BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20210206T000000Z
DTEND:20210206T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/1
DESCRIPTION:Title: Reduction Theory\, revisited\nby Yiannis Sakellaridis (John
s Hopkins University) as part of Automorphic Project & Research Seminar\n\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Atobe (Hokkaido University)
DTSTART:20210220T000000Z
DTEND:20210220T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/2
DESCRIPTION:Title: Construction of local A-packets\nby Hiraku Atobe (Hokkaido
University) as part of Automorphic Project & Research Seminar\n\n\nAbstrac
t\nA-packets for classical groups were introduced in Arthur's endoscopic c
lassification. Elements of local A-packets are the local components of dis
crete automorphic representations. Since they are characterized by endosco
pic character identities\, it is difficult to make local A-packets explici
t. In this talk\, I will talk about a refinement of Moeglin's explicit con
struction of local A-packets. In particular\, I will explain a non-vanishi
ng criterion\, and how to specify elements of a given local A-packet. Furt
hermore\, I will propose a conjectural formula for the Aubert duality of r
epresentations of Arthur type.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20210213T000000Z
DTEND:20210213T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/4
DESCRIPTION:Title: Reduction theory: proofs.\nby Yiannis Sakellaridis (Johns H
opkins University) as part of Automorphic Project & Research Seminar\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Michigan)
DTSTART:20210306T000000Z
DTEND:20210306T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/5
DESCRIPTION:Title: Background on the Gan-Gross-Prasad Conjecture\nby David Sch
wein (University of Michigan) as part of Automorphic Project & Research Se
minar\n\n\nAbstract\nIn 2009 Gan\, Gross\, and Prasad conjectured a branch
ing law\nfor a classical group over a local field\, in other words\, a rul
e for\nhow irreducible representations decompose on restriction to\n(class
ical) subgroups. Last year the authors generalized their\nconjecture to n
on-tempered parameters\, as Gan will explain in a future\ntalk.\n\nThis ta
lk serves as background for Gan's talk. In the first part\,\nwe'll use th
e Ramanujan-Petersson Conjecture and Satake's\ngeneralization of it to mot
ivate and introduce several concepts\nsurrounding the conjectural branchin
g law\, among them L- and A-packets\nand tempered and generic representati
ons. In the second part\, a warm\nup to the general conjecture\, we'll su
mmarize some of what is known\nabout the branching law of the general line
ar group.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wee Teck Gan (National University of Singapore)
DTSTART:20210313T000000Z
DTEND:20210313T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/6
DESCRIPTION:Title: Nontempered Restriction Problems for Classical Groups\nby W
ee Teck Gan (National University of Singapore) as part of Automorphic Proj
ect & Research Seminar\n\n\nAbstract\nI will discuss an extension of the G
ross-Pasad conjectures to the setting of nontempered A-packets\, mention s
ome progress and highlight some subtleties in the nontempered setting. In
particular\, I will highlight how our conjecture can be viewed as a concre
te manifestation of the framework of Ben-Zvi-Sakellaridis-Venkatesh relati
ng restriction problems to symplectic geometry. This is joint work with Gr
oss and Prasad.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spencer Leslie (Duke University)
DTSTART:20210320T000000Z
DTEND:20210320T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/7
DESCRIPTION:Title: Pre-stabilization and endoscopic groups\nby Spencer Leslie
(Duke University) as part of Automorphic Project & Research Seminar\n\n\nA
bstract\nThe stabilization of the (twisted) trace formula is an enormous p
rogram that lies behind many of the topics in this seminar (L- and A-packe
ts\, for example). An important first step in this program is pre-stabiliz
ation of the geometric side\, where one introduces stable and unstable orb
ital integrals. As background for the talk on my work towards stabilizing
certain relative trace formulas\, I review this concept in a general setti
ng of a reductive group G acting on a smooth affine variety X. A goal is t
o highlight problems that arise in this more general setting\, adding simp
lifying assumptions as we go. I will then specialize to the group case and
review the introduction of endoscopic groups to account for the unstable
terms.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spencer Leslie (Duke University)
DTSTART:20210327T000000Z
DTEND:20210327T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/8
DESCRIPTION:Title: Endoscopy for certain symmetric spaces\nby Spencer Leslie (
Duke University) as part of Automorphic Project & Research Seminar\n\n\nAb
stract\nRelative trace formulas are powerful tools in the study of periods
of automorphic forms. However in many cases of interest\, basic stability
problems have not been addressed. I will discuss a notion of endoscopy wi
th the goal of stabilizing the relative trace formula associated to a symm
etric subgroup. The main example is that of unitary Friedberg–Jacquet pe
riods\, which are related to special cycles in certain unitary Shimura var
ieties. After introducing the endoscopic symmetric spaces in this case\, I
will sketch the proof of the\nfundamental lemma.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Delorme (Institut de Mathématiques de Marseille)
DTSTART:20210410T000000Z
DTEND:20210410T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/9
DESCRIPTION:Title: On the spectral theorem of Langlands\nby Patrick Delorme (I
nstitut de Mathématiques de Marseille) as part of Automorphic Project & R
esearch Seminar\n\n\nAbstract\nWe show that the Hilbert subspace of $L^2(
G(F)\\backslash G(\\mathbb A))$ is generated by wave packets of Eisenstei
n series built from discrete series is the whole space.\n\nTogether with t
he work of E. Lapid on the asymptotic formula for the truncated inner prod
uct of Eisenstein series built from discrete series\, it achieves a proo
f of the spectral theorem of R.P. Langlands based on the work of J. Berns
tein and E. Lapid on the meromorphic continuation of these Eisenstein s
eries.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20210417T000000Z
DTEND:20210417T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/10
DESCRIPTION:Title: An introduction to Vogan's refinement of the local Langlands c
onjecture\nby Tasho Kaletha (University of Michigan) as part of Automo
rphic Project & Research Seminar\n\n\nAbstract\nIn an influential paper fr
om 1993\, Vogan introduced many new ideas into the realm of the local Lang
lands correspondence. These include the notion of a pure inner form\, comp
ound L-packets\, the infinitesimal character of a Langlands parameters\, t
he stable Bernstein center\, and a geometric point of view on Langlands pa
rameters. I will give an introduction to these ideas as a preparation for
upcoming research talks by Clifton Cunningham and Peter Dillery.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART:20210424T000000Z
DTEND:20210424T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/11
DESCRIPTION:Title: The geometry of local Arthur packets\nby Clifton Cunningha
m (University of Calgary) as part of Automorphic Project & Research Semina
r\n\n\nAbstract\nThis talk presents Vogan's geometric perspective on L-pac
kets 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 $\\Pi^\\text{ABV}_
\\phi$\, 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 stable dis
tributions and that ABV-packets are A-packets when $\\phi$ is of Arthur ty
pe. We will discuss evidence for this conjecture and progress toward a pro
of.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill Casselman (University of British Columbia)
DTSTART:20210403T000000Z
DTEND:20210403T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/12
DESCRIPTION:Title: Analysis on arithmetic quotients: solved and open problems
\nby Bill Casselman (University of British Columbia) as part of Automorphi
c Project & Research Seminar\n\n\nAbstract\nGodement suggested a long time
ago that in the long run the proper way to understand the theory of autom
orphic forms from an analytic point of view was to interpret them as distr
ibutions of moderate growth on arithmetic quotients. This allows some usef
ul clarification about foundations\, but also a few novel proofs of old re
sults — for example the trace formula for SL(2) — as well as some natu
ral if probably difficult conjectures. I'll try to give an introduction to
this somewhat vast topic.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Zhang (MIT)
DTSTART:20210508T000000Z
DTEND:20210508T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/13
DESCRIPTION:Title: AFL over F\nby Wei Zhang (MIT) as part of Automorphic Proj
ect & Research Seminar\n\n\nAbstract\nThe Arithmetic Fundamental Lemma (AF
L) conjecture over a p-adic field $F$ arises from relative trace formula a
pproach to the arithmetic Gan-Gross-Prasad conjecture for unitary groups.
It is an identity relating the first derivative of Jacquet--Rallis orbital
integrals and arithmetic intersection numbers on unitary Rapoport--Zink m
oduli 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 conjecture f
or a general p-adic field $F$.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masao Oi (Kyoto University)
DTSTART:20210515T000000Z
DTEND:20210515T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/14
DESCRIPTION:Title: Geometric L-packets of Howe-unramified toral supercuspidal rep
resentations I\nby Masao Oi (Kyoto University) as part of Automorphic
Project & Research Seminar\n\n\nAbstract\nIn our talks\, I and Charlotte C
han are going to talk about our comparison result on Yu’s supercuspidal
representations and representations geometrically constructed by Chan-Ivan
ov.\nIn my talk of the first week\, I will focus on the algebraic part of
our result.\nEspecially\, I will first review Yu's construction of supercu
spidal representations.\nThen I will explain that some of those supercuspi
dals (which we call Howe-unramified toral supercuspidals) can be recovered
by looking at their Harish-Chandra characters only at some specific eleme
nts.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART:20210522T000000Z
DTEND:20210522T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/15
DESCRIPTION:Title: Geometric L-packets of Howe-unramified toral supercuspidal rep
resentations II\nby Charlotte Chan (MIT) as part of Automorphic Projec
t & Research Seminar\n\n\nAbstract\nLast week Masao discussed a characteri
zation theorem for some regular supercuspidal representations. This week\,
we discuss geometric aspects of our project. I will talk about Deligne--L
usztig varieties and their deeper-level analogues\, and illustrate the rol
e of a characterization theorem for representations of parahoric subgroups
. We will see that the cohomology of these varieties respects Kaletha's L-
packets in a very natural way.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Krishna (Brandeis University)
DTSTART:20210501T000000Z
DTEND:20210501T010000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/16
DESCRIPTION:Title: An introduction to the arithmetic GGP conjecture and the arith
metic fundamental lemma.\nby Rahul Krishna (Brandeis University) as pa
rt 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 refreshe
r on the relative trace formula of Jacquet–Rallis\, I will give a somewh
at impressionistic description of the RTF approach to this conjecture\, an
d explain the statement of the "main local ingredient": the arithmetic fun
damental lemma. This is background material for Wei Zhang's talk next week
.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Michigan)
DTSTART:20211015T130000Z
DTEND:20211015T143000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/17
DESCRIPTION:Title: Rigid inner forms over function fields\nby Peter Dillery (
University of Michigan) as part of Automorphic Project & Research Seminar\
n\n\nAbstract\nThe goal of this talk is to define rigid inner forms\, firs
t introduced by Kaletha in the setting of fields of characteristic zero\,
for local and global function fields. This entails studying torsors on ger
bes $E$ canonically associated to a class in $H^2(F\,A)$\, for $A$ a speci
al canonically-defined profinite group over F our field. We will spend tim
e introducing the abstract machinery required to work with such objects. W
e then discuss the applications to the local and global Langlands conjectu
res. Locally\, this includes a statement of the refined local Langlands co
njectures for a general (i.e.\, not necessarily quasi-split) connected red
uctive group G over a local function field which generalizes Vogan's state
ment that used pure inner twists (as discussed in Kaletha's talk*). Global
ly\, this includes a statement of the conjectural multiplicity formula for
automorphic representations of a connected reductive G over a global func
tion field.\n\n*Kaletha's background talk from last semester is available
for viewing under the "past talks" column on researchseminars.org.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (Jussieu)
DTSTART:20211022T130000Z
DTEND:20211022T143000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/18
DESCRIPTION:Title: A nonabelian Fourier transform for tempered unipotent represen
tations of p-adic groups I\nby Anne-Marie Aubert (Jussieu) as part of
Automorphic Project & Research Seminar\n\n\nAbstract\nIn the representatio
n theory of finite reductive groups\, an essential role is played by Luszt
ig's nonabelian Fourier transform\, an involution on the space of unipoten
t characters the group. This involution is the change of bases matrix betw
een the basis of irreducible characters and the basis of `almost character
s'\, certain class functions attached to character sheaves. \nFor reductiv
e p-adic groups\, the unipotent local Langlands correspondence gives a nat
ural parametrization of irreducible smooth representations with unipotent
cuspidal support. However\, many questions about the characters of these r
epresentations are still open. Motivated by the study of the characters on
compact elements\, we introduce in joint work with B. Romano (arXiv:2106.
13969) an involution on the spaces of elliptic and compact tempered unipot
ent representations of pure inner twists of a split simple p-adic group. T
his generalizes a construction by Moeglin and Waldspurger (2003\, 2016) fo
r elliptic tempered representations of split orthogonal groups\, and poten
tially gives another interpretation of a Fourier transform for p-adic grou
ps introduced by Lusztig (2014). We conjecture that the restriction to red
uctive quotients of maximal compact open subgroups intertwines this involu
tion with a disconnected version of Lusztig's nonabelian Fourier transform
for finite reductive groups. \nIn these talks\, we will present the nece
ssary background (the unipotent local Langlands correspondence\, families
of representations of finite reductive groups\, complex nilpotent orbits)\
, explain the definition and basic properties of the nonabelian Fourier tr
ansform\, the conjecture about compact restrictions\, and give supporting
evidence for the conjecture.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Ciubotaru (University of Oxford)
DTSTART:20211029T130000Z
DTEND:20211029T143000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/19
DESCRIPTION:Title: A nonabelian Fourier transform for tempered unipotent represen
tations of p-adic groups II\nby Dan Ciubotaru (University of Oxford) a
s part of Automorphic Project & Research Seminar\n\n\nAbstract\nIn the rep
resentation theory of finite reductive groups\, an essential role is playe
d by Lusztig's nonabelian Fourier transform\, an involution on the space o
f unipotent characters the group. This involution is the change of bases m
atrix between the basis of irreducible characters and the basis of `almost
characters'\, certain class functions attached to character sheaves. \nFo
r reductive p-adic groups\, the unipotent local Langlands correspondence g
ives a natural parametrization of irreducible smooth representations with
unipotent cuspidal support. However\, many questions about the characters
of these representations are still open. Motivated by the study of the cha
racters on compact elements\, we introduce in joint work with B. Romano (a
rXiv:2106.13969) an involution on the spaces of elliptic and compact tempe
red unipotent representations of pure inner twists of a split simple p-adi
c group. This generalizes a construction by Moeglin and Waldspurger (2003\
, 2016) for elliptic tempered representations of split orthogonal groups\,
and potentially gives another interpretation of a Fourier transform for p
-adic groups introduced by Lusztig (2014). We conjecture that the restrict
ion to reductive quotients of maximal compact open subgroups intertwines t
his involution with a disconnected version of Lusztig's nonabelian Fourier
transform for finite reductive groups. \nIn these talks\, we will presen
t the necessary background (the unipotent local Langlands correspondence\,
families of representations of finite reductive groups\, complex nilpoten
t orbits)\, explain the definition and basic properties of the nonabelian
Fourier transform\, the conjecture about compact restrictions\, and give s
upporting evidence for the conjecture.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (CNRS Marseille)
DTSTART:20211105T130000Z
DTEND:20211105T143000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/20
DESCRIPTION:Title: Review of Rankin-Selberg integrals and the non-Archimedean the
ory of new vectors\nby Raphaël Beuzart-Plessis (CNRS Marseille) as pa
rt of Automorphic Project & Research Seminar\n\n\nAbstract\nAs a preparati
on for Peter Humphries' talk\, I will review the basics on Rankin-Selberg
theory and the non-Archimedean theory of new (or essential) vectors mostly
following work of Jacquet\, Piatetski-Shapiro and Shalika.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University of Virginia)
DTSTART:20211112T133000Z
DTEND:20211112T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/21
DESCRIPTION:Title: Newform Theory for $\\mathrm{GL}_n$\nby Peter Humphries (U
niversity of Virginia) as part of Automorphic Project & Research Seminar\n
\n\nAbstract\nWe shall discuss three interrelated notions in the theory of
automorphic forms and automorphic representations: newforms\, $L$-functio
ns\, and conductors. In particular\, we cover how to define the newform as
sociated to an automorphic representation of $\\mathrm{GL}_n$\, how to rea
lise certain $L$-functions as period integrals involving newforms\, and ho
w to quantify the ramification of an automorphic representation in terms o
f properties of the newform. A key emphasis is the union of approaches to
defining newforms in both nonarchimedean and archimedean settings. Finally
\, we will briefly discuss notions of newforms for groups other than $\\ma
thrm{GL}_n$.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20211119T133000Z
DTEND:20211119T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/22
DESCRIPTION:Title: no seminar\nby no seminar as part of Automorphic Project &
Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20211126T133000Z
DTEND:20211126T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/23
DESCRIPTION:Title: no seminar\nby no seminar as part of Automorphic Project &
Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilbert Moss (University of Utah)
DTSTART:20211203T133000Z
DTEND:20211203T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/24
DESCRIPTION:Title: Moduli spaces of Langlands parameters\nby Gilbert Moss (Un
iversity of Utah) as part of Automorphic Project & Research Seminar\n\n\nA
bstract\nThe local Langlands correspondence connects representation of p-a
dic groups to Langlands parameters\, which are certain representations of
Galois groups of local fields. In recent work with Dat\, Helm\, and Kurinc
zuk\, we have shown that Langlands parameters\, when viewed through the ri
ght 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 geometry shou
ld be reflected in the representation theory of p-adic groups\, on the oth
er side of the local Langlands correspondence. The "local Langlands in fam
ilies" conjecture describes the moduli space of Langlands parameters in te
rms of the integral center of the category of representations of the p-adi
c group. It was established for GL(n) in 2018 and we will discuss some wor
k in progress toward generalizing it to quasi-split classical groups.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Vogan (MIT)
DTSTART:20211210T133000Z
DTEND:20211210T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/25
DESCRIPTION:Title: Unipotent Representations of Complex Groups I\nby David Vo
gan (MIT) as part of Automorphic Project & Research Seminar\n\n\nAbstract\
nArthur in 1983 conjectured the existence of a family of representations o
f reductive groups over local fields\, intermediate between tempered repre
sentations and unitary representations. In 1985 Barbasch and I constructed
representations for complex reductive groups satisfying some of Arthur's
desiderata.\n\nI was charged with explaining this 1985 paper\, because of
the seminar target of "topics which have not been covered in the best poss
ible way in the literature." In fact I will talk about the general structu
re of the local Langlands conjecture\, and try to explain how that leads (
conjecturally over any local field) to a construction of Arthur's represen
tations. I will try to say in passing what Barbasch and I did.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (Oxford University)
DTSTART:20211217T133000Z
DTEND:20211217T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/26
DESCRIPTION:Title: Unipotent Representations of Complex Groups II\nby Lucas M
ason-Brown (Oxford University) as part of Automorphic Project & Research S
eminar\n\n\nAbstract\nUnipotent representations are a mysterious class of
representations of a semisimple Lie group over the real or complex numbers
\, which are conjectured to form the `building blocks' of the unitary dual
. In 1985\, Barbasch and Vogan defined a class of representations of a com
plex semisimple Lie group called `special unipotent representations.' Thes
e representations have proven to be fundamental objects in the study of un
itary representations\, but they constitute only a fraction of all unipote
nt representations (for example\, the metaplectic representations are excl
uded). In this talk\, I will propose a more general definition of 'unipote
nt\,' inspired by the Orbit Method. I will catalog the properties of our u
nipotent representations (including their classification) and describe an
intriguing relationship between our representations and those of Barbasch-
Vogan\, which I call "refined Barbasch-Vogan duality." This talk is based
on joint work with Ivan Losev and Dmitryo Matvieievskyi.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Chenevier & Olivier Taïbi (École Normale Supérieure)
DTSTART:20220128T133000Z
DTEND:20220128T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/28
DESCRIPTION:Title: Inexistence\, dimension formulas and classification for level
one algebraic cusp forms\nby Gaëtan Chenevier & Olivier Taïbi (Écol
e Normale Supérieure) as part of Automorphic Project & Research Seminar\n
\n\nAbstract\n[Please note: there will be 2 talks\, 45' each.]\n\nIn the f
irst lecture we will explain how improvements on using\nan old tool in ana
lytic number theory\, Riemann-Weil's explicit formula\nfor L-functions\, a
llowed us to prove the non-existence of level one\nalgebraic cusp forms fo
r general linear groups over Q for lots of\ninfinitesimal characters (=set
s of Hodge weights). In the second\nlecture we will explain how these van
ishing results yield an\n"effortless" method to compute the geometric side
of Arthur's\n$L^2$-Lefschetz trace formula for split classical groups wit
h the unit of\nthe unramified Hecke algebra. We obtain dimension formulas
as a\nconsequence. Together these results give classification theorems f
or\nlevel one algebraic cusp forms in motivic weight <=23.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit Nijmegen)
DTSTART:20220204T133000Z
DTEND:20220204T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/29
DESCRIPTION:Title: Affine Hecke algebras in the representation theory of p-adic g
roups\nby Maarten Solleveld (Radboud Universiteit Nijmegen) as part of
Automorphic Project & Research Seminar\n\n\nAbstract\nThe main goal of th
ese two talks is to discuss a local Langlands correspondence for unipotent
representations of reductive p-adic groups. We will focus on the most imp
ortant technique that goes into it\, namely affine Hecke algebras. This te
chnique is available in large generality\, and likewise a substantial part
of talks will play in a general setting. \n\nIn the first we talk we surv
ey the role of affine Hecke algebras for representations of reductive p-ad
ic groups. We will look at types and progenerators for Bernstein blocks\,
and we will see how they give rise to some sort of Hecke algebras. We intr
oduce affine Hecke algebras and discuss some aspects of their representati
on theory. That will be used for a parametrization of irreducible represen
tations in one Bernstein block. Then we will discuss the basic properties
of unipotent representations of reductive groups over finite or p-adic fie
lds. We end with the Hecke algebras for unipotent Bernstein blocks.\n\nThe
second talk is situated on the Galois side of the local Langlands corresp
ondence. There we will build structures analogous to those for representat
ions of reductive p-adic groups: cuspidality\, Bernstein components and af
fine Hecke algebras. Generalizing work of Lusztig\, we show that the irred
ucible representations of these Hecke algebras are naturally parametrized
by suitable sets of enhanced L-parameters.\n\nIn the case of unipotent rep
resentations\, we are able to match all the aforementioned structure on th
e p-adic side with the similar structure on the Galois side\, in bijective
fashion. This leads to a local Langlands correspondence for unipotent rep
resentations\, which satisfies many functorial properties.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit Nijmegen)
DTSTART:20220211T133000Z
DTEND:20220211T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/30
DESCRIPTION:Title: Hecke algebras and a local Langlands correspondence for unipot
ent representations\nby Maarten Solleveld (Radboud Universiteit Nijmeg
en) as part of Automorphic Project & Research Seminar\n\n\nAbstract\nThe m
ain goal of these two talks is to discuss a local Langlands correspondence
for unipotent representations of reductive p-adic groups. We will focus o
n the most important technique that goes into it\, namely affine Hecke alg
ebras. This technique is available in large generality\, and likewise a su
bstantial part of talks will play in a general setting. \n\nIn the first w
e talk we survey the role of affine Hecke algebras for representations of
reductive p-adic groups. We will look at types and progenerators for Berns
tein blocks\, and we will see how they give rise to some sort of Hecke alg
ebras. We introduce affine Hecke algebras and discuss some aspects of thei
r representation theory. That will be used for a parametrization of irredu
cible representations in one Bernstein block. Then we will discuss the bas
ic properties of unipotent representations of reductive groups over finite
or p-adic fields. We end with the Hecke algebras for unipotent Bernstein
blocks.\n\nThe second talk is situated on the Galois side of the local Lan
glands correspondence. There we will build structures analogous to those f
or representations of reductive p-adic groups: cuspidality\, Bernstein com
ponents and affine Hecke algebras. Generalizing work of Lusztig\, we show
that the irreducible representations of these Hecke algebras are naturally
parametrized by suitable sets of enhanced L-parameters.\n\nIn the case of
unipotent representations\, we are able to match all the aforementioned s
tructure on the p-adic side with the similar structure on the Galois side\
, in bijective fashion. This leads to a local Langlands correspondence for
unipotent representations\, which satisfies many functorial properties.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (Institut De Mathématiques De Marseille)
DTSTART:20220222T133000Z
DTEND:20220222T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/31
DESCRIPTION:Title: Root systems and geometry at infinity for reductive groups and
spherical varieties\nby Raphaël Beuzart-Plessis (Institut De Mathém
atiques De Marseille) as part of Automorphic Project & Research Seminar\n\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Beuzart-Plessis (Institut De Mathématiques De Marseille)
DTSTART:20220223T010000Z
DTEND:20220223T023000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/32
DESCRIPTION:Title: Watch party: Root systems and geometry at infinity for reducti
ve groups and spherical varieties\nby Raphaël Beuzart-Plessis (Instit
ut De Mathématiques De Marseille) as part of Automorphic Project & Resear
ch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220301T133000Z
DTEND:20220301T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/33
DESCRIPTION:Title: Watch party: Asymptotics on real and p-adic spaces\nby Yia
nnis Sakellaridis (Johns Hopkins University) as part of Automorphic Projec
t & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220301T010000Z
DTEND:20220301T023000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/34
DESCRIPTION:Title: Asymptotics on real and p-adic spaces\nby Yiannis Sakellar
idis (Johns Hopkins University) as part of Automorphic Project & Research
Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Krötz (Universität Paderborn)
DTSTART:20220315T123000Z
DTEND:20220315T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/35
DESCRIPTION:Title: Construction of discrete series\nby Bernhard Krötz (Unive
rsität Paderborn) as part of Automorphic Project & Research Seminar\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Krötz (Universität Paderborn)
DTSTART:20220316T000000Z
DTEND:20220316T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/36
DESCRIPTION:Title: Watch party: Construction of discrete series\nby Bernhard
Krötz (Universität Paderborn) as part of Automorphic Project & Research
Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (Johns Hopkins University)
DTSTART:20220322T123000Z
DTEND:20220322T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/37
DESCRIPTION:Title: Orbit method and the Kirillov–Rossman formula\nby Rahul
Dalal (Johns Hopkins University) as part of Automorphic Project & Research
Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (Johns Hopkins University)
DTSTART:20220323T000000Z
DTEND:20220323T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/38
DESCRIPTION:Title: Watch party: Orbit method and the Kirillov–Rossman formula\nby Rahul Dalal (Johns Hopkins University) as part of Automorphic Proje
ct & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220308T133000Z
DTEND:20220308T150000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/39
DESCRIPTION:Title: Watch party: Differential operators and asymptotics on real re
ductive groups and spherical varieties\nby Yiannis Sakellaridis (Johns
Hopkins University) as part of Automorphic Project & Research Seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART:20220308T010000Z
DTEND:20220308T023000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/40
DESCRIPTION:Title: Differential operators and asymptotics on real reductive group
s and spherical varieties\nby Yiannis Sakellaridis (Johns Hopkins Univ
ersity) as part of Automorphic Project & Research Seminar\n\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20220329T123000Z
DTEND:20220329T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/41
DESCRIPTION:Title: A step-by-step introduction to p-adic Hodge theory\nby Jar
ed Weinstein (Boston University) as part of Automorphic Project & Research
Seminar\n\n\nAbstract\nShimura varieties are families of Hodge structures
. If our goal is to understand the p-adic analogues of the Shimura variet
ies\, it will be necessary to understand some p-adic Hodge theory. We wil
l build up our understanding in four steps: the complex picture\, the per
fect field picture\, the C_p picture\, and the picture over a perfectoid b
ase.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20220330T000000Z
DTEND:20220330T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/42
DESCRIPTION:Title: Watch Party: A step-by-step introduction to p-adic Hodge theor
y\nby Jared Weinstein (Boston University) as part of Automorphic Proje
ct & Research Seminar\n\n\nAbstract\nShimura varieties are families of Hod
ge structures. If our goal is to understand the p-adic analogues of the S
himura varieties\, it will be necessary to understand some p-adic Hodge th
eory. We will build up our understanding in four steps: the complex pict
ure\, the perfect field picture\, the C_p picture\, and the picture over a
perfectoid base.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220405T123000Z
DTEND:20220405T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/43
DESCRIPTION:Title: Overview of the Fargues–Fontaine curve\nby Gabriel Dospi
nescu (ENS Lyon) as part of Automorphic Project & Research Seminar\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220406T000000Z
DTEND:20220406T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/44
DESCRIPTION:Title: Watch Party: Overview of the Fargues–Fontaine curve\nby
Gabriel Dospinescu (ENS Lyon) as part of Automorphic Project & Research Se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (MPIM Bonn)
DTSTART:20220419T123000Z
DTEND:20220419T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/45
DESCRIPTION:Title: Towards the geometry of Bun_G\nby David Hansen (MPIM Bonn)
as part of Automorphic Project & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (MPIM Bonn)
DTSTART:20220420T000000Z
DTEND:20220420T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/46
DESCRIPTION:Title: Watch Party: Towards the geometry of Bun_G\nby David Hanse
n (MPIM Bonn) as part of Automorphic Project & Research Seminar\n\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (Université Paris XIII)
DTSTART:20220426T123000Z
DTEND:20220426T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/47
DESCRIPTION:Title: The Fargues-Fontaine curve and local Langlands\nby Arthur-
César Le Bras (Université Paris XIII) as part of Automorphic Project & R
esearch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (Université Paris XIII)
DTSTART:20220427T000000Z
DTEND:20220427T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/48
DESCRIPTION:Title: Watch Party: The Fargues-Fontaine curve and local Langlands\nby Arthur-César Le Bras (Université Paris XIII) as part of Automorphi
c Project & Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220412T123000Z
DTEND:20220412T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/49
DESCRIPTION:Title: Vector bundles on the Fargues-Fontaine curve\nby Gabriel D
ospinescu (ENS Lyon) as part of Automorphic Project & Research Seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20220413T000000Z
DTEND:20220413T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/50
DESCRIPTION:Title: Watch Party: Vector bundles on the Fargues-Fontaine curve\
nby Gabriel Dospinescu (ENS Lyon) as part of Automorphic Project & Researc
h Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (Johns Hopkins University)
DTSTART:20220510T123000Z
DTEND:20220510T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/51
DESCRIPTION:Title: Deforming Galois representations\nby Ashwin Iyengar (Johns
Hopkins University) as part of Automorphic Project & Research Seminar\n\n
\nAbstract\nI will introduce the deformation theory of Galois representati
ons following Mazur\, Kisin and others. I'll talk about ring theoretic pro
perties of local and global deformation rings. I will start from scratch a
nd assume very little background. If time permits\, I'll talk about how su
ch tools get used in modularity lifting theorems.\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Iyengar (Johns Hopkins University)
DTSTART:20220511T000000Z
DTEND:20220511T013000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/52
DESCRIPTION:Title: Watch party: Deforming Galois representations\nby Ashwin I
yengar (Johns Hopkins University) as part of Automorphic Project & Researc
h Seminar\n\n\nAbstract\nI will introduce the deformation theory of Galois
representations following Mazur\, Kisin and others. I'll talk about ring
theoretic properties of local and global deformation rings. I will start f
rom 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://researchseminars.org/talk/AutomorphicProject/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin (University of Glasgow)
DTSTART:20220524T123000Z
DTEND:20220524T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/53
DESCRIPTION:Title: Local conditions on Galois deformation rings\nby Rebecca B
ellovin (University of Glasgow) as part of Automorphic Project & Research
Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gal Porat (University of Chicago)
DTSTART:20220531T123000Z
DTEND:20220531T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/55
DESCRIPTION:Title: $(\\phi\,\\Gamma)$-modules and the Emerton–Gee stack.\nb
y Gal Porat (University of Chicago) as part of Automorphic Project & Resea
rch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Savitt (Johns Hopkins University)
DTSTART:20220607T123000Z
DTEND:20220607T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/56
DESCRIPTION:Title: The Breuil–Mezard conjecture\nby David Savitt (Johns Hop
kins University) as part of Automorphic Project & Research Seminar\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/AutomorphicProject/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion
DTSTART:20220614T123000Z
DTEND:20220614T140000Z
DTSTAMP:20260416T220515Z
UID:AutomorphicProject/57
DESCRIPTION:Title: Discussion session on deformations of Galois representations\nby Discussion as part of Automorphic Project & Research Seminar\n\n\nA
bstract\nDuring the last 2 meetings of the semester\, we revisit and discu
ss the latest series of expository talks. One goal will be to connect what
we learned with the classical picture of the Langlands program. This 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://researchseminars.org/talk/AutomorphicProject/57/
END:VEVENT
END:VCALENDAR