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BEGIN:VEVENT
SUMMARY:Sug Woo Shin (UC Berkeley)
DTSTART:20201016T143000Z
DTEND:20201016T150000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/1
DESCRIPTION:Title: On GSpin(2n)-valued automorphic Galois representations\nby Sug Woo Sh
in (UC Berkeley) as part of The 2020 Paul J. Sally\, Jr. Midwest Represent
ation Theory Conference\n\n\nAbstract\nI will present my joint work with A
rno Kret\, where we construct a GSpin(2n)-valued ell-adic Galois represent
ation attached to a cuspidal cohomological automorphic representation pi o
f a suitable quasi-split form of GSO(2n) over a totally real field\, under
the hypothesis that pi has a Steinberg component at a finite place. This
uses input from the cohomology of certain Shimura varieties for GSO(2n)\;
as such we need to take a suitable form of GSO(2n) depending on the parity
of n. (We take the split form if and only if n is even.)\n
LOCATION:https://researchseminars.org/talk/MRTC2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Haley (University of Michigan)
DTSTART:20201016T153000Z
DTEND:20201016T160000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/2
DESCRIPTION:Title: Parametrizations of Unramified Tori\nby Jacob Haley (University of Mi
chigan) as part of The 2020 Paul J. Sally\, Jr. Midwest Representation The
ory Conference\n\n\nAbstract\nIf G is a reductive group over a p-adic fiel
d k\, then DeBacker gives a paramaterization of the G(k)-conjugacy classes
of maximal unramified k-tori using Bruhat–Tits theory. On the other han
d\, for classical groups\, Waldspurger gives a parameterization in terms o
f triples of partitions. Given one of these triples\, Waldspurger construc
ts a regular semisimple element for the maximal unramified torus by defini
ng an endomorphism on an algebra whose structure is determined by the part
s of the three partitions. After giving an overview of the two parameteriz
ations\, we will give a comparison\, emphasizing the case of the symplecti
c group.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeongseong Jo (University of Iowa)
DTSTART:20201016T160000Z
DTEND:20201016T163000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/3
DESCRIPTION:Title: Local symmetric square L-functions for GL(2)\nby Yeongseong Jo (Unive
rsity of Iowa) as part of The 2020 Paul J. Sally\, Jr. Midwest Representat
ion Theory Conference\n\n\nAbstract\nIn the influential work\, Gelbart and
Jacquet analyzed the integral representation for local symmetric square $
L$-functions on $GL(2)$ at finite places based on the work of Shimura. In
doing so\, Gelbart and Jacquet explicitly constructed the local functorial
lifting from $GL(2)$ to $GL(3)$. In this talk we present a natural way to
define the $L$-function from the family of integrals for the space of goo
d sections proposed by Piatetski-Shapiro and Rallis. We show that this ana
lytic local $L$-function for an irreducible admissible representation of $
GL(2)$ agrees with the corresponding symmetric square Artin $L$-function f
or its Langlnads parameter through the local Langlands correspondence.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Gleason (UC Berkeley)
DTSTART:20201016T180000Z
DTEND:20201016T183000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/4
DESCRIPTION:Title: On the geometric connected components of unramified local Shimura varieti
es\nby Ian Gleason (UC Berkeley) as part of The 2020 Paul J. Sally\, J
r. Midwest Representation Theory Conference\n\n\nAbstract\nThrough the rec
ent theory of diamonds\, P. Scholze constructs local Shimura varieties att
ached to any reductive group. These are rigid-analytic spaces that general
ize the generic fiber of a Rapoport–Zink space. It is widely expected th
at these interesting spaces realize in their cohomology instances of the l
ocal Langlands correspondence. In this talk\, we describe the set of conne
cted components of unramified local Shimura varieties (more generally modu
li spaces of mixed characteristic shtukas)\, and describe the relation to
local class field theory.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Kutzko
DTSTART:20201016T183000Z
DTEND:20201016T190000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/5
DESCRIPTION:Title: "A Jew and an Irishman went to Heaven": My Friendship with Paul Sally\nby Phil Kutzko as part of The 2020 Paul J. Sally\, Jr. Midwest Represen
tation Theory Conference\n\n\nAbstract\nI have had the honor on several oc
casions to speak or write about my relationship with Paul J. Sally\, Jr.
– one of the finest human beings I have known in my 73 years on this ear
th. I\, and others\, have detailed Paul's mathematical prowess\, his rema
rkable commitment to social justice and his keen and subtle sense of humor
. Today\, with so many young folks in the audience\, I would like to prov
ide a context for our relationship as well as for the professional lives t
hat we led: that not too many years before we entered the world of mathem
atics\, it was a profession that would not have been particularly happy to
see the likes of either of us. Paul and I discussed this throughout our
time together and I learned a great deal from him about the similarities\,
and the differences\, of the way in which each of us experienced this con
text. I will share what I learned from him and how his perceptions\, as w
ell as his work in social justice\, shaped my own activities in this area.
And I hope\, in closing\, to discuss some policy implications for our pr
ofession.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dubravka Ban (Southern Illinois University)
DTSTART:20201017T143000Z
DTEND:20201017T150000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/6
DESCRIPTION:Title: From $\\mathrm{GL}(2\,Q_p)$ to $\\mathrm{SL}(2\,Q_p)$\nby Dubravka Ba
n (Southern Illinois University) as part of The 2020 Paul J. Sally\, Jr. M
idwest Representation Theory Conference\n\n\nAbstract\nLet $E$ be a finite
extension of $\\mathbb{Q}_p$. The $p$-adic Langlands correspondence for $
G=GL_2(\\mathbb{Q}_p)$ is a bijection between the set of absolutely irredu
cible 2-dimensional $E$-representations of \n${\\rm Gal} \\overline{\\math
bb{Q}}_p/\\mathbb{Q}_p)$ and the set of absolutely irreducible admissible
non-ordinary $E$-Banach space representations of $G$. We study the corresp
onding objects for $H=SL_2(\\mathbb{Q}_p)$. Let $\\Pi$ be an irreducible a
dmissible Banach space representation of $G$. Then $\\Pi|_H$ decomposes as
a direct sum of inequivalent representations.\n\nLet $\\psi: {\\rm Gal}(\
\overline{\\mathbb{Q}}_p/\\mathbb{Q}_p) \\to GL_2(E)$ be the associated Ga
lois representation.\nAssume that $\\psi$ is de Rham with Hodge-Tate weigh
ts 0 and 1. We compute the centralizer in $PGL_2(\\overline{E})$ of the i
mage of the corresponding projective Galois representation $\\overline{\\p
si}: {\\rm Gal}(\\overline{\\mathbb{Q}}_p/\\mathbb{Q}_p) \\to PGL_2(E)$. W
e show that the order of the centralizer is equal to the number of compone
nts of $\\Pi|_H$.\n\nEncapsulated in the $p$-adic Langlands correspondence
for $G$ is the classical smooth Langlands correspondence.\nThe representa
tion $\\Pi$ contains a smooth representation $\\pi$. In the case when $\\p
si$ is non-trianguline\, $\\pi$ is supercuspidal.\nWe investigate the conn
ection between $\\Pi|_H$ and $\\pi|_H$. This is a joint work with Matthias
Strauch.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Brown (IST\, Austria)
DTSTART:20201017T153000Z
DTEND:20201017T160000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/7
DESCRIPTION:Title: Unitary representations of GL(n) and the geometry of Langlands parameters
\nby Adam Brown (IST\, Austria) as part of The 2020 Paul J. Sally\, Jr
. Midwest Representation Theory Conference\n\n\nAbstract\nHarish-Chandra's
Lefschetz principle suggests that representations of real and p-adic spli
t reductive groups are closely related\, even though the methods used to s
tudy these groups are quite different. The local Langlands correspondence
indicates that these representation theoretic relationships stem from geom
etric relationships between real and p-adic Langlands parameters. In this
talk\, we will discuss how the geometric structure of real and p-adic Lang
lands parameters lead to functorial relationships between representations
of real and p-adic groups. I will describe work in progress\, joint with P
eter Trapa\, which applies this functoriality to the study of unitary repr
esentations and signatures of invariant hermitian forms\, for GL(n). The r
esult expresses signatures of invariant hermitian forms on graded affine H
ecke algebra modules in terms of signature characters of Harish-Chandra mo
dules\, which are computable via the unitary algorithm for real reductive
groups by Adams–van Leeuwen–Trapa–Vogan.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Jantzen (East Carolina University)
DTSTART:20201017T160000Z
DTEND:20201017T163000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/8
DESCRIPTION:Title: Generic representations for quasi-split similitude groups\nby Chris J
antzen (East Carolina University) as part of The 2020 Paul J. Sally\, Jr.
Midwest Representation Theory Conference\n\n\nAbstract\nIn this talk\, we
discuss the classification of irreducible generic representations for quas
i-split $p$-adic similitude groups\, as well as some of the background nee
ded to determine the classification.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stella Sue Gastineau (Boston College)
DTSTART:20201017T180000Z
DTEND:20201017T183000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/9
DESCRIPTION:Title: Diving into the Shallow End\nby Stella Sue Gastineau (Boston College)
as part of The 2020 Paul J. Sally\, Jr. Midwest Representation Theory Con
ference\n\n\nAbstract\nIn 2013\, Reeder–Yu gave a construction of superc
uspidal representations by starting with stable characters coming from the
shallowest depth of the Moy–Prasad filtration. In this talk\, we will b
e diving deeper—but not too deep. In doing so\, we will construct exampl
es of supercuspidal representations coming from a larger class of “shall
ow” characters. Using methods similar to Reeder–Yu\, we can begin to m
ake predictions about the Langlands parameters for these representations.\
n
LOCATION:https://researchseminars.org/talk/MRTC2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamanna Chatterjee (LSU)
DTSTART:20201017T183000Z
DTEND:20201017T190000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/10
DESCRIPTION:Title: Study of parity sheaves arising from graded Lie algebras\nby Tamanna
Chatterjee (LSU) as part of The 2020 Paul J. Sally\, Jr. Midwest Represen
tation Theory Conference\n\n\nAbstract\nLet $G$ be a complex\, connected\,
reductive\, algebraic group\, and $\\chi:\\mathbb{C}^\\times \\to G$ be a
fixed cocharacter that defines a grading on $\\mathfrak{g}$\, the Lie alg
ebra of $G$. Let $G_0$ be the centralizer of $\\chi(\\mathbb{C}^\\times)$.
In this paper\, we study $G_0$-equivariant parity sheaves on $\\mathfrak{
g}_n$\, under some assumptions on the field $\\Bbbk$ and the group $G$. Th
e assumption on $G$ holds for $GL_n$ and for any $G$\, it recovers results
of Lusztig in characteristic $0$. The main result is that every parity sh
eaf occurs as a direct summand of the parabolic induction of some cuspidal
pair.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Gordon (University of British Columbia)
DTSTART:20201018T143000Z
DTEND:20201018T150000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/11
DESCRIPTION:Title: Coefficients of the local character expansion are motivic\nby Julia
Gordon (University of British Columbia) as part of The 2020 Paul J. Sally\
, Jr. Midwest Representation Theory Conference\n\n\nAbstract\nIn 1994\, M
. Assem observed that with a suitable\nchoice of Haar measures\, the unipo
tent orbital integrals\non a connected reductive group G over a p-adic fie
ld are rational-valued for rational-valued test functions. He concluded th
at Shalika germs\, and in some cases\, the coefficients of the Harish-Chan
dras local character expansion are rational\, and conjectured that it shou
ld always be the case. I will try to outline a proof of the general case\,
which now uses the new kind of local character expansion due to Loren Spi
ce\, and motivic integration (to get a uniform result for almost all local
fields).\nThis is joint work in progress with Thomas Hales and Loren Spic
e.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Michigan)
DTSTART:20201018T153000Z
DTEND:20201018T160000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/12
DESCRIPTION:Title: The formal degree of a regular supercuspidal representation\nby Davi
d Schwein (University of Michigan) as part of The 2020 Paul J. Sally\, Jr.
Midwest Representation Theory Conference\n\n\nAbstract\nSupercuspidal rep
resentations are the building blocks for the representation theory of redu
ctive p-adic groups. Using a general and explicit construction of supercus
pidals due to J. K. Yu\, one can probe the fine structure of these represe
ntations. This talk studies a positive real number called the "formal degr
ee" that measures the size of the representation. In the first part we cal
culate the formal degree of a Yu representation. In the second part we exp
lain how the local Langlands correspondence predicts our calculation\, ver
ifying a conjecture of Hiraga\, Ichino\, and Ikeda.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Nevins (University of Ottawa)
DTSTART:20201018T160000Z
DTEND:20201018T163000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/13
DESCRIPTION:Title: Interpreting the Harish-Chandra—Howe local character expansion via bra
nching rules\nby Monica Nevins (University of Ottawa) as part of The 2
020 Paul J. Sally\, Jr. Midwest Representation Theory Conference\n\n\nAbst
ract\nThe Harish-Chandra–Howe local character expansion expresses the ch
aracter of an admissible representation of a $p$-adic group $G$ as a linea
r combination of Fourier transforms of nilpotent orbital integrals $\\wide
hat{\\mu}_{\\mathcal{O}}$ near the identity. We show that for $G=\\mathrm
{SL}(2\,k)$\, where the branching rules to maximal compact open subgroups
$K$ are known\, each of these terms $\\widehat{\\mu}_{\\mathcal{O}}$ can b
e interpreted as the character $\\tau_{\\mathcal{O}}$ of an infinite sum o
f representations of $K$\, up to an error term arising from the zero orbit
. Moreover\, the irreducible components of $\\tau_{\\mathcal{O}}$ are exp
licitly constructed from the $K$ -orbits in $\\mathcal{O}$. This work in
progress offers a conjectural alternative interpretation of branching rule
s of admissible representations.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Harris
DTSTART:20201018T180000Z
DTEND:20201018T183000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/14
DESCRIPTION:Title: Ramification of supercuspidal parameters\nby Michael Harris as part
of The 2020 Paul J. Sally\, Jr. Midwest Representation Theory Conference\n
\n\nAbstract\nLet $G$ be a reductive group over a local field $F$ of chara
cteristic $p$. Genestier and V. Lafforgue have constructed a\nsemi-simpl
e local Langlands parametrization for irreducible admissible representatio
ns of $G$\, with values in the $\\ell$-adic points\nof the $L$-group of $G
$\; the local parametrization is compatible with Lafforgue's global parame
trization of cuspidal \nautomorphic representations. Using this parametriz
ation and the theory of Frobenius weights\, we can define what it \nmeans
for a representation of $G$ to be "pure". \n\nAssume $G$ is split semisim
ple. In work in progress with three collaborators\, whose names will be
\nrevealed on October 18\, we have shown that a pure supercuspidal represe
ntation has ramified local parameter\, \nprovided the field of constants i
n $F$ has at least $3$ elements and has order prime to the order of the \n
Weyl group of $G$. In particular\, if the parameter of a pure representat
ion $\\pi$ is unramified then $\\pi$ is a\nconstituent of an unramified pr
incipal series. We are also able to prove in some cases that the ramifica
tion is wild.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20201018T183000Z
DTEND:20201018T190000Z
DTSTAMP:20260416T085349Z
UID:MRTC2020/15
DESCRIPTION:Title: Singular modular forms on quaternionic $\\mathrm{E}_8$\nby Aaron Pol
lack (UC San Diego) as part of The 2020 Paul J. Sally\, Jr. Midwest Repres
entation Theory Conference\n\n\nAbstract\nThe exceptional group $\\mathrm{
E}_{7\,3}$ has a symmetric space with Hermitian tube structure. On it\, H
enry Kim wrote down low weight holomorphic modular forms that are "singula
r" in the sense that their Fourier expansion has many terms equal to zero.
The exceptional group $\\mathrm{E}_{8\,4}$ does not have a Hermitian str
ucture\, but it has what might be the next best thing: a quaternionic stru
cture and associated "modular forms". I will explain the construction of s
ingular modular forms on $\\mathrm{E}_{8\,4}$\, and the proof that these s
pecial modular forms have rational Fourier expansions\, in a precise sense
. This builds off of work of Wee Teck Gan and uses key input from Gordan
Savin.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/15/
END:VEVENT
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