BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yupeng Wang (Chinese Academy of Sciences) DTSTART:20230315T070000Z DTEND:20230315T080000Z DTSTAMP:20260422T212929Z UID:PekiNT/1 DESCRIPTION:Title: I ntegral p-adic non-abelian Hodge theory for small representations\nby Yupeng Wang (Chinese Academy of Sciences) as part of PKU/BICMR Number Theo ry Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nThe abstrac t rendered in LaTeX is available on https://wwli.asia/index.php/en/seminar s-item-en/points2023-item-en\n\nZoom ID: 743 736 2326\n\nZoom Password: 01 3049\n LOCATION:https://researchseminars.org/talk/PekiNT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Li Lai (Tsinghua University) DTSTART:20230405T073000Z DTEND:20230405T083000Z DTSTAMP:20260422T212929Z UID:PekiNT/2 DESCRIPTION:Title: O n the irrationality of certain 2-adic zeta values\nby Li Lai (Tsinghua University) as part of PKU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nLet $\\zeta_2(\\cdot)$ be the Kubota-Leo poldt $2$-adic zeta function. We prove that\, for every nonnegative intege r $s$\, there exists an odd integer $j$ in the interval $[s+3\,3s+5]$ such that $\\zeta_2(j)$ is irrational. In particular\, at least one of $\\zeta _2(7)\,\\zeta_2(9)\,\\zeta_2(11)\,\\zeta_2(13)$ is irrational.\n\nOur appr oach is inspired by the recent work of Sprang. We construct explicit ratio nal functions. The Volkenborn integrals of the (higher order) derivatives of these rational functions produce good linear combinations of $1$ and $2 $-adic Hurwitz zeta values. The most difficult step is to prove that certa in Volkenborn integrals are nonzero\, which is resolved by careful manipul ation of the binomial coefficients.\n\nZoom number: 743 736 2326\n\nPasswo rd: 013049\n LOCATION:https://researchseminars.org/talk/PekiNT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fan Gao (Zhejiang University) DTSTART:20230412T073000Z DTEND:20230412T083000Z DTSTAMP:20260422T212929Z UID:PekiNT/3 DESCRIPTION:Title: S ome satisfactory and unsatisfactory aspects of the dual groups for central covers\nby Fan Gao (Zhejiang University) as part of PKU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nWe cons ider finite degree central covers of a linear reductive group in the local setting. Using some examples as the highlights\, we will explain the dual group of such a central cover\, and illustrate how much it captures the r epresentation-theoretic information of the central cover\, and also how mu ch it fails for the same purpose. We concentrate on two aspects of a repre sentation: formal degree and wavefront set.\n\nZoom number: 743 736 2326\n Zoom password: 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:King Fai Lai DTSTART:20230426T073000Z DTEND:20230426T083000Z DTSTAMP:20260422T212929Z UID:PekiNT/4 DESCRIPTION:Title: A remark on homological algebra\nby King Fai Lai as part of PKU/BICMR N umber Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\n( The talk is supposed to be in Chinese\, beamer-based)\n\n谈一谈关于 非交换环的同调代数的几方面。\n\nZoom number: 743 736 2326\n\ nZoom password: 013049\n LOCATION:https://researchseminars.org/talk/PekiNT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Koji Shimizu (YMSC) DTSTART:20230531T073000Z DTEND:20230531T083000Z DTSTAMP:20260422T212929Z UID:PekiNT/6 DESCRIPTION:Title: R obba site and Robba cohomology\nby Koji Shimizu (YMSC) as part of PKU/ BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbst ract\nWe will discuss a $p$-adic cohomology theory for rigid analytic vari eties with overconvergent structure (dagger spaces) over a local field of characteristic $p$. After explaining the motivation\, we will define a sit e (Robba site) and discuss its basic properties.\n\nFor online or hybrid t alks\, the Zoom number is 743 736 2326\, and the password is 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Esteban Rodríguez Camargo (Max-Planck-Institut für Mathemat ik) DTSTART:20230517T070000Z DTEND:20230517T083000Z DTSTAMP:20260422T212929Z UID:PekiNT/7 DESCRIPTION:Title: S olid locally analytic representations (Joint with Joaquín Rodrigues Jacin to)\nby Juan Esteban Rodríguez Camargo (Max-Planck-Institut für Math ematik) as part of PKU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nIn this talk I will introduce different categ ories of $p$-adic representations in the framework of condensed mathematic s. We give different geometric interpretations to them\, construct explici t adjunctions that serve to compare cohomology theories\, and see an appli cation to $p$-adic categorical local Langlands for $\\mathrm{GL}_1$.\n\nOn line talk. The Zoom number is 743 736 2326\, and the password is 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Bett (Harvard University) DTSTART:20230607T010000Z DTEND:20230607T020000Z DTSTAMP:20260422T212929Z UID:PekiNT/8 DESCRIPTION:Title: p -adic obstructions and Selmer sections\nby Alexander Bett (Harvard Uni versity) as part of PKU/BICMR Number Theory Seminar\n\n\nAbstract\nIn 1983 \, shortly after Faltings' resolution of the Mordell Conjecture\, Grothend ieck formulated his famous Section Conjecture\, positing that the set of r ational points on a projective curve Y of genus at least two should be equ al to a certain section set defined in terms of the etale fundamental grou p of Y. To this day\, this conjecture remains wide open\, with only a smal l handful of very special examples known. In this talk\, I will discuss re cent work with Jakob Stix\, in which we proved a Mordell-like finiteness t heorem for the "Selmer" part of the section set for any smooth projective curve Y of genus at least 2 over the rationals. This generalises the Falti ngs-Mordell Theorem\, and implies strong constraints on the finite descent locus from obstruction theory. The key new idea in our proof is an adapta tion of the recent proof of Mordell by Lawrence and Venkatesh to the study of the Selmer section set. Time permitting\, I will also briefly describe recent work with Theresa Kumpitsch and Martin Lüdtke in which we compute the Selmer section set in one example using the Chabauty-Kim method.\n\nO nline only. The Zoom number is 743 736 2326\, and the password is 013049.\ n LOCATION:https://researchseminars.org/talk/PekiNT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rui Chen (Zhejiang University) DTSTART:20230621T063000Z DTEND:20230621T073000Z DTSTAMP:20260422T212929Z UID:PekiNT/9 DESCRIPTION:Title: E xt-vanishing result for Gan-Gross-Prasad model\nby Rui Chen (Zhejiang University) as part of PKU/BICMR Number Theory Seminar\n\n\nAbstract\nIn t his talk we will show that the Ext-analogue of GGP model vanishes for temp ered representations\, as conjectured by D. Prasad. As a corollary\, this implies that the geometric multiplicity equals the Euler-Poincare characte ristic.\n\nthe Zoom number is 743 736 2326\, and the password is 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Lie Qian (Stanford University) DTSTART:20230719T010000Z DTEND:20230719T020000Z DTSTAMP:20260422T212929Z UID:PekiNT/10 DESCRIPTION:Title: Local Compatibility for Trianguline Representations\nby Lie Qian (Stan ford University) as part of PKU/BICMR Number Theory Seminar\n\nLecture hel d in Room 77201\, BICMR.\n\nAbstract\nTrianguline representations are a bi g class of $p$-adic representations that contain all nice enough (cristall ine) ones but allow a continuous variation of weights. Global consideratio n suggests that the $GL_2(\\mathbb{Q}_p)$ representation arising from a tr ianguline representation should have nonzero eigenspace under Emerton's Ja cquet functor. We prove this result using purely local method as well as a generalization to $p$-adic representation of $G_F$ for $F$ unramified ove r $\\mathbb{Q}_p$.\n\nFor online or hybrid talks\, the Zoom number is 743 736 2326\, and the password is 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiajun Ma (Xiamen University) DTSTART:20230904T070000Z DTEND:20230904T080000Z DTSTAMP:20260422T212929Z UID:PekiNT/11 DESCRIPTION:Title: Applications of Hecke Algebra in the Representation of Reductive Groups\nby Jiajun Ma (Xiamen University) as part of PKU/BICMR Number Theory Sem inar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nConsider a reduct ive linear algebraic group G. Let H be the generic Hecke algebra attached to the Weyl group of G. The representations of G and H have many deep con nections. In this talk\, I will discuss our two recent works where Hecke a lgebras play a crucial role: \n 1. Counting special unipotent representat ions of real reductive groups\n 2. Determining the theta correspondence o ver finite fields.\nI will also discuss the analog picture in the theta co rrespondence over p-adic fields when time permits.\n\nHybrid talk\n\nZoom livestream: ID 743 736 2326 / Password 013049\n LOCATION:https://researchseminars.org/talk/PekiNT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenji Fu (Bonn University) DTSTART:20230913T060000Z DTEND:20230913T070000Z DTSTAMP:20260422T212929Z UID:PekiNT/12 DESCRIPTION:Title: Explicit categorical mod l local Langlands correspondence for depth-zero s upercuspidal part of GL_2\nby Chenji Fu (Bonn University) as part of P KU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nA bstract\nLet $F$ be a non-archimedean local field. I will explicitly descr ibe:\n\n(1) (The category of quasicoherent sheaves on) The connected compo nent of the moduli space of Langlands parameters over $\\overline{\\mathbb {Z}_l}$ containing an irreducible tame L-parameter with $\\overline{\\math bb{F}_l}$ coefficients\;\n(2) the block of the category of smooth represen tations of $G(F)$ with $\\overline{\\mathbb{Z}_l}$ coefficients containing a depth-zero supercuspidal representation with $\\overline{\\mathbb{F}_l} $ coefficients.\n\nThe argument works at least for (simply connected) spli t reductive group $G$\, but I will focus on the example of $\\mathrm{GL}_2 $ for simplicity. The two sides turn out to match abstractly. If time perm its\, I will explain how to get the categorical local Langlands correspond ence for depth-zero supercuspidal part of $\\mathrm{GL}_2$ with $\\overlin e{\\mathbb{Z}_l}$ coefficients in Fargues-Scholze's form.\n\nHybrid talk\n \nZoom livestream: ID 743 736 2326 / Password 013049\n LOCATION:https://researchseminars.org/talk/PekiNT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Haruzo Hida (UCLA) DTSTART:20231011T070000Z DTEND:20231011T080000Z DTSTAMP:20260422T212929Z UID:PekiNT/13 DESCRIPTION:Title: Adjoint L-value formula and Period conjecture\nby Haruzo Hida (UCLA) a s part of PKU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nAbstract\nFor a Hecke eigenform $f$\, we state an adjoint L-val ue formula relative to each division quaternion algebra $D$ over ${\\mat hbb Q}$ with discriminant $\\partial$ and reduced norm $N$. A key to pr ove the formula is the theta correspondence for the quadratic ${\\mathbb Q }$-space $(D\,N)$. Under the $R=T$-theorem\, the $p$-part of the Bloch-Ka to conjecture is known\; so\, the formula is an adjoint Selmer class numbe r formula. We also describe how to relate the formula to a conjecture on p eriods of Shimura subvarieties of quaternionic Shimura varieties.\n\nZoom number: 743 736 2326\n\nZoom password: 013049\n LOCATION:https://researchseminars.org/talk/PekiNT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Weixiao Lu (MIT) DTSTART:20240104T070000Z DTEND:20240104T080000Z DTSTAMP:20260422T212929Z UID:PekiNT/14 DESCRIPTION:Title: Fourier-Jacobi period on unitary group\nby Weixiao Lu (MIT) as part of PKU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\ nAbstract\nWe formulate coarse spectral and geometric expansion of relativ e trace formula developed by Yifeng Liu and Hang Xue，and prove GGP conje ctures for Fourier-Jacobi period for unitary groups with arbitrary corank as a consequence. This is a joint work with Hang Xue and Paul Boisseau.\n\ nThe Zoom number is 743 736 2326\, and the password is 013049.\n LOCATION:https://researchseminars.org/talk/PekiNT/14/ END:VEVENT END:VCALENDAR