BEGIN:VCALENDAR
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PRODID:researchseminars.org
CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Arnaud Mayeux (BICMR)
DTSTART;VALUE=DATE-TIME:20200506T080000Z
DTEND;VALUE=DATE-TIME:20200506T090000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200506T090000Z
DTEND;VALUE=DATE-TIME:20200506T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200513T100000Z
DTEND;VALUE=DATE-TIME:20200513T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200617T070000Z
DTEND;VALUE=DATE-TIME:20200617T080000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200520T050000Z
DTEND;VALUE=DATE-TIME:20200520T060000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200527T013000Z
DTEND;VALUE=DATE-TIME:20200527T023000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200708T010000Z
DTEND;VALUE=DATE-TIME:20200708T020000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200610T100000Z
DTEND;VALUE=DATE-TIME:20200610T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200603T013000Z
DTEND;VALUE=DATE-TIME:20200603T023000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200624T013000Z
DTEND;VALUE=DATE-TIME:20200624T023000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200701T080000Z
DTEND;VALUE=DATE-TIME:20200701T090000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200722T080000Z
DTEND;VALUE=DATE-TIME:20200722T090000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200813T070000Z
DTEND;VALUE=DATE-TIME:20200813T080000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20200826T023000Z
DTEND;VALUE=DATE-TIME:20200826T033000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20201021T080000Z
DTEND;VALUE=DATE-TIME:20201021T090000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20201125T063000Z
DTEND;VALUE=DATE-TIME:20201125T073000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20201223T030000Z
DTEND;VALUE=DATE-TIME:20201223T040000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20210121T070000Z
DTEND;VALUE=DATE-TIME:20210121T080000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20210407T070000Z
DTEND;VALUE=DATE-TIME:20210407T080000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20210521T020000Z
DTEND;VALUE=DATE-TIME:20210521T030000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20210602T020000Z
DTEND;VALUE=DATE-TIME:20210602T030000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20210610T020000Z
DTEND;VALUE=DATE-TIME:20210610T030000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20211202T005000Z
DTEND;VALUE=DATE-TIME:20211202T015000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20220106T020000Z
DTEND;VALUE=DATE-TIME:20220106T030000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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;VALUE=DATE-TIME:20220113T010000Z
DTEND;VALUE=DATE-TIME:20220113T020000Z
DTSTAMP;VALUE=DATE-TIME:20220128T023710Z
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
END:VCALENDAR