BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yujie Xu (Columbia) DTSTART:20231129T160000Z DTEND:20231129T170000Z DTSTAMP:20260418T065211Z UID:LNTS/110 DESCRIPTION:Title: H ecke algebras for p-adic groups and explicit Local Langlands Correspondenc e\nby Yujie Xu (Columbia) as part of London number theory seminar\n\nL ecture held in Room 140\, the Huxley Building\, Imperial College London.\n \nAbstract\nI will talk about several results on Hecke algebras attached t o Bernstein blocks of (arbitrary) reductive p-adic groups\, where we const ruct a local Langlands correspondence for these Bernstein blocks. Our tech niques draw inspirations from the foundational works of Deligne\, Kazhdan and Lusztig. \n\nAs an application\, we prove the (classical) Local Langla nds Conjecture for G_2\, which is the first known case in literature of (c lassical) LLC for exceptional groups. Our correspondence satisfies an expe cted property on cuspidal support\, which is compatible with the generaliz ed Springer correspondence (for Lusztig's perverse sheaves)\, along with a list of characterizing properties including the stabilization of characte r sums. In particular\, we obtain "mixed" L-packets containing "F-singular " supercuspidals and non-supercuspidals. Such "mixed" L-packets had been e lusive up until this point and very little was known prior to our work. I will give explicit examples of such mixed L-packets using Deligne-Lusztig theory and Kazhdan-Lusztig parametrization. \n\nIf time permits\, I will e xplain how to pin down certain choices in the construction of the correspo ndence using stability of L-packets\; one key input is a homogeneity resul t due to Waldspurger and DeBacker. Moreover\, I will mention how to adapt our general strategy to construct explicit LLC for other reductive groups\ , such as GSp(4)\, Sp(4)\, etc. Such explicit description of the L-packets (e.g. the Kazhdan-Lusztig parameters) has been useful in applications to modularity lifting questions as in the recent work of Whitmore. \n\nSome p arts of this talk are based on my joint work with Aubert\, and some other parts are based on my joint work with Suzuki.\n LOCATION:https://researchseminars.org/talk/LNTS/110/ END:VEVENT END:VCALENDAR