameters for G, a bijection known as the local Langlands correspondence (LLC). While several constructions of the LLC exist in the literature, each typically applies to particular groups or specific classes of representations. Comparing these various constructions is a subtle and challenging problem.
In this talk, I will present joint work with Tasho Kaletha and Cheng-Chiang Tsai, in which we collect a list of desiderata for the LLC for general p-adic groups from the literature. Our main theorem establishes that, when p is sufficiently large, any LLC satisfying these desiderata is unique (if it exists). This provides a unified framework for comparing different LLC.