BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xu Gao (UC Santa Cruz) DTSTART:20230316T210000Z DTEND:20230316T220000Z DTSTAMP:20260423T022806Z UID:UCSD_NTS/83 DESCRIPTION:Title: $p$-adic representations and simplicial distance in Bruhat-Tits building s\nby Xu Gao (UC Santa Cruz) as part of UCSD number theory seminar\n\n Lecture held in APM 6402 and online.\n\nAbstract\n$p$-adic representations are important objects in number theory\, and stable lattices serve as a c onnection between the study of ordinary and modular representations. These stable lattices can be understood as stable vertices in Bruhat-Tits build ings. From this viewpoint\, the study of fixed point sets in these buildin gs can aid research on $p$-adic representations. The simplicial distance h olds an important role as it connects the combinatorics of lattices and th e geometry of root systems. In particularly\, the fixed-point sets of Moy- Prasad subgroups are precisely the simplicial balls. In this talk\, I'll e xplain those findings and compute their simplicial volume under certain co nditions.\n\npre-talk at 1:20pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/83/ END:VEVENT END:VCALENDAR