BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arnaud Mayeux (BICMR) DTSTART:20200506T080000Z DTEND:20200506T090000Z DTSTAMP:20260422T212923Z UID:POINTS/1 DESCRIPTION:Title: D ilatations and Néron blowups (with Timo Richarz and Matthieu Romagny) \nby Arnaud Mayeux (BICMR) as part of POINTS - Peking Online International Number Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/POINTS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Timo Richarz (TU Darmstadt) DTSTART:20200506T090000Z DTEND:20200506T100000Z DTSTAMP:20260422T212923Z UID:POINTS/2 DESCRIPTION:Title: A pplications of Néron blowups to integral models of moduli stacks of shtuk as\nby Timo Richarz (TU Darmstadt) as part of POINTS - Peking Online I nternational Number Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/POINTS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:James Newton (King's College London) DTSTART:20200513T100000Z DTEND:20200513T110000Z DTSTAMP:20260422T212923Z UID:POINTS/3 DESCRIPTION:Title: S ymmetric power functoriality for modular forms\nby James Newton (King' s College London) as part of POINTS - Peking Online International Number T heory Seminar\n\n\nAbstract\nLanglands functoriality predicts the transfer of automorphic representations along maps of L-groups. In particular\, th e symmetric power representation $\\mathrm{Symm}^{n-1}$ of $\\mathrm{GL}(2 )$ should give rise to a lifting from automorphic representations of $\\ma thrm{GL}(2)$ to automorphic representations of $\\mathrm{GL}(n)$. I will d iscuss joint work with Jack Thorne\, in which we prove the existence of al l symmetric power lifts for many cuspidal Hecke eigenforms (for example\, those of square-free level).\n\nZoom ID = 616 2536 2002 \; PIN = 672097\n LOCATION:https://researchseminars.org/talk/POINTS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Miyu Suzuki (Kanazawa University) DTSTART:20200617T070000Z DTEND:20200617T080000Z DTSTAMP:20260422T212923Z UID:POINTS/4 DESCRIPTION:Title: P rehomogeneous zeta functions and toric periods for inner forms of GL(2)\nby Miyu Suzuki (Kanazawa University) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nI will explain a new ap plication of prehomogeneous zeta functions to non-vanishing of periods of automorphic forms. The zeta functions we use were first introduced by F. S ato and a general theory is developed by the recent work of Wen-Wei Li. Th ey can be used to show non-vanishing of infinitely many toric periods of c uspidal representations of inner forms of $\\mathrm{GL}(2)$. If time permi ts\, I will mention future works based on the local theory of Wen-Wei Li. This is a joint work with Satoshi Wakatsuki.\n\nZoom ID = 691 6842 4338\n\ nPIN = 902454\n\nLink: https://zoom.com.cn/j/69168424338?pwd=Tms3bnlBRWl0V 1htMVV5dTZSZk9qQT09\n LOCATION:https://researchseminars.org/talk/POINTS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Huy Dang (University of Virginia) DTSTART:20200520T050000Z DTEND:20200520T060000Z DTSTAMP:20260422T212923Z UID:POINTS/5 DESCRIPTION:Title: H urwitz trees and deformations of Artin-Schreier covers\nby Huy Dang (U niversity of Virginia) as part of POINTS - Peking Online International Num ber Theory Seminar\n\n\nAbstract\nIn this talk\, we introduce the notion o f Hurwitz tree for an Artin-Schreier deformation (deformation of $\\mathbb {Z}/p$-covers in characteristic $p > 0$). It is a combinatorial-differenti al object that is endowed with essential degeneration data\, measured by K ato's refined Swan conductors\, of the deformation. We then show how the e xistence of a deformation between two covers with different branching data (e.g.\, different number of branch points) equates to the presence of a H urwitz tree with behaviors determined by the branching data. One applicati on of this result is to prove that the moduli space of Artin-Schreier cove rs of fixed genus $g$ is connected when $g$ is sufficiently large. If time permits\, we will discuss a generalization of the Hurwitz tree technique to all cyclic covers and beyond.\n\nZoom ID: 625 5863 1654\n\nPassword: 80 9410\n LOCATION:https://researchseminars.org/talk/POINTS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiyuan Wang (Johns Hopkins University) DTSTART:20200527T013000Z DTEND:20200527T023000Z DTSTAMP:20260422T212923Z UID:POINTS/6 DESCRIPTION:Title: T he Tate conjecture for a concrete family of elliptic surfaces\nby Xiyu an Wang (Johns Hopkins University) as part of POINTS - Peking Online Inter national Number Theory Seminar\n\n\nAbstract\nWe prove the Tate conjecture for a concrete family of elliptic surfaces. This is a joint work with Lia n Duan. In this talk\, I will begin with an general introduction to the Ta te conjecture and the Fontaine-Mazur conjecture. Then I will focus on the Tate conjecture for a family of elliptic surfaces introduced by Geemen and Top\, and try to explain the motivation and elementary idea behind the pr oof.\n\nZoom Conference number = 643 5504 3567\n\nPassword = 904742\n LOCATION:https://researchseminars.org/talk/POINTS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaolei Wan (National University of Singapore) DTSTART:20200708T010000Z DTEND:20200708T020000Z DTSTAMP:20260422T212923Z UID:POINTS/7 DESCRIPTION:Title: E xamples related to the Sakellaridis-Venkatesh conjecture\nby Xiaolei W an (National University of Singapore) as part of POINTS - Peking Online In ternational Number Theory Seminar\n\n\nAbstract\nIn this talk\, I will int roduce the Sakellaridis-Venkatesh conjecture on the decomposition of globa l period\, and give examples related to this conjecture. More specifically \, the cases $X = \\mathrm{SO}(n-1) \\backslash \\mathrm{SO}(n)$ and $X = \\mathrm{U}(2) \\backslash \\mathrm{SO}(5)$. In both cases\, I will determ ine the Plancherel decompositions of $L^2(X_v)$\, where $v$ is a local pla ce. Then I will prove the local relative character identity. In the global setting\, I will give the factorization of the global period of $X = \\ma thrm{SO}(n-1) \\backslash \\mathrm{SO}(n)$\, where the local functional co mes from the local Plancherel decomposition. The example $X = \\mathrm{U}( 2) \\backslash \\mathrm{SO}(5)$ is slightly beyond the SV conjecture but w e still have a decomposition of the global period as the sum of two factor izable elements.\n\nZoom ID: 646 0419 2446\n\nZoom password: 984662\n LOCATION:https://researchseminars.org/talk/POINTS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaoyu Zhang (Universität Duisburg-Essen) DTSTART:20200610T100000Z DTEND:20200610T110000Z DTSTAMP:20260422T212923Z UID:POINTS/8 DESCRIPTION:Title: p -adic family of modular forms on GSpin Shimura varieties\nby Xiaoyu Zh ang (Universität Duisburg-Essen) as part of POINTS - Peking Online Intern ational Number Theory Seminar\n\n\nAbstract\nThe theory of $p$-adic interp olation of modular forms on the upper half plane started with Serre for Ei senstein series and then was developed by Hida for ordinary cuspidal modul ar forms. This theory plays an important role in the construction of $p$-a dic $L$-functions\, modularity theorems\, etc. In this talk\, I will gener alize this theory to modular forms on $\\mathrm{GSpin}$ Shimura varieties. In such cases\, the ordinary locus may be empty and we need to work with the $\\mu$-ordinary locus. Then we follow Hida’s idea to construct $p$-a dic families of modular forms and give the control theorem on the dimensio n of the space of such $p$-adic families.\n\nZoom number: 682 6223 4350\n\ nPassword: 300890\n LOCATION:https://researchseminars.org/talk/POINTS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Linhui Shen (Michigan State University) DTSTART:20200603T013000Z DTEND:20200603T023000Z DTSTAMP:20260422T212923Z UID:POINTS/9 DESCRIPTION:Title: Q uantum geometry of moduli spaces of local systems\nby Linhui Shen (Mic higan State University) as part of POINTS - Peking Online International Nu mber Theory Seminar\n\n\nAbstract\nLet $G$ be a split semi-simple algebrai c group over $\\mathbb{Q}$. We introduce a natural cluster structure on mo duli spaces of G-local systems over surfaces with marked points. As a cons equence\, the moduli spaces of $G$-local systems admit natural Poisson str uctures\, and can be further quantized. We will study the principal series representations of such quantum spaces. It will recover many classical to pics\, such as the $q$-deformed Toda systems\, quantum groups\, and the mo dular functor conjecture for such representations. This talk will mainly b e based on joint work with A.B. Goncharov.\n\nZoom number: 681 9707 4659\n \nZoom password: 929593\n LOCATION:https://researchseminars.org/talk/POINTS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Dotto (University of Chicago) DTSTART:20200624T013000Z DTEND:20200624T023000Z DTSTAMP:20260422T212923Z UID:POINTS/10 DESCRIPTION:Title: Mod p Bernstein centres of p-adic groups\nby Andrea Dotto (University of Chicago) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nThe centre of the category of smooth mod $p$ repres entations of a $p$-adic reductive group does not distinguish the blocks of finite length representations\, in contrast with Bernstein's theory in ch aracteristic zero. Motivated by this observation and the known connections between the Bernstein centre and the local Langlands correspondence in fa milies\, we consider the case of $\\mathrm{GL}_2(\\mathbb{Q}_p)$ and we pr ove that its category of representations extends to a stack on the Zariski site of a simple geometric object: a chain $X$ of projective lines\, whos e points are in bijection with Paskunas's blocks. Taking the centre over e ach open subset we obtain a sheaf of rings on $X$\, and we expect the resu lting space to be closely related to the Emerton-Gee stack for $2$-dimensi onal representations of the absolute Galois group of $\\mathbb{Q}_p$. Join t work in progress with Matthew Emerton and Toby Gee.\n\nZoom ID: 650 3772 0269\n\nPassword: 585279\n LOCATION:https://researchseminars.org/talk/POINTS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jun Su (Cambridge University) DTSTART:20200701T080000Z DTEND:20200701T090000Z DTSTAMP:20260422T212923Z UID:POINTS/11 DESCRIPTION:Title: Arithmetic group cohomology: coefficients and automorphy\nby Jun Su (C ambridge University) as part of POINTS - Peking Online International Numbe r Theory Seminar\n\n\nAbstract\nCohomology of arithmetic subgroups\, with coefficients being algebraic representations of the corresponding reductiv e group\, has played an important role in the construction of Langlands co rrespondence. Traditionally the first step to access these objects is to v iew them as cohomology of (locally constant) sheaves on locally symmetric spaces and hence connect them with spaces of functions. However\, sometime s infinite dimensional coefficients also naturally arise\, e.g. when you t ry to attach elliptic curves to weight 2 eigenforms on $\\mathrm{GL}_2$ / an imaginary cubic field\, and the sheaf theoretic viewpoint might no long er be fruitful. In this talk we’ll explain a different but very simple u nderstanding of the connection between arithmetic group cohomology (with f inite dimensional coefficients) and function spaces\, and discuss the appl ication of this idea to infinite dimensional coefficients.\n\nZoom ID: 663 6110 0929\n\nZoom password: 059123\n\nLink: https://zoom.com.cn/j/6636110 0929?pwd=Y2JQdTd5QnhEOFBKWVRDR1JsV1VZZz09\n LOCATION:https://researchseminars.org/talk/POINTS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Esmail Arasteh Rad (Universität Münster) DTSTART:20200722T080000Z DTEND:20200722T090000Z DTSTAMP:20260422T212923Z UID:POINTS/12 DESCRIPTION:Title: Local models for moduli of global and local shtukas\nby Esmail Arasteh Rad (Universität Münster) as part of POINTS - Peking Online Internation al Number Theory Seminar\n\n\nAbstract\nModuli spaces for global $G$-shtuk as appear as function fields analogs for Shimura varieties. This can be ob served for example through Langlands philosophy. They possess local counte rparts which are called Rapoport-Zink spaces for local $P$-shtukas which s imilarly arise as function fields analogs for Rapoport-Zink spaces for $p$ -divisible groups. In this talk we first recall the construction of these moduli stacks (spaces)\, and after providing some preliminary backgrounds\ , we discuss the theory of local models for them. If time permits we also discuss some of the applications.\n\nZoom ID: 646 7802 6902\n\nPassword: 7 62858\n\nLink: https://zoom.com.cn/j/64678026902?pwd=VUdTbUsvQmtYamhwT2dWb TZCSmx6Zz09\n LOCATION:https://researchseminars.org/talk/POINTS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Kei Yuen Chan (Shanghai Center for Mathematical Sciences) DTSTART:20200813T070000Z DTEND:20200813T080000Z DTSTAMP:20260422T212923Z UID:POINTS/13 DESCRIPTION:Title: Gan-Gross-Prasad conjectures for general linear groups\nby Kei Yuen Ch an (Shanghai Center for Mathematical Sciences) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nIn this talk\, I will talk about restriction problems of general linear groups over local and global fields\, surrounding Gan-Gross-Prasad conjectures. In particula r\, I will discuss a local conjecture on predicting the branching laws of the non-tempered representations arisen from Arthur packets and my recent work on a proof of the conjecture. Along the way\, I will also discuss som e significant properties of restrictions such as multiplicity one\, Ext-va nishing\, projectivity and indecomposability.\n\nZoom ID: 688 0605 5569\n\ nZoom Password: 773605\n\nZoom Link: https://zoom.com.cn/j/68806055569?pwd =MFczUVdvc1JpeWdKVEhyR3J2VXdMZz09\n LOCATION:https://researchseminars.org/talk/POINTS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuanqing Cai (Kyoto University) DTSTART:20200826T023000Z DTEND:20200826T033000Z DTSTAMP:20260422T212923Z UID:POINTS/14 DESCRIPTION:Title: Doubling integrals for Brylinski-Deligne extensions of classical groups\nby Yuanqing Cai (Kyoto University) as part of POINTS - Peking Online In ternational Number Theory Seminar\n\n\nAbstract\nIn the 1980s\, Piatetski- Shapiro and Rallis discovered a family of Rankin-Selberg integrals for the classical groups that did not rely on Whittaker models. This is the so-ca lled doubling method. It grew out of Rallis' work on the inner products of theta lifts -- the Rallis inner product formula.\n\nRecently\, a family o f global integrals that represent the tensor product L-functions for class ical groups (joint with Friedberg\, Ginzburg\, and Kaplan) and the tensor product L-functions for covers of symplectic groups (Kaplan) was discovere d. These can be viewed as generalizations of the doubling method. In this talk\, we explain how to develop the doubling integrals for Brylinski-Deli gne extensions of all connected classical groups. This gives a family of E ulerian global integrals for this class of non-linear extensions.\n\nZoom ID = 688 8198 6448\n\nZoom Password = 472875\n\nZoom Link = https://zoom.c om.cn/j/68881986448?pwd=d3BCRzR2Q1AwM0hyV1RHVCtFcnR4UT09\n LOCATION:https://researchseminars.org/talk/POINTS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jinhe Ye (MSRI) DTSTART:20201021T080000Z DTEND:20201021T090000Z DTSTAMP:20260422T212923Z UID:POINTS/15 DESCRIPTION:Title: Lovely pairs of valued fields and adic spaces\nby Jinhe Ye (MSRI) as p art of POINTS - Peking Online International Number Theory Seminar\n\nLectu re held in Science Building 1\, room 1303\, Peking University (Yanyuan cam pus).\n\nAbstract\nHrushovski and Loeser used the space \\(\\widehat{V}\\) of generically stable types concentrating on \\(V\\) to study the topolog y of Berkovich analytification \\(V^{an}\\) of \\(V\\). In this talk we wi ll give a brief introduction to this object and present an alternative app roach\, based on lovely pairs of valued fields\, to study various analytif ications using model theory. We will provide a model-theoretic counterpart \\(\\widetilde{V}\\) of the Huber's analytification of \\(V\\). We show t hat\, the same as for \\(\\widehat{V}\\)\, the space \\(\\widetilde{V}\\) is strict pro-definable.\n\nFurthermore\, we will discuss canonical liftin gs of the deformation retraction developed by Hrushovski and Loeser. This is a joint project with Pablo Cubides-Kovacsics and Martin Hils.\n\nThe ta lk will be given in the offline + online duplex mode.\n\nZoom ID: 649 4104 826\n\nPassowrd: 143688\n\nLink: https://zoom.com.cn/j/64941048264?pwd=aU I5ZWQvbTYwVmlEekowZ0w0eTZ4UT09\n LOCATION:https://researchseminars.org/talk/POINTS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg-Universität Mainz) DTSTART:20201125T063000Z DTEND:20201125T073000Z DTSTAMP:20260422T212923Z UID:POINTS/16 DESCRIPTION:Title: Hilbert's irreducibility theorem for abelian varieties\nby Ariyan Java npeykar (Johannes Gutenberg-Universität Mainz) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nWe will discuss joint work with Corvaja\, Demeio\, Lombardo\, and Zannier in which we ext end Hilbert's irreducibility theorem (for rational varieties) to the setti ng of abelian varieties. Roughly speaking\, given an abelian variety A ove r a number field k and a ramified covering X of A\, we show that X has "le ss" k-rational points than A.\n\nZoom ID: 637 7860 6108\n\nZoom Password: 742636\n\nURL: https://zoom.com.cn/j/63778606108?pwd=RlpyQWR2MlRDbTZzcmlha 09oRVd6QT09\n LOCATION:https://researchseminars.org/talk/POINTS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Yang (Harvard University) DTSTART:20201223T030000Z DTEND:20201223T040000Z DTSTAMP:20260422T212923Z UID:POINTS/17 DESCRIPTION:Title: Finiteness and the Tate Conjecture in Codimension 2 for K3 Squares\nby Ziquan Yang (Harvard University) as part of POINTS - Peking Online Intern ational Number Theory Seminar\n\n\nAbstract\nTwo years ago\, via a refined CM lifting theory\, Ito-Ito-Koshikawa proved the Tate Conjecture for squa res of K3 surfaces over finite fields by reducing to Tate's theorem on the endomorphisms of abelian varieties. I will explain a different proof\, wh ich is based on a twisted version of Fourier-Mukai transforms between K3 s urfaces. In particular\, I do not use Tate's theorem after assuming some k nown properties of individual K3's. The main purpose of doing so is to ill ustrate Tate's insight on the connection between the Tate conjecture and t he positivity results in algebraic geometry for codimension 2 cycles\, thr ough some "geometry in cohomological degree 2".\n\nZoom ID = 613 5332 8443 \n\nPassword = 182269\n\nLink = https://zoom.com.cn/j/61353328443?pwd=eEpa NkpCdTBER3o1eFJER2NaS29qUT09\n LOCATION:https://researchseminars.org/talk/POINTS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiroshi Ishimoto (Kyoto University) DTSTART:20210121T070000Z DTEND:20210121T080000Z DTSTAMP:20260422T212923Z UID:POINTS/18 DESCRIPTION:Title: A proof of Ibukiyama's conjecture on Siegel modular forms of half-integra l weight and of degree 2\nby Hiroshi Ishimoto (Kyoto University) as pa rt of POINTS - Peking Online International Number Theory Seminar\n\n\nAbst ract\nIn 2006\, Ibukiyama conjectured that there is a linear isomorphism between a space of Siegel cusp forms of degree $2$ of integral weight and that of half-integral weight. With Arthur's multiplicity formula on the odd special orthogonal group $\\mathrm{SO}(5)$ and Gan-Ichino's multiplic ity formula on the metaplectic group $\\mathrm{Mp}(4)$\, Ibukiyama's conj ecture can be proven in a representation theoretic way.\n\nZoom Link: http s://zoom.com.cn/j/68649455267?pwd=RjZ1RXNZRGxIVkM5cnIzd3pmVnBjdz09\n\nID: 686 4945 5267\n\nPassword: 376422\n LOCATION:https://researchseminars.org/talk/POINTS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhixiang Wu (Université Paris-Saclay) DTSTART:20210407T070000Z DTEND:20210407T080000Z DTSTAMP:20260422T212923Z UID:POINTS/19 DESCRIPTION:Title: Companion forms and partially classical eigenvarieties\nby Zhixiang Wu (Université Paris-Saclay) as part of POINTS - Peking Online Internationa l Number Theory Seminar\n\n\nAbstract\nIn general\, there exist $p$-adic a utomorphic forms of different weights with the same associated $p$-adic Ga lois representation. The existence of these companion forms is also predic ted by Breuil's locally analytic socle conjecture in the $p$-adic local La nglands program. Under the Taylor-Wiles assumption\, Breuil-Hellmann-Schra en proved the existence of all companion forms when the associated crystal line Galois representations have regular Hodge-Tate weights. In this talk\ , I will explain how to generalize their results to some cases when the Ho dge-Tate weights are not necessarily regular. The method relies on Ding's construction of partially classical eigenvarieties and their relationships with some spaces of Galois representations.\n\nZoom ID: 648 9548 7663\n\n Zoom password: 525224\n LOCATION:https://researchseminars.org/talk/POINTS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jinbo Ren (University of Virginia) DTSTART:20210521T020000Z DTEND:20210521T030000Z DTSTAMP:20260422T212923Z UID:POINTS/20 DESCRIPTION:Title: Some applications of Diophantine Approximation to Group theory\nby Jin bo Ren (University of Virginia) as part of POINTS - Peking Online Internat ional Number Theory Seminar\n\n\nAbstract\nTranscendental Number Theory te lls us an essential difference between transcendental numbers and algebrai c numbers is that the former can be approximated by rational numbers ``ver y well’’ but not the latter. More specifically\, one has the following Fields Medal work by Roth. Given a real algebraic number $a$ of degree $\ \geq 3$ and any $\\delta>0$\, there is a constant $c=c(a\,\\delta)>0$ such that for any rational number $\\eta$\, we have $|\\eta-a|>c H(\\eta)^{-\\ delta}$\, where $H(\\eta)$ is the height of $\\eta$. Moreover\, we have Sc hmidt’s Subspace theorem\, a non-trivial generalization of Roth’s theo rem.\n \nOn the other hand\, we have the notion of Bounded Generation in G roup Theory. An abstract group $\\Gamma$ is called Boundedly Generated if there exist $g_1\,g_2\,\\cdots\, g_r\\in \\Gamma$ such that $\\Gamma=\\lan gle g_1\\rangle \\cdots \\langle g_r\\rangle$ where $\\langle g\\rangle$ i s the cyclic group generated by $g$. While being a purely combinatorial pr operty of groups\, bounded generation has a number of interesting conseque nces and applications in different areas. For example\, bounded generation has close relation with Serre’s Congruence Subgroup Problem and Marguli s-Zimmer conjecture.\n \nIn my recent joint work with Corvaja\, Rapinchuk and Zannier\, we applied an ``algebraic geometric’’ version of Roth an d Schmidt’s theorems\, i.e. Laurent’s theorem\, to prove a series of r esults about when a group is boundedly generated. In particular\, we have shown that a finitely generated anisotropic linear group over a field of c haracteristic zero has bounded generation if and only if it is virtually a belian\, i.e. contains an abelian subgroup of finite index.\n \nIn my talk \, I will explain the idea of this proof and give certain open questions.\ n\nZoom ID: 854 7383 4027\n\nPassword: 562471\n LOCATION:https://researchseminars.org/talk/POINTS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Zicheng Qian (Toronto University) DTSTART:20210602T020000Z DTEND:20210602T030000Z DTSTAMP:20260422T212923Z UID:POINTS/21 DESCRIPTION:Title: Moduli of Fontaine-Laffaille modules and mod p local-global compatibility< /a>\nby Zicheng Qian (Toronto University) as part of POINTS - Peking Onlin e International Number Theory Seminar\n\nLecture held in 77201\, Beijing I nternational Center for Mathematical Research\, Peking University.\n\nAbst ract\nWe introduce a set of invariant functions on the moduli of Fontaine- Laffaille modules and prove that they separate points on the moduli in a s uitable sense. Consequently\, we prove the following local-lobal compatibi lity result for suitable global set up and under standard Kisin-Taylor-Wil es conditions: the Hecke eigenspace attached to a modular mod \\(p\\) glob al Galois representation determines its restriction at a place unramified over \\(p\\)\, if the restriction is Fontaine-Laffaille and has a generic semisimplification. The genericity assumption is mild and explicit. This i s a joint work with D. Le\, B.V. Le Hung\, S. Morra and C. Park.\n\nZoom I D: 881 3287 2530\n\nZoom Password: 898924\n LOCATION:https://researchseminars.org/talk/POINTS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Tsimerman (University of Toronto) DTSTART:20210610T020000Z DTEND:20210610T030000Z DTSTAMP:20260422T212923Z UID:POINTS/22 DESCRIPTION:Title: Abelian Varieties not Isogeneous to Jacobians - in Arbitrary Characteristi c\nby Jacob Tsimerman (University of Toronto) as part of POINTS - Peki ng Online International Number Theory Seminar\n\nLecture held in Room 7720 1 at BICMR.\n\nAbstract\n(Joint w/ Ananth Shankar) We prove that over an a rbitrary global field\, for every $g>3$ there exists an abelian variety wh ich is not isogenous to a Jacobian.\n\nZOOM ID: 869 4660 9830\n\nCode: 219 147\n LOCATION:https://researchseminars.org/talk/POINTS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Weibo Fu (Princeton University) DTSTART:20211202T005000Z DTEND:20211202T015000Z DTSTAMP:20260422T212923Z UID:POINTS/23 DESCRIPTION:Title: A derived construction of eigenvarieties\nby Weibo Fu (Princeton Unive rsity) as part of POINTS - Peking Online International Number Theory Semin ar\n\nLecture held in 77201\, Beijing International Center for Mathematica l Research\, Peking University.\n\nAbstract\nWe construct a derived varian t of Emerton's eigenvarieties using the locally analytic representation th eory of p-adic groups. The main innovations include comparison and exploit ation of two homotopy equivalent completed complexes associated to the loc ally symmetric spaces of a quasi-split reductive group 𝔾\, comparison t o overconvergent cohomology\, proving exactness of finite slope part funct or\, together with some representation-theoretic statements. As a global a pplication\, we exhibit an eigenvariety coming from data of $\\mathrm{GL}_ n$ over a CM field as a subeigenvariety for a quasi-split unitary group.\n \nZoom number: 828 5069 1379\n\nPassword: 046645\n LOCATION:https://researchseminars.org/talk/POINTS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Chung-Ru Lee (Duke University) DTSTART:20220106T020000Z DTEND:20220106T030000Z DTSTAMP:20260422T212923Z UID:POINTS/24 DESCRIPTION:Title: Endoscopic Relative Orbital Integrals on a Unitary Group\nby Chung-Ru Lee (Duke University) as part of POINTS - Peking Online International Numb er Theory Seminar\n\n\nAbstract\nThe characterization of distinguished rep resentations is crucial for studying automorphic representations. The cele brated conjectures of Sakellaridis and Venkatesh provide such a characteri zation in many cases. In particular\, they provide a conjectural descripti on of the representations of a split reductive group that are distinguishe d by a split reductive spherical subgroup. However\, there remain many mys teries when the generic stabilizer is disconnected.\n\nThe comparison of r elative trace formulae\, initially suggested by Jacquet\, has been one of the most effective ways to study distinction problems in automorphic repre sentation theory. Stabilization is a pivotal step for the comparison of re lative trace formulae. To prepare for stabilization\, one needs to investi gate the endoscopic relative orbital integrals.\n\nIn this talk\, we study the endoscopy theory for unitary groups in a relative setting where the g eneric stabilizer is disconnected and finite over a $p$-adic field. This t alk aims to compute an explicit formula for endoscopic relative orbital in tegrals.\n\nZoom number: 859 0713 0926\n\nPassword: 243862\n LOCATION:https://researchseminars.org/talk/POINTS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Liyang Yang (Princeton University) DTSTART:20220113T010000Z DTEND:20220113T020000Z DTSTAMP:20260422T212923Z UID:POINTS/25 DESCRIPTION:Title: The Jacquet-Zagier Trace Formula for GL(n)\nby Liyang Yang (Princeton University) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nThe so-called Jacquet-Zagier trace formula was esta blished by Jacquet and Zagier for GL(2) for two main reasons: deducing the holomorphy of adjoint L-functions and generalizing Selberg's trace formul a in a different way from Arthur's truncation process. In this talk we wil l describe Jacquet-Zagier'strace formula in higher ranks. It plays a role in the study of holomorphic continuation of automorphic L-functions and ce rtain Artin L-functions.\n\nZoom number: 816 7216 0068\n\nPassword: 536786 \n LOCATION:https://researchseminars.org/talk/POINTS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Yasuhiro Terakado (National Center for Theoretical Sciences) DTSTART:20220303T023000Z DTEND:20220303T040000Z DTSTAMP:20260422T212923Z UID:POINTS/26 DESCRIPTION:Title: Mass formula on the basic loci of unitary Shimura varieties\nby Yasuhi ro Terakado (National Center for Theoretical Sciences) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nWe study a mass of the group of self-quasi-isogenies of the abelian variety corres ponding to a point on the basic locus in the reduction modulo p of a GU(r\ ,s) Shimura variety. We give explicit formulas for the number of irreducib le components of the basic locus\, and for the cardinality of the zero-dim ensional Ekedahl-Oort stratum\, in a Shimura variety associated with a uni modular Hermitian lattice. On the way\, we also give a formula for the num ber of connected components of a Shimura variety. This is joint work with Chia-Fu Yu.\n\nZoom ID: 830 7759 2753\n\nPassword: 814734\n LOCATION:https://researchseminars.org/talk/POINTS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Shih-Yu Chen (Academia Sinica) DTSTART:20220314T023000Z DTEND:20220314T033000Z DTSTAMP:20260422T212923Z UID:POINTS/27 DESCRIPTION:Title: Algebraicity of critical values of automorphic L-functions: Examples and C onjectures\nby Shih-Yu Chen (Academia Sinica) as part of POINTS - Peki ng Online International Number Theory Seminar\n\n\nAbstract\nIn this talk\ , we introduce some algebraicity results on the critical values of automor phic $L$-functions. The techniques in these examples are integral represen tation of automorphic $L$-functions\, constant terms of Eisenstein series\ , and their cohomological interpretations. \nThese results are compatible with Clozel's conjecture on existence of motives associated to algebraic c uspidal automorphic representations of general linear groups and Deligne's conjecture on algebraicity of critical values of motivic $L$-functions.\n \nZoom ID：817 4314 0004\n\nZoom PW：199319\n LOCATION:https://researchseminars.org/talk/POINTS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Shih-Yu Chen (Academia Sinica) DTSTART:20220316T023000Z DTEND:20220316T033000Z DTSTAMP:20260422T212923Z UID:POINTS/28 DESCRIPTION:Title: On Deligne's conjecture for critical values of tensor product L-functions and symmetric power L-functions of modular forms\nby Shih-Yu Chen (Aca demia Sinica) as part of POINTS - Peking Online International Number Theor y Seminar\n\n\nAbstract\nIn this talk\, we introduce our result on the alg ebraicity of ratios of product of critical values of Rankin--Selberg $L$-f unctions and its applications. \nMore precisely\, let $\\mathit{\\Sigma\,\ \Sigma'}$ (resp. $\\mathit{\\Pi\,\\Pi'}$) be cohomological tamely isobaric automorphic representations of $\\mathrm{GL}_n(\\mathbb{A})$ (resp. $\\ma thrm{GL}_{n'}(\\mathbb{A})$) such that $\\mathit{\\Sigma}_\\infty = \\math it{\\Sigma}_\\infty'$ and $\\mathit{\\Pi}_\\infty = \\mathit{\\Pi}_\\infty '$. It is a consequence of Deligne's conjecture on critical $L$-values tha t the ratio \n\\[\n\\frac{L(s\, \\mathit{\\Sigma} \\times \\mathit{\\Pi}) \\cdot L(s\,\\mathit{\\Sigma}' \\times \\mathit{\\Pi}')}{L(s\,\\mathit{\\S igma} \\times \\mathit{\\Pi}')\\cdot L(s\,\\mathit{\\Sigma}' \\times \\mat hit{\\Pi})}\n\\]\nis algebraic and Galois-equivariant at critical points.\ nWe show that this assertion holds under certain parity and regularity con ditions.\nAs applications\, we prove Deligne's conjecture for some tensor product $L$-functions and symmetric odd power $L$-functions for $\\mathrm{ GL}_2$.\n\nZoom ID：817 4314 0004\n\nZoom password：199319\n LOCATION:https://researchseminars.org/talk/POINTS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandeep Varma (Tata Institute of Fundamental Research) DTSTART:20220406T023000Z DTEND:20220406T033000Z DTSTAMP:20260422T212923Z UID:POINTS/29 DESCRIPTION:Title: On residues of certain intertwining operators\nby Sandeep Varma (Tata Institute of Fundamental Research) as part of POINTS - Peking Online Inter national Number Theory Seminar\n\n\nAbstract\nLet $G$ be a connected reduc tive group over a finite extension $F$ of $\\mathbb{Q}_p$. Let $P = MN$ be a Levi decomposition of a maximal parabolic subgroup of $G$\, and $\\pi$ an irreducible unitary supercuspidal representation of $M(F)$. One can the n consider the representation $Ind_{P(F)}^{G(F)} \\pi$ (normalized parabol ic induction). Assume that $P$ is conjugate to an opposite by an element $ w_0 \\in G(F)$ that normalizes $M$\, and which fixes the isomorphism class of $\\pi$ (i.e.\, $\\pi \\cong \\\,^{w_0}\\pi$). Then\, by the work of Ha rish-Chandra\, $Ind_{P(F)}^{G(F)} \\pi$ is irreducible if and only if a ce rtain family $A(s\, \\pi\, w_0)$ of so called intertwining operators has a pole at $s = 0$. In this case\, after making certain choices\, the residu e of $A(s\, \\pi\, w_0)$ at $s = 0$ can be captured by a scalar $R(\\tilde \\pi) \\in \\mathbb{C}$\, which has a conjectural expression in terms of some gamma factors related to Shahidi's local coefficients\, as described by Arthur's local intertwining relation.\n\nFollowing a program pioneered by Freydoon Shahidi\, and furthered by him as well as David Goldberg\, Ste ven Spallone\, Wen-Wei Li\, Li Cai\, Bin Xu\, Xiaoxiang Yu etc.\, one seek s to:\n\n(a) get explicit expressions to describe $R(\\tilde \\pi)$ \; and \n(b) interpret the resulting expression for $R(\\tilde \\pi)$ suitably\, using the theory of endoscopy when applicable.\n\nSo far\, these questions have been studied mostly for classical (including unitary) groups\, or in some simple situations. We will discuss (a) above in a non-classical and slightly "less simple" situation\, in the cases where $G$ is an almost sim ple group whose absolute root system is of exceptional type or of type $B_ n$ with $n \\geq 3$ or $D_n$ with $n \\geq 4$\, and where $P$ is a "Heisen berg parabolic subgroup". We will then comment on what we can say of (b) a bove in the $G_2$\, $B_3$ and $D_4$ cases. Though the reducibility results and the $R(\\tilde \\pi)$ values are more or less already known in these cases by the Langlands-Shahidi method and related results (e.g.\, the work of Henniart and Lomeli and Caihua Luo in the case of $D_4$)\, our investi gations also suggest the existence of harmonic analytic expressions for ce rtain gamma values\, which in some cases just amount to the formal degree conjecture of Ichino\, Ikeda and Hiraga\, but in other cases seem slightly unwieldy and perhaps intriguing.\n\nZoom link: https://us02web.zoom.us/j/ 81501452154?pwd=OWVtRmU0bFpoMEY3OUxrVW04STFJQT09\n\nZoom number: 815 0145 2154\n\nZoom password: 363804\n LOCATION:https://researchseminars.org/talk/POINTS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Petrov (Harvard University) DTSTART:20220330T020000Z DTEND:20220330T033000Z DTSTAMP:20260422T212923Z UID:POINTS/30 DESCRIPTION:Title: On arithmetic characterization of local systems of geometric origin\nb y Alexander Petrov (Harvard University) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nI will talk about the p roblem of classifying local systems of geometric origin on algebraic varie ties over complex numbers.\n\nConjecture: For a smooth algebraic variety \ \(S\\) over a finitely generated field \\(F\\) \, a semi-simple \\(\\mathb b{Q}_l\\)-local system on \\(S_{\\bar{F}}\\) is of geometric origin if and only if it extends to a local system on \\(S_{F'} \\) for a finite extens ion \\(F' \\supset F\\) .\n\nMy main goal will be to provide motivation fo r this conjecture arising from the Fontaine-Mazur conjecture\, and survey known results and related problems.\n\nZoom number: 827 4915 3248\n\nZoom password: 623413\n LOCATION:https://researchseminars.org/talk/POINTS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Heuer (Universität Bonn) DTSTART:20220413T073000Z DTEND:20220413T083000Z DTSTAMP:20260422T212923Z UID:POINTS/31 DESCRIPTION:Title: Moduli spaces in p-adic non-abelian Hodge theory\nby Ben Heuer (Univer sität Bonn) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nIn analogy to Simpson's non-abelian Hodge theory o ver the complex numbers\, the p-adic Simpson correspondence over non-archi medean fields like \\(C_p\\) aims to relate p-adic representations of the étale fundamental group of a smooth proper rigid space \\(X\\) to Higgs b undles on \\(X\\). In this talk\, I will introduce p-adic moduli spaces fo r either side of the correspondence\, and explain how these can be compare d by way of a non-abelian generalisation of the Hodge-Tate sequence. This allows one to construct new geometric incarnations of the p-adic Simpson c orrespondence\, and to interpret the choices necessary for its formulation in a geometric fashion.\n\nZoom ID: 818 0595 3631\n\nZoom password: 74630 4\n LOCATION:https://researchseminars.org/talk/POINTS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Haoyang Guo (Max-Planck-Institut für Mathematik) DTSTART:20220420T073000Z DTEND:20220420T083000Z DTSTAMP:20260422T212923Z UID:POINTS/32 DESCRIPTION:Title: Prismatic approach to crystalline local systems\nby Haoyang Guo (Max-P lanck-Institut für Mathematik) as part of POINTS - Peking Online Internat ional Number Theory Seminar\n\n\nAbstract\nLet \\(X\\) be a smooth proper scheme over a \\(p\\)-adic field such that \\(X\\) has a good reduction. I nspired by the de Rham comparison theorem in complex geometry\, Grothendie ck asked if there is a "mysterious functor" relating étale cohomology of the generic fiber and crystalline cohomology of the special fiber. This qu estion was answered by work of many people\, including Fontaine and Faltin gs. In particular\, this motivates the definition of a \\(p\\)-adic Galois representation being crystalline\, generalizing the étale cohomology of \\(X\\) as above. In this talk\, we will give an overview for the prismati c approach of Bhatt-Scholze on crystalline representations. Moreover\, joi ntly with Emanuel Reinecke\, we will consider the higher dimensional gener alization of this approach on crystalline local systems.\n\nZoom ID: 818 0 595 3631\n\nZoom password: 746304\n LOCATION:https://researchseminars.org/talk/POINTS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Hongjie Yu (IST Austria) DTSTART:20220427T073000Z DTEND:20220427T083000Z DTSTAMP:20260422T212923Z UID:POINTS/33 DESCRIPTION:Title: Number of irreducible representations in the cuspidal automorphic spectrum \nby Hongjie Yu (IST Austria) as part of POINTS - Peking Online Intern ational Number Theory Seminar\n\n\nAbstract\nLet \\(G\\) be a reductive gr oup defined and split over a global function field. We are interested in t he sum of multiplicities of irreducible representations containing a regul ar depth zero representation of \\(G(O)\\)\, where \\(O\\) is the ring of integral adeles\, in the automorphic cuspidal spectrum. The sum is express ed in terms of the number of \\(\\mathbb{F}_q\\)-points of Hitchin moduli spaces of groups associated to \\(G\\). When \\( G=GL(n) \\)\, it implies some cases of Deligne's conjecture by Langlands correspondence.\n\nZoom in fo: TBA\n LOCATION:https://researchseminars.org/talk/POINTS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Romanov (University of New South Wales) DTSTART:20220511T070000Z DTEND:20220511T083000Z DTSTAMP:20260422T212923Z UID:POINTS/34 DESCRIPTION:Title: A Soergel bimodule approach to the character theory of real groups\nby Anna Romanov (University of New South Wales) as part of POINTS - Peking O nline International Number Theory Seminar\n\n\nAbstract\nAdmissible repres entations of real reductive groups are a key player in the world of unitar y representation theory. The characters of irreducible admissible represen tations were described by Lustig-Vogan in the 80's in terms of a geometric ally-defined module over the associated Hecke algebra. In this talk\, I'll describe a categorification of a block of the LV module using Soergel bim odules.\n\nZoom ID: 820 4104 2066\n\nZoom password: 456409\n LOCATION:https://researchseminars.org/talk/POINTS/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Chung Pang Mok (Soochow University) DTSTART:20220415T023000Z DTEND:20220415T040000Z DTSTAMP:20260422T212923Z UID:POINTS/35 DESCRIPTION:Title: Pseudorandom Vectors Generation Using Elliptic Curves And Applications to Wiener Processes\nby Chung Pang Mok (Soochow University) as part of PO INTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nUs ing the arithmetic of elliptic curves over finite fields\, we present an a lgorithm for the efficient generation of sequence of uniform pseudorandom vectors in high dimension with long period\, that simulates sample sequenc e of a sequence of independent identically distributed random variables\, with values in the hypercube $[0\,1]^d$ with uniform distribution. As an a pplication\, we obtain\, in the discrete time simulation\, an efficient al gorithm to simulate\, uniformly distributed sample path sequence of a sequ ence of independent standard Wiener processes.\n\nZoom ID: 873 3108 4904\n \nZoom password: 750799\n LOCATION:https://researchseminars.org/talk/POINTS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Frahm (Aarhus Universitet) DTSTART:20220518T070000Z DTEND:20220518T083000Z DTSTAMP:20260422T212923Z UID:POINTS/36 DESCRIPTION:Title: Analytic continuation of branching laws for unitary representations\nb y Jan Frahm (Aarhus Universitet) as part of POINTS - Peking Online Interna tional Number Theory Seminar\n\n\nAbstract\nBranching problems ask for the behaviour of the restriction of an irreducible representation of a group $G$ to a subgroup $H$. In the context of smooth representations of real re ductive groups\, this typically leads to the study of multiplicities with which an irreducible representation of $H$ occurs as a quotient of an irre ducible representation of $G$. Here\, both quantitative results such as mu ltiplicity-one theorems and qualitative results such as the Gan-Gross-Pras ad conjectures are of interest.\n\nIn the context of unitary representatio ns of real reductive groups\, one can go a step further and explicitly dec ompose an irreducible representation of $G$ into a direct integral of irre ducible representations of $H$. I will explain how branching laws for unit ary representations are related to those in the smooth category\, and how one can use an analytic continuation procedure along a principal series pa rameter to obtain explicit branching laws from certain Plancherel formulas for homogeneous spaces.\n\nZoom ID: 863 3902 9748\n\nZoom password: 83135 2\n LOCATION:https://researchseminars.org/talk/POINTS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Cheng Chen (University of Minnesota) DTSTART:20220601T113000Z DTEND:20220601T123000Z DTSTAMP:20260422T212923Z UID:POINTS/37 DESCRIPTION:Title: The local Gross-Prasad conjecture over archimedean local fields\nby Ch eng Chen (University of Minnesota) as part of POINTS - Peking Online Inter national Number Theory Seminar\n\n\nAbstract\nThe local Gross-Prasad conje cture is a refinement of the multiplicity one theorem for spherical pairs of Bessel type defined by a pair of special orthogonal groups. The conject ure shows that there is exactly one representation having multiplicity equ al to one in each Vogan packet (with generic parameter) and it also depict s this unique representation with an epsilon character. I will introduce s ome recent progress for the conjecture over \\(\\mathbb{R}\\) and \\(\\mat hbb{C}\\)\, part of the work was joint with Z. Luo. This local conjecture is a necessary ingredient for the global Gross-Prasad conjecture. Besides\ , the codimension-one case of the conjecture is closely related to the bra nching problem for special orthogonal groups.\n\nZoom ID: 852 3108 0387\n\ nZoom password: 625020\n LOCATION:https://researchseminars.org/talk/POINTS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Masatosho Kitagawa (Waseda University) DTSTART:20220824T060000Z DTEND:20220824T070000Z DTSTAMP:20260422T212923Z UID:POINTS/38 DESCRIPTION:Title: Uniformly bounded multiplicities in the branching problem and D-modules\nby Masatosho Kitagawa (Waseda University) as part of POINTS - Peking On line International Number Theory Seminar\n\n\nAbstract\nIn the representat ion theory of real reductive Lie groups\, several finiteness results of le ngths and multiplicities are known and fundamental. The Harish-Chandra adm issibility theorem and the finiteness of the length of Verma modules and p rincipal series representations are typical examples.\n\nMore precisely\, such multiplicities and lengths are bounded on some parameter sets. T. Osh ima and T. Kobayashi ('13 adv. math.) gave a criterion on which branching laws have (uniformly) bounded multiplicities.\n\nIn arXiv:2109.05556\, I d efined uniform boundedness of a family of $\\mathscr{D}$-modules (and $\\m athfrak{g}$-modules) to treat the boundedness properties uniformly. I will talk about its definition and applications. In particular\, I will give a necessary and sufficient condition on uniform boundedness of multipliciti es in the branching problem of real reductive Lie groups.\n\nZoom Number: 949 6559 4176\n\nZoom password: 071166\n LOCATION:https://researchseminars.org/talk/POINTS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Lue Pan (Princeton University) DTSTART:20220830T013000Z DTEND:20220830T030000Z DTSTAMP:20260422T212923Z UID:POINTS/39 DESCRIPTION:Title: Regular de Rham Galois representations in the completed cohomology of modu lar curves\nby Lue Pan (Princeton University) as part of POINTS - Peki ng Online International Number Theory Seminar\n\nLecture held in 77201\, B ICMR.\n\nAbstract\nLet $p$ be a prime. I want to explain how to use the ge ometry of modular curves at infinite level and Hodge-Tate period map to st udy $p$-adic regular de Rham Galois representations appearing in the $p$-a dically completed cohomology of modular curves. We will show that these Ga lois representations up to twists come from modular forms and give a geome tric description of the locally analytic representations of $\\mathrm{GL}_ 2(\\mathbb{Q}_p)$ associated to them. These results were previously known by totally different methods.\n\nZoom ID = 953 6788 4415\n\nZoom password = 373352\n LOCATION:https://researchseminars.org/talk/POINTS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Arthur-César Le Bras (CNRS - IRMA Strasbourg) DTSTART:20220914T070000Z DTEND:20220914T080000Z DTSTAMP:20260422T212923Z UID:POINTS/40 DESCRIPTION:Title: A Fourier transform for Banach-Colmez spaces\nby Arthur-César Le Bras (CNRS - IRMA Strasbourg) as part of POINTS - Peking Online International Number Theory Seminar\n\n\nAbstract\nI will explain how to define an \\(\\ ell\\)-adic Fourier transform for Banach-Colmez spaces and discuss some e xamples. This is a joint work with Anschütz\, which was motivated by the study of Fargues' geometrization conjecture for \\(\\mathrm{GL}_n\\).\n\nZ oom number: 921 5562 6500\n\nPassword: 760747\n LOCATION:https://researchseminars.org/talk/POINTS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhiyou Wu (BICMR) DTSTART:20220921T053000Z DTEND:20220921T070000Z DTSTAMP:20260422T212923Z UID:POINTS/41 DESCRIPTION:Title: S=T for Shimura varieties\nby Zhiyou Wu (BICMR) as part of POINTS - Pe king Online International Number Theory Seminar\n\n\nAbstract\nI will expl ain how the new $p$-adic geometry developed by Scholze can help prove the Eichler-Shimura relation for Shimura varieties of Hodge type\, which has n othing to do with $p$-adic geometry a priori.\n\nZoom number: 916 4653 889 4\n\nPassword: 275417\n LOCATION:https://researchseminars.org/talk/POINTS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Xinwen Zhu (Stanford University) DTSTART:20221019T053000Z DTEND:20221019T063000Z DTSTAMP:20260422T212923Z UID:POINTS/42 DESCRIPTION:Title: The p-adic Borel hyperbolicity of A_g\nby Xinwen Zhu (Stanford Univers ity) as part of POINTS - Peking Online International Number Theory Seminar \n\n\nAbstract\nA theorem of Borel says that any holomorphic map from a sm ooth complex algebraic variety to a smooth arithmetic variety is automatic ally an algebraic map. The key ingredient is to show that any holomorphic map from the punctured disc to the arithmetic variety has no essential sin gularity. I will discuss some work towards a p-adic analogue of this theor em for Shimura varieties of Hodge type. Joint with Abhishek Oswal and Anan th Shankar.\n\nZoom ID: 995 9287 0950\n\nZoom password: 311062\n LOCATION:https://researchseminars.org/talk/POINTS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Haoyang Guo (MPIM) DTSTART:20221026T070000Z DTEND:20221026T080000Z DTSTAMP:20260422T212923Z UID:POINTS/43 DESCRIPTION:Title: Prismatic approach to Fontaine's C_crys conjecture\nby Haoyang Guo (MP IM) as part of POINTS - Peking Online International Number Theory Seminar\ n\n\nAbstract\nGiven a smooth proper scheme over a \\(p\\)-adic ring of in tegers\, Fontaine's \\(C_{\\mathrm{crys}}\\) conjecture says that the éta le cohomology of its generic fiber is isomorphic to the crystalline cohomo logy of its special fiber\, after base changing them to the crystalline pe riod ring. In this talk\, we give a prismatic proof of the conjecture\, fo r general coefficients\, in the relative setting\, and allowing ramified b ase rings. This is a joint work with Emanuel Reinecke.\n\nLink: https://zo om.us/j/7437362326?pwd=UXd3RzBiUWZNK2Vhdm05R0c5VlJEUT09\n\nZoom ID: 743 73 6 2326\n\nZoom password: 013049\n LOCATION:https://researchseminars.org/talk/POINTS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuel Scheidegger (BICMR) DTSTART:20221102T053000Z DTEND:20221102T063000Z DTSTAMP:20260422T212923Z UID:POINTS/44 DESCRIPTION:Title: Aspects of modularity for Calabi-Yau threefolds\nby Emanuel Scheidegge r (BICMR) as part of POINTS - Peking Online International Number Theory Se minar\n\n\nAbstract\nWe give an overview of some mostly conjectural aspect s of modularity for Calabi-Yau threefolds. We focus on one parameter famil ies of hypergeometric type and give computational results in terms of clas sical modular forms. In one case we show an explicit correspondence.\n\nLi nk: https://zoom.us/j/7437362326?pwd=UXd3RzBiUWZNK2Vhdm05R0c5VlJEUT09\n\nZ oom ID: 743 736 2326\n\nZoom password: 013049\n LOCATION:https://researchseminars.org/talk/POINTS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Breuil (CNRS - Orsay) DTSTART:20221130T080000Z DTEND:20221130T090000Z DTSTAMP:20260422T212923Z UID:POINTS/45 DESCRIPTION:Title: Multivariable (phi\, Gamma)-modules and modular representations of Galois and GL2\nby Christophe Breuil (CNRS - Orsay) as part of POINTS - Pekin g Online International Number Theory Seminar\n\n\nAbstract\nLet \\(p\\) be a prime number\, \\(K\\) a finite unramified extension of \\(\\mathbf{Q}_ p\\)\, and \\(\\pi\\) a smooth representation of \\(\\mathrm{GL}_2(K)\\) o n some Hecke eigenspace in the \\(H^1\\) mod \\(p\\) of a Shimura curve. O ne can associate to \\(\\pi\\) a multivariable \\( (\\phi\, O_K^*)\\)-modu le \\(D_A(\\pi) \\). I will state a conjecture which describes \\( D_A(\\p i) \\) in terms of the underlying 2-dimensional mod \\(p\\) representation of \\(\\mathrm{Gal}(\\bar{K}/K)\\). When the latter is semi-simple (suffi ciently generic)\, I will sketch a proof of this conjecture. This is joint work with F. Herzig\, Y. Hu\, S. Morra and B. Schraen.\n\nZoom number: 74 3 736 2326\n\nZoom password: 013049\n LOCATION:https://researchseminars.org/talk/POINTS/45/ END:VEVENT END:VCALENDAR