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BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20210206T000000Z
DTEND:20210206T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/1
DESCRIPTION:Title: Reduction Theory\, revisited\nby Yiannis Sakellaridi
s (Johns Hopkins University) as part of Automorphic Project & Research Sem
inar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Atobe (Hokkaido University)
DTSTART:20210220T000000Z
DTEND:20210220T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/2
DESCRIPTION:Title: Construction of local A-packets\nby Hiraku Atobe (Ho
kkaido University) as part of Automorphic Project & Research Seminar\n\n\n
Abstract\nA-packets for classical groups were introduced in Arthur's endos
copic classification. Elements of local A-packets are the local components
of discrete automorphic representations. Since they are characterized by
endoscopic character identities\, it is difficult to make local A-packets
explicit. In this talk\, I will talk about a refinement of Moeglin's expli
cit construction of local A-packets. In particular\, I will explain a non-
vanishing criterion\, and how to specify elements of a given local A-packe
t. Furthermore\, I will propose a conjectural formula for the Aubert duali
ty of representations of Arthur type.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20210213T000000Z
DTEND:20210213T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/4
DESCRIPTION:Title: Reduction theory: proofs.\nby Yiannis Sakellaridis (
Johns Hopkins University) as part of Automorphic Project & Research Semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Michigan)
DTSTART:20210306T000000Z
DTEND:20210306T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/5
DESCRIPTION:Title: Background on the Gan-Gross-Prasad Conjecture\nby Da
vid Schwein (University of Michigan) as part of Automorphic Project & Rese
arch Seminar\n\n\nAbstract\nIn 2009 Gan\, Gross\, and Prasad conjectured a
branching law\nfor a classical group over a local field\, in other words\
, a rule for\nhow irreducible representations decompose on restriction to\
n(classical) subgroups. Last year the authors generalized their\nconjectu
re to non-tempered parameters\, as Gan will explain in a future\ntalk.\n\n
This talk serves as background for Gan's talk. In the first part\,\nwe'll
use the Ramanujan-Petersson Conjecture and Satake's\ngeneralization of it
to motivate and introduce several concepts\nsurrounding the conjectural b
ranching law\, among them L- and A-packets\nand tempered and generic repre
sentations. In the second part\, a warm\nup to the general conjecture\, w
e'll summarize some of what is known\nabout the branching law of the gener
al linear group.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wee Teck Gan (National University of Singapore)
DTSTART:20210313T000000Z
DTEND:20210313T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/6
DESCRIPTION:Title: Nontempered Restriction Problems for Classical Groups\nby Wee Teck Gan (National University of Singapore) as part of Automorph
ic Project & Research Seminar\n\n\nAbstract\nI will discuss an extension o
f the Gross-Pasad conjectures to the setting of nontempered A-packets\, me
ntion some progress and highlight some subtleties in the nontempered setti
ng. In particular\, I will highlight how our conjecture can be viewed as a
concrete manifestation of the framework of Ben-Zvi-Sakellaridis-Venkatesh
relating restriction problems to symplectic geometry. This is joint work
with Gross and Prasad.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spencer Leslie (Duke University)
DTSTART:20210320T000000Z
DTEND:20210320T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/7
DESCRIPTION:Title: Pre-stabilization and endoscopic groups\nby Spencer
Leslie (Duke University) as part of Automorphic Project & Research Seminar
\n\n\nAbstract\nThe stabilization of the (twisted) trace formula is an eno
rmous program that lies behind many of the topics in this seminar (L- and
A-packets\, for example). An important first step in this program is pre-s
tabilization of the geometric side\, where one introduces stable and unsta
ble orbital integrals. As background for the talk on my work towards stabi
lizing certain relative trace formulas\, I review this concept in a genera
l setting of a reductive group G acting on a smooth affine variety X. A go
al is to highlight problems that arise in this more general setting\, addi
ng simplifying assumptions as we go. I will then specialize to the group c
ase and review the introduction of endoscopic groups to account for the un
stable terms.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spencer Leslie (Duke University)
DTSTART:20210327T000000Z
DTEND:20210327T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/8
DESCRIPTION:Title: Endoscopy for certain symmetric spaces\nby Spencer L
eslie (Duke University) as part of Automorphic Project & Research Seminar\
n\n\nAbstract\nRelative trace formulas are powerful tools in the study of
periods of automorphic forms. However in many cases of interest\, basic st
ability problems have not been addressed. I will discuss a notion of endos
copy with the goal of stabilizing the relative trace formula associated to
a symmetric subgroup. The main example is that of unitary Friedberg–Jac
quet periods\, which are related to special cycles in certain unitary Shim
ura varieties. After introducing the endoscopic symmetric spaces in this c
ase\, I will sketch the proof of the\nfundamental lemma.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Delorme (Institut de Mathématiques de Marseille)
DTSTART:20210410T000000Z
DTEND:20210410T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/9
DESCRIPTION:Title: On the spectral theorem of Langlands\nby Patrick Del
orme (Institut de Mathématiques de Marseille) as part of Automorphic Proj
ect & Research Seminar\n\n\nAbstract\nWe show that the Hilbert subspace o
f $L^2(G(F)\\backslash G(\\mathbb A))$ is generated by wave packets of Ei
senstein series built from discrete series is the whole space.\n\nTogether
with the work of E. Lapid on the asymptotic formula for the truncated inn
er product of Eisenstein series built from discrete series\, it achieves
a proof of the spectral theorem of R.P. Langlands based on the work of J
. Bernstein and E. Lapid on the meromorphic continuation of these Eisen
stein series.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20210417T000000Z
DTEND:20210417T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/10
DESCRIPTION:Title: An introduction to Vogan's refinement of the local Lang
lands conjecture\nby Tasho Kaletha (University of Michigan) as part of
Automorphic Project & Research Seminar\n\n\nAbstract\nIn an influential p
aper from 1993\, Vogan introduced many new ideas into the realm of the loc
al Langlands correspondence. These include the notion of a pure inner form
\, compound L-packets\, the infinitesimal character of a Langlands paramet
ers\, the stable Bernstein center\, and a geometric point of view on Langl
ands parameters. I will give an introduction to these ideas as a preparati
on for upcoming research talks by Clifton Cunningham and Peter Dillery.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART:20210424T000000Z
DTEND:20210424T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/11
DESCRIPTION:Title: The geometry of local Arthur packets\nby Clifton Cu
nningham (University of Calgary) as part of Automorphic Project & Research
Seminar\n\n\nAbstract\nThis talk presents Vogan's geometric perspective o
n L-packets and A-packets for $p$-adic groups. We will explain how every L
-packet $\\Pi_\\phi$ can be enlarged to a so-called ABV-packet $\\Pi^\\tex
t{ABV}_\\phi$\, roughly determined by studying the conormal bundle to the
moduli space of Langlands parameters with the same infinitesimal parameter
as $\\phi$. This study also defines a distribution attached to every ABV-
packet. It is conjectured that these distributions provide a basis for sta
ble distributions and that ABV-packets are A-packets when $\\phi$ is of Ar
thur type. We will discuss evidence for this conjecture and progress towar
d a proof.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill Casselman (University of British Columbia)
DTSTART:20210403T000000Z
DTEND:20210403T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/12
DESCRIPTION:Title: Analysis on arithmetic quotients: solved and open probl
ems\nby Bill Casselman (University of British Columbia) as part of Aut
omorphic Project & Research Seminar\n\n\nAbstract\nGodement suggested a lo
ng time ago that in the long run the proper way to understand the theory o
f automorphic forms from an analytic point of view was to interpret them a
s distributions of moderate growth on arithmetic quotients. This allows so
me useful clarification about foundations\, but also a few novel proofs of
old results — for example the trace formula for SL(2) — as well as so
me natural if probably difficult conjectures. I'll try to give an introduc
tion to this somewhat vast topic.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Zhang (MIT)
DTSTART:20210508T000000Z
DTEND:20210508T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/13
DESCRIPTION:Title: AFL over F\nby Wei Zhang (MIT) as part of Automorph
ic Project & Research Seminar\n\n\nAbstract\nThe Arithmetic Fundamental Le
mma (AFL) conjecture over a p-adic field $F$ arises from relative trace fo
rmula approach to the arithmetic Gan-Gross-Prasad conjecture for unitary g
roups. It is an identity relating the first derivative of Jacquet--Rallis
orbital integrals and arithmetic intersection numbers on unitary Rapoport-
-Zink moduli space. The case $F=Q_p$ was proved about two years ago\, and
I will speak on a recent proof (joint work with A. Mihatsch) of this conje
cture for a general p-adic field $F$.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masao Oi (Kyoto University)
DTSTART:20210515T000000Z
DTEND:20210515T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/14
DESCRIPTION:Title: Geometric L-packets of Howe-unramified toral supercuspi
dal representations I\nby Masao Oi (Kyoto University) as part of Autom
orphic Project & Research Seminar\n\n\nAbstract\nIn our talks\, I and Char
lotte Chan are going to talk about our comparison result on Yu’s supercu
spidal representations and representations geometrically constructed by Ch
an-Ivanov.\nIn my talk of the first week\, I will focus on the algebraic p
art of our result.\nEspecially\, I will first review Yu's construction of
supercuspidal representations.\nThen I will explain that some of those sup
ercuspidals (which we call Howe-unramified toral supercuspidals) can be re
covered by looking at their Harish-Chandra characters only at some specifi
c elements.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART:20210522T000000Z
DTEND:20210522T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/15
DESCRIPTION:Title: Geometric L-packets of Howe-unramified toral supercuspi
dal representations II\nby Charlotte Chan (MIT) as part of Automorphic
Project & Research Seminar\n\n\nAbstract\nLast week Masao discussed a cha
racterization theorem for some regular supercuspidal representations. This
week\, we discuss geometric aspects of our project. I will talk about Del
igne--Lusztig varieties and their deeper-level analogues\, and illustrate
the role of a characterization theorem for representations of parahoric su
bgroups. We will see that the cohomology of these varieties respects Kalet
ha's L-packets in a very natural way.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Krishna (Brandeis University)
DTSTART:20210501T000000Z
DTEND:20210501T010000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/16
DESCRIPTION:Title: An introduction to the arithmetic GGP conjecture and th
e arithmetic fundamental lemma.\nby Rahul Krishna (Brandeis University
) as part of Automorphic Project & Research Seminar\n\n\nAbstract\nI will
explain the statement of\, and some motivation for\, the arithmetic Gan–
Gross–Prasad (GGP) conjecture for unitary groups. Then after a quick ref
resher on the relative trace formula of Jacquet–Rallis\, I will give a s
omewhat impressionistic description of the RTF approach to this conjecture
\, and explain the statement of the "main local ingredient": the arithmeti
c fundamental lemma. This is background material for Wei Zhang's talk next
week.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Michigan)
DTSTART:20211015T130000Z
DTEND:20211015T143000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/17
DESCRIPTION:Title: Rigid inner forms over function fields\nby Peter Di
llery (University of Michigan) as part of Automorphic Project & Research S
eminar\n\n\nAbstract\nThe goal of this talk is to define rigid inner forms
\, first introduced by Kaletha in the setting of fields of characteristic
zero\, for local and global function fields. This entails studying torsors
on gerbes $E$ canonically associated to a class in $H^2(F\,A)$\, for $A$
a special canonically-defined profinite group over F our field. We will sp
end time introducing the abstract machinery required to work with such obj
ects. We then discuss the applications to the local and global Langlands c
onjectures. Locally\, this includes a statement of the refined local Langl
ands conjectures for a general (i.e.\, not necessarily quasi-split) connec
ted reductive group G over a local function field which generalizes Vogan'
s statement that used pure inner twists (as discussed in Kaletha's talk*).
Globally\, this includes a statement of the conjectural multiplicity form
ula for automorphic representations of a connected reductive G over a glob
al function field.\n\n*Kaletha's background talk from last semester is ava
ilable for viewing under the "past talks" column on researchseminars.org.\
n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (Jussieu)
DTSTART:20211022T130000Z
DTEND:20211022T143000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/18
DESCRIPTION:Title: A nonabelian Fourier transform for tempered unipotent r
epresentations of p-adic groups I\nby Anne-Marie Aubert (Jussieu) as p
art of Automorphic Project & Research Seminar\n\n\nAbstract\nIn the repres
entation theory of finite reductive groups\, an essential role is played b
y Lusztig's nonabelian Fourier transform\, an involution on the space of u
nipotent characters the group. This involution is the change of bases matr
ix between the basis of irreducible characters and the basis of `almost ch
aracters'\, certain class functions attached to character sheaves. \nFor r
eductive p-adic groups\, the unipotent local Langlands correspondence give
s a natural parametrization of irreducible smooth representations with uni
potent cuspidal support. However\, many questions about the characters of
these representations are still open. Motivated by the study of the charac
ters on compact elements\, we introduce in joint work with B. Romano (arXi
v:2106.13969) an involution on the spaces of elliptic and compact tempered
unipotent representations of pure inner twists of a split simple p-adic g
roup. This generalizes a construction by Moeglin and Waldspurger (2003\, 2
016) for elliptic tempered representations of split orthogonal groups\, an
d potentially gives another interpretation of a Fourier transform for p-ad
ic groups introduced by Lusztig (2014). We conjecture that the restriction
to reductive quotients of maximal compact open subgroups intertwines this
involution with a disconnected version of Lusztig's nonabelian Fourier tr
ansform for finite reductive groups. \nIn these talks\, we will present t
he necessary background (the unipotent local Langlands correspondence\, fa
milies of representations of finite reductive groups\, complex nilpotent o
rbits)\, explain the definition and basic properties of the nonabelian Fou
rier transform\, the conjecture about compact restrictions\, and give supp
orting evidence for the conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Ciubotaru (University of Oxford)
DTSTART:20211029T130000Z
DTEND:20211029T143000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/19
DESCRIPTION:Title: A nonabelian Fourier transform for tempered unipotent r
epresentations of p-adic groups II\nby Dan Ciubotaru (University of Ox
ford) as part of Automorphic Project & Research Seminar\n\n\nAbstract\nIn
the representation theory of finite reductive groups\, an essential role i
s played by Lusztig's nonabelian Fourier transform\, an involution on the
space of unipotent characters the group. This involution is the change of
bases matrix between the basis of irreducible characters and the basis of
`almost characters'\, certain class functions attached to character sheave
s. \nFor reductive p-adic groups\, the unipotent local Langlands correspon
dence gives a natural parametrization of irreducible smooth representation
s with unipotent cuspidal support. However\, many questions about the char
acters of these representations are still open. Motivated by the study of
the characters on compact elements\, we introduce in joint work with B. Ro
mano (arXiv:2106.13969) an involution on the spaces of elliptic and compac
t tempered unipotent representations of pure inner twists of a split simpl
e p-adic group. This generalizes a construction by Moeglin and Waldspurger
(2003\, 2016) for elliptic tempered representations of split orthogonal g
roups\, and potentially gives another interpretation of a Fourier transfor
m for p-adic groups introduced by Lusztig (2014). We conjecture that the r
estriction to reductive quotients of maximal compact open subgroups intert
wines this involution with a disconnected version of Lusztig's nonabelian
Fourier transform for finite reductive groups. \nIn these talks\, we will
present the necessary background (the unipotent local Langlands correspon
dence\, families of representations of finite reductive groups\, complex n
ilpotent orbits)\, explain the definition and basic properties of the nona
belian Fourier transform\, the conjecture about compact restrictions\, and
give supporting evidence for the conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (CNRS Marseille)
DTSTART:20211105T130000Z
DTEND:20211105T143000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/20
DESCRIPTION:Title: Review of Rankin-Selberg integrals and the non-Archimed
ean theory of new vectors\nby Raphaël Beuzart-Plessis (CNRS Marseille
) as part of Automorphic Project & Research Seminar\n\n\nAbstract\nAs a pr
eparation for Peter Humphries' talk\, I will review the basics on Rankin-S
elberg theory and the non-Archimedean theory of new (or essential) vectors
mostly following work of Jacquet\, Piatetski-Shapiro and Shalika.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University of Virginia)
DTSTART:20211112T133000Z
DTEND:20211112T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/21
DESCRIPTION:Title: Newform Theory for $\\mathrm{GL}_n$\nby Peter Humph
ries (University of Virginia) as part of Automorphic Project & Research Se
minar\n\n\nAbstract\nWe shall discuss three interrelated notions in the th
eory of automorphic forms and automorphic representations: newforms\, $L$-
functions\, and conductors. In particular\, we cover how to define the new
form associated to an automorphic representation of $\\mathrm{GL}_n$\, how
to realise certain $L$-functions as period integrals involving newforms\,
and how to quantify the ramification of an automorphic representation in
terms of properties of the newform. A key emphasis is the union of approac
hes to defining newforms in both nonarchimedean and archimedean settings.
Finally\, we will briefly discuss notions of newforms for groups other tha
n $\\mathrm{GL}_n$.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20211119T133000Z
DTEND:20211119T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/22
DESCRIPTION:Title: no seminar\nby no seminar as part of Automorphic Pr
oject & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20211126T133000Z
DTEND:20211126T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/23
DESCRIPTION:Title: no seminar\nby no seminar as part of Automorphic Pr
oject & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilbert Moss (University of Utah)
DTSTART:20211203T133000Z
DTEND:20211203T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/24
DESCRIPTION:Title: Moduli spaces of Langlands parameters\nby Gilbert M
oss (University of Utah) as part of Automorphic Project & Research Seminar
\n\n\nAbstract\nThe local Langlands correspondence connects representation
of p-adic groups to Langlands parameters\, which are certain representati
ons of Galois groups of local fields. In recent work with Dat\, Helm\, and
Kurinczuk\, we have shown that Langlands parameters\, when viewed through
the right lens\, occur naturally within a moduli space over Z[1/p]\, and
we can say some things about the geometry of this moduli space. Its geomet
ry should be reflected in the representation theory of p-adic groups\, on
the other side of the local Langlands correspondence. The "local Langlands
in families" conjecture describes the moduli space of Langlands parameter
s in terms of the integral center of the category of representations of th
e p-adic group. It was established for GL(n) in 2018 and we will discuss s
ome work in progress toward generalizing it to quasi-split classical group
s.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Vogan (MIT)
DTSTART:20211210T133000Z
DTEND:20211210T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/25
DESCRIPTION:Title: Unipotent Representations of Complex Groups I\nby D
avid Vogan (MIT) as part of Automorphic Project & Research Seminar\n\n\nAb
stract\nArthur in 1983 conjectured the existence of a family of representa
tions of reductive groups over local fields\, intermediate between tempere
d representations and unitary representations. In 1985 Barbasch and I cons
tructed representations for complex reductive groups satisfying some of Ar
thur's desiderata.\n\nI was charged with explaining this 1985 paper\, beca
use of the seminar target of "topics which have not been covered in the be
st possible way in the literature." In fact I will talk about the general
structure of the local Langlands conjecture\, and try to explain how that
leads (conjecturally over any local field) to a construction of Arthur's r
epresentations. I will try to say in passing what Barbasch and I did.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (Oxford University)
DTSTART:20211217T133000Z
DTEND:20211217T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/26
DESCRIPTION:Title: Unipotent Representations of Complex Groups II\nby
Lucas Mason-Brown (Oxford University) as part of Automorphic Project & Res
earch Seminar\n\n\nAbstract\nUnipotent representations are a mysterious cl
ass of representations of a semisimple Lie group over the real or complex
numbers\, which are conjectured to form the `building blocks' of the unita
ry dual. In 1985\, Barbasch and Vogan defined a class of representations o
f a complex semisimple Lie group called `special unipotent representations
.' These representations have proven to be fundamental objects in the stud
y of unitary representations\, but they constitute only a fraction of all
unipotent representations (for example\, the metaplectic representations a
re excluded). In this talk\, I will propose a more general definition of '
unipotent\,' inspired by the Orbit Method. I will catalog the properties o
f our unipotent representations (including their classification) and descr
ibe an intriguing relationship between our representations and those of Ba
rbasch-Vogan\, which I call "refined Barbasch-Vogan duality." This talk is
based on joint work with Ivan Losev and Dmitryo Matvieievskyi.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Chenevier & Olivier Taïbi (École Normale Supérieure)
DTSTART:20220128T133000Z
DTEND:20220128T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/28
DESCRIPTION:Title: Inexistence\, dimension formulas and classification for
level one algebraic cusp forms\nby Gaëtan Chenevier & Olivier Taïbi
(École Normale Supérieure) as part of Automorphic Project & Research Se
minar\n\n\nAbstract\n[Please note: there will be 2 talks\, 45' each.]\n\nI
n the first lecture we will explain how improvements on using\nan old tool
in analytic number theory\, Riemann-Weil's explicit formula\nfor L-functi
ons\, allowed us to prove the non-existence of level one\nalgebraic cusp f
orms for general linear groups over Q for lots of\ninfinitesimal character
s (=sets of Hodge weights). In the second\nlecture we will explain how th
ese vanishing results yield an\n"effortless" method to compute the geometr
ic side of Arthur's\n$L^2$-Lefschetz trace formula for split classical gro
ups with the unit of\nthe unramified Hecke algebra. We obtain dimension f
ormulas as a\nconsequence. Together these results give classification the
orems for\nlevel one algebraic cusp forms in motivic weight <=23.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit Nijmegen)
DTSTART:20220204T133000Z
DTEND:20220204T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/29
DESCRIPTION:Title: Affine Hecke algebras in the representation theory of p
-adic groups\nby Maarten Solleveld (Radboud Universiteit Nijmegen) as
part of Automorphic Project & Research Seminar\n\n\nAbstract\nThe main goa
l of these two talks is to discuss a local Langlands correspondence for un
ipotent representations of reductive p-adic groups. We will focus on the m
ost important technique that goes into it\, namely affine Hecke algebras.
This technique is available in large generality\, and likewise a substanti
al part of talks will play in a general setting. \n\nIn the first we talk
we survey the role of affine Hecke algebras for representations of reducti
ve p-adic groups. We will look at types and progenerators for Bernstein bl
ocks\, and we will see how they give rise to some sort of Hecke algebras.
We introduce affine Hecke algebras and discuss some aspects of their repre
sentation theory. That will be used for a parametrization of irreducible r
epresentations in one Bernstein block. Then we will discuss the basic prop
erties of unipotent representations of reductive groups over finite or p-a
dic fields. We end with the Hecke algebras for unipotent Bernstein blocks.
\n\nThe second talk is situated on the Galois side of the local Langlands
correspondence. There we will build structures analogous to those for repr
esentations of reductive p-adic groups: cuspidality\, Bernstein components
and affine Hecke algebras. Generalizing work of Lusztig\, we show that th
e irreducible representations of these Hecke algebras are naturally parame
trized by suitable sets of enhanced L-parameters.\n\nIn the case of unipot
ent representations\, we are able to match all the aforementioned structur
e on the p-adic side with the similar structure on the Galois side\, in bi
jective fashion. This leads to a local Langlands correspondence for unipot
ent representations\, which satisfies many functorial properties.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit Nijmegen)
DTSTART:20220211T133000Z
DTEND:20220211T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/30
DESCRIPTION:Title: Hecke algebras and a local Langlands correspondence for
unipotent representations\nby Maarten Solleveld (Radboud Universiteit
Nijmegen) as part of Automorphic Project & Research Seminar\n\n\nAbstract
\nThe main goal of these two talks is to discuss a local Langlands corresp
ondence for unipotent representations of reductive p-adic groups. We will
focus on the most important technique that goes into it\, namely affine He
cke algebras. This technique is available in large generality\, and likewi
se a substantial part of talks will play in a general setting. \n\nIn the
first we talk we survey the role of affine Hecke algebras for representati
ons of reductive p-adic groups. We will look at types and progenerators fo
r Bernstein blocks\, and we will see how they give rise to some sort of He
cke algebras. We introduce affine Hecke algebras and discuss some aspects
of their representation theory. That will be used for a parametrization of
irreducible representations in one Bernstein block. Then we will discuss
the basic properties of unipotent representations of reductive groups over
finite or p-adic fields. We end with the Hecke algebras for unipotent Ber
nstein blocks.\n\nThe second talk is situated on the Galois side of the lo
cal Langlands correspondence. There we will build structures analogous to
those for representations of reductive p-adic groups: cuspidality\, Bernst
ein components and affine Hecke algebras. Generalizing work of Lusztig\, w
e show that the irreducible representations of these Hecke algebras are na
turally parametrized by suitable sets of enhanced L-parameters.\n\nIn the
case of unipotent representations\, we are able to match all the aforement
ioned structure on the p-adic side with the similar structure on the Galoi
s side\, in bijective fashion. This leads to a local Langlands corresponde
nce for unipotent representations\, which satisfies many functorial proper
ties.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (Institut De Mathématiques De Marseille)
DTSTART:20220222T133000Z
DTEND:20220222T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/31
DESCRIPTION:Title: Root systems and geometry at infinity for reductive gro
ups and spherical varieties\nby Raphaël Beuzart-Plessis (Institut De
Mathématiques De Marseille) as part of Automorphic Project & Research Sem
inar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (Institut De Mathématiques De Marseille)
DTSTART:20220223T010000Z
DTEND:20220223T023000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/32
DESCRIPTION:Title: Watch party: Root systems and geometry at infinity for
reductive groups and spherical varieties\nby Raphaël Beuzart-Plessis
(Institut De Mathématiques De Marseille) as part of Automorphic Project &
Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220301T133000Z
DTEND:20220301T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/33
DESCRIPTION:Title: Watch party: Asymptotics on real and p-adic spaces\
nby Yiannis Sakellaridis (Johns Hopkins University) as part of Automorphic
Project & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220301T010000Z
DTEND:20220301T023000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/34
DESCRIPTION:Title: Asymptotics on real and p-adic spaces\nby Yiannis S
akellaridis (Johns Hopkins University) as part of Automorphic Project & Re
search Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Krötz (Universität Paderborn)
DTSTART:20220315T123000Z
DTEND:20220315T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/35
DESCRIPTION:Title: Construction of discrete series\nby Bernhard Krötz
(Universität Paderborn) as part of Automorphic Project & Research Semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Krötz (Universität Paderborn)
DTSTART:20220316T000000Z
DTEND:20220316T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/36
DESCRIPTION:Title: Watch party: Construction of discrete series\nby Be
rnhard Krötz (Universität Paderborn) as part of Automorphic Project & Re
search Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (Johns Hopkins University)
DTSTART:20220322T123000Z
DTEND:20220322T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/37
DESCRIPTION:Title: Orbit method and the Kirillov–Rossman formula\nby
Rahul Dalal (Johns Hopkins University) as part of Automorphic Project & R
esearch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (Johns Hopkins University)
DTSTART:20220323T000000Z
DTEND:20220323T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/38
DESCRIPTION:Title: Watch party: Orbit method and the Kirillov–Rossman fo
rmula\nby Rahul Dalal (Johns Hopkins University) as part of Automorphi
c Project & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220308T133000Z
DTEND:20220308T150000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/39
DESCRIPTION:Title: Watch party: Differential operators and asymptotics on
real reductive groups and spherical varieties\nby Yiannis Sakellaridis
(Johns Hopkins University) as part of Automorphic Project & Research Semi
nar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220308T010000Z
DTEND:20220308T023000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/40
DESCRIPTION:Title: Differential operators and asymptotics on real reductiv
e groups and spherical varieties\nby Yiannis Sakellaridis (Johns Hopki
ns University) as part of Automorphic Project & Research Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20220329T123000Z
DTEND:20220329T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/41
DESCRIPTION:Title: A step-by-step introduction to p-adic Hodge theory\
nby Jared Weinstein (Boston University) as part of Automorphic Project & R
esearch Seminar\n\n\nAbstract\nShimura varieties are families of Hodge str
uctures. If our goal is to understand the p-adic analogues of the Shimura
varieties\, it will be necessary to understand some p-adic Hodge theory.
We will build up our understanding in four steps: the complex picture\,
the perfect field picture\, the C_p picture\, and the picture over a perfe
ctoid base.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20220330T000000Z
DTEND:20220330T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/42
DESCRIPTION:Title: Watch Party: A step-by-step introduction to p-adic Hodg
e theory\nby Jared Weinstein (Boston University) as part of Automorphi
c Project & Research Seminar\n\n\nAbstract\nShimura varieties are families
of Hodge structures. If our goal is to understand the p-adic analogues o
f the Shimura varieties\, it will be necessary to understand some p-adic H
odge theory. We will build up our understanding in four steps: the compl
ex picture\, the perfect field picture\, the C_p picture\, and the picture
over a perfectoid base.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220405T123000Z
DTEND:20220405T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/43
DESCRIPTION:Title: Overview of the Fargues–Fontaine curve\nby Gabrie
l Dospinescu (ENS Lyon) as part of Automorphic Project & Research Seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220406T000000Z
DTEND:20220406T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/44
DESCRIPTION:Title: Watch Party: Overview of the Fargues–Fontaine curve\nby Gabriel Dospinescu (ENS Lyon) as part of Automorphic Project & Rese
arch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (MPIM Bonn)
DTSTART:20220419T123000Z
DTEND:20220419T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/45
DESCRIPTION:Title: Towards the geometry of Bun_G\nby David Hansen (MPI
M Bonn) as part of Automorphic Project & Research Seminar\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (MPIM Bonn)
DTSTART:20220420T000000Z
DTEND:20220420T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/46
DESCRIPTION:Title: Watch Party: Towards the geometry of Bun_G\nby Davi
d Hansen (MPIM Bonn) as part of Automorphic Project & Research Seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (Université Paris XIII)
DTSTART:20220426T123000Z
DTEND:20220426T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/47
DESCRIPTION:Title: The Fargues-Fontaine curve and local Langlands\nby
Arthur-César Le Bras (Université Paris XIII) as part of Automorphic Proj
ect & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (Université Paris XIII)
DTSTART:20220427T000000Z
DTEND:20220427T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/48
DESCRIPTION:Title: Watch Party: The Fargues-Fontaine curve and local Langl
ands\nby Arthur-César Le Bras (Université Paris XIII) as part of Aut
omorphic Project & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220412T123000Z
DTEND:20220412T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/49
DESCRIPTION:Title: Vector bundles on the Fargues-Fontaine curve\nby Ga
briel Dospinescu (ENS Lyon) as part of Automorphic Project & Research Semi
nar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220413T000000Z
DTEND:20220413T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/50
DESCRIPTION:Title: Watch Party: Vector bundles on the Fargues-Fontaine cur
ve\nby Gabriel Dospinescu (ENS Lyon) as part of Automorphic Project &
Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (Johns Hopkins University)
DTSTART:20220510T123000Z
DTEND:20220510T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/51
DESCRIPTION:Title: Deforming Galois representations\nby Ashwin Iyengar
(Johns Hopkins University) as part of Automorphic Project & Research Semi
nar\n\n\nAbstract\nI will introduce the deformation theory of Galois repre
sentations following Mazur\, Kisin and others. I'll talk about ring theore
tic properties of local and global deformation rings. I will start from sc
ratch and assume very little background. If time permits\, I'll talk about
how such tools get used in modularity lifting theorems.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (Johns Hopkins University)
DTSTART:20220511T000000Z
DTEND:20220511T013000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/52
DESCRIPTION:Title: Watch party: Deforming Galois representations\nby A
shwin Iyengar (Johns Hopkins University) as part of Automorphic Project &
Research Seminar\n\n\nAbstract\nI will introduce the deformation theory of
Galois representations following Mazur\, Kisin and others. I'll talk abou
t ring theoretic properties of local and global deformation rings. I will
start from scratch and assume very little background. If time permits\, I'
ll talk about how such tools get used in modularity lifting theorems.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Glasgow)
DTSTART:20220524T123000Z
DTEND:20220524T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/53
DESCRIPTION:Title: Local conditions on Galois deformation rings\nby Re
becca Bellovin (University of Glasgow) as part of Automorphic Project & Re
search Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gal Porat (University of Chicago)
DTSTART:20220531T123000Z
DTEND:20220531T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/55
DESCRIPTION:Title: $(\\phi\,\\Gamma)$-modules and the Emerton–Gee stack.
\nby Gal Porat (University of Chicago) as part of Automorphic Project
& Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Savitt (Johns Hopkins University)
DTSTART:20220607T123000Z
DTEND:20220607T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/56
DESCRIPTION:Title: The Breuil–Mezard conjecture\nby David Savitt (Jo
hns Hopkins University) as part of Automorphic Project & Research Seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion
DTSTART:20220614T123000Z
DTEND:20220614T140000Z
DTSTAMP:20260404T095134Z
UID:AutomorphicProject/57
DESCRIPTION:Title: Discussion session on deformations of Galois representa
tions\nby Discussion as part of Automorphic Project & Research Seminar
\n\n\nAbstract\nDuring the last 2 meetings of the semester\, we revisit an
d discuss the latest series of expository talks. One goal will be to conne
ct what we learned with the classical picture of the Langlands program. Th
is week\, we will focus on deformations of Galois representations\, based
on the talks between May 10–June 7\, which the audience is encouraged to
review.\n
LOCATION:https://stable.researchseminars.org/talk/AutomorphicProject/57/
END:VEVENT
END:VCALENDAR