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SUMMARY:Jessica Fintzen (University of Bonn)
DTSTART:20250924T220000Z
DTEND:20250924T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/1
DESCRIPTION:Title: Reduction to depth-zero for $\\bar{\\mathbb{Z}}[1/p]$-representations of
p-adic groups\nby Jessica Fintzen (University of Bonn) as part of Univ
ersity of Utah Representation Theory / Number Theory Seminar\n\nLecture he
ld in LCB 222.\n\nAbstract\nThe category of smooth complex representations
of p-adic groups decomposes into Bernstein blocks and by a joint result w
ith Adler\, Mishra and Ohara from August 2024 we know that under some mino
r tameness assumptions each Bernstein block is equivalent to a depth-zero
Bernstein block\, which are the representations that correspond roughly to
representations of finite group of Lie type. This result allows to reduce
a lot of problems about representations of p-adic groups and the Langland
s correspondence to their depth-zero counterpart that is often easier to s
olve or already known. For number theoretic applications one likes to have
a similar result when working with representations whose coefficients are
a more general ring than the complex numbers. \n\nIn this talk we present
analogous results for R-representations of p-adic groups where R is any r
ing that contains all p-power roots of unity\, a fourth root of unity and
the inverse of a square-root of p\, for example\, R could be a field of ch
aracteristic different from p or the ring $\\bar{\\mathbb{Z}}[1/p]$. This
is joint work in progress with Jean-François Dat. While the result is ana
logous to the result with complex coefficients (except for the “blocks
” being “larger”)\, the proof is of a very different nature. In the
complex setting the proof is achieved via type theory and an isomorphism o
f Hecke algebras\, which are techniques not available for general R-repres
entations. We will sketch in the talk how we deal with the category of R-r
epresentations instead.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20250827T220000Z
DTEND:20250827T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/2
DESCRIPTION:Title: Boundedness of singularities (joint with AG seminar)\nby Chenyang Xu
(Princeton) as part of University of Utah Representation Theory / Number T
heory Seminar\n\nLecture held in LCB 222.\n\nAbstract\n(Joint with Ziquan
Zhuang) In this lecture\, I will explain our boundedness results for klt s
ingularities with normalized volume bounded\nfrom below by a positive cons
tant.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Peterson (Institut de Mathématiques de Jussieu)
DTSTART:20250910T220000Z
DTEND:20250910T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/3
DESCRIPTION:Title: The multitemporal wave equation on Bruhat–Tits buildings\nby Carste
n Peterson (Institut de Mathématiques de Jussieu) as part of University o
f Utah Representation Theory / Number Theory Seminar\n\nLecture held in LC
B 222.\n\nAbstract\nThe Satake isomorphism is an algebra isomorphism from
the spherical Hecke algebra $H(G\, K)$ of a (adjoint) semisimple group ove
r a non-archimedean local field to $W$-invariant elements in the group rin
g of the coweight lattice $P$. The multitemporal wave equation on the Bruh
at–Tits building\, first introduced in the work of Anker–Rémy–Troja
n '23\, then corresponds to functions $G/K \\times P \\to \\mathbb{C}$ su
ch that applying an element in $H(G\, K)$ to the “space variable” $G/K
$ is equal to applying its image under the Satake isomorphism in the “ti
me variable” $P$. \n\nIn this talk we shall motivate this equation\, lar
gely by focusing on the rank one case\, and discuss several of its propert
ies such as existence and uniqueness of solutions\, finite speed of propag
ation\, conservation of energy\, scattering theory\, and the connection wi
th objects of central interest in representation theory such as Schur poly
nomials and Kazhdan–Lusztig polynomials. This is based on joint ongoing
work with Jean–Philippe Anker\, Bertrand Rémy\, and Bartosz Trojan.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20251105T230000Z
DTEND:20251106T000000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/4
DESCRIPTION:Title: Fourier coefficients of Eisenstein series and applications\nby Aaron
Pollack (UC San Diego) as part of University of Utah Representation Theory
/ Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nA classi
cal topic in modular forms is the computation of the Fourier coefficients
of the Eisenstein series for GL(2). Computing the Fourier coefficients of
Eisenstein series on higher rank groups has been more difficult. I will de
scribe a method to do this computation in some new cases: for certain Eise
nstein series on groups of type D_4\, F_4\, and E_n. I will also describe
some arithmetic applications\, including to solving an "exceptional" coun
ting problem. This is joint work in progress with Bryan Hu\, Jennifer Joh
nson-Leung\, Finn McGlade\, and Manami Roy.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Utah)
DTSTART:20250917T220000Z
DTEND:20250917T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/5
DESCRIPTION:Title: The Minimal Denominator in Function Fields\nby Noy Soffer Aranov (Uta
h) as part of University of Utah Representation Theory / Number Theory Sem
inar\n\nLecture held in LCB 222.\n\nAbstract\nMeiss and Sanders proposed a
n experiment in which they fix $\\delta>0$ and study the statistics of the
minimal denominator $Q$ for which there exists a rational $\\frac{P}{Q}\\
in (x-\\delta\,x+\\delta)$\, where $x$ is varied. In this talk\, I will di
scuss the history of this problem and its generalizations\, as well as the
function field analogue of the minimal denominator problem and open quest
ions. This is based off the preprint https://arxiv.org/pdf/2501.00171.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (University of East Anglia)
DTSTART:20251015T220000Z
DTEND:20251015T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/7
DESCRIPTION:Title: The universal Harish-Chandra j-function\nby Justin Trias (University
of East Anglia) as part of University of Utah Representation Theory / Numb
er Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nThe Harish–Ch
andra μ-function plays a central role in the explicit Plancherel formula
for a p-adic group G. It arises as the normalising factor for the Plancher
el measure on the unitary dual of G\, and is defined through the theory of
intertwining operators.\n\nIn this talk\, we show how to extend the const
ruction of the μ-function—or more precisely its inverse\, the j-functio
n—to all finitely generated representations\, and over general coefficie
nt rings such as Z[1/p]. This leads to a universal j-function with values
in the Bernstein centre\, which specialises to the classical j-function.\n
Beyond its role in harmonic analysis\, the universal j-function also encod
es arithmetic information: it reflects aspects of the local Langlands corr
espondence for classical groups\, via Mœglin’s criterion and its connec
tion to reducibility points of parabolically induced representations. Time
permitting\, we will illustrate how this perspective applies to the study
of the local Langlands correspondence in families. This is joint work wit
h Gil Moss.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Young (Utah State University)
DTSTART:20251112T230000Z
DTEND:20251113T000000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/8
DESCRIPTION:Title: $\\widehat{Z}$-invariants for Lie superalgebras\nby Matt Young (Utah
State University) as part of University of Utah Representation Theory / Nu
mber Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nThe goal of t
his talk is to explain a representation theoretic approach to physicists'
so-called $\\widehat{Z}$-invariants of $3$-manifolds\, as introduced by Gu
kov\, Pei\, Putrov and Vafa in the context of $3$d $\\mathcal{N}=2$ supers
ymmetric gauge theory. Specifically\, we use the representation theory qua
ntum supergroups to construct non-semisimple analogues of the modular tens
or categories Reshetikhin\, Turaev\, Andersen and others. These categories
can in turn be used to construct quantum invariants of $3$-manifolds\, ce
rtain limits of which recover the $\\widehat{Z}$-invariants. I will focus
on specific examples and will not assume any familiarity with quantum topo
logy. Based on joint work with Francesco Costantino\, Matthew Harper and A
dam Robertson.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kim (Stanford University)
DTSTART:20251119T230000Z
DTEND:20251120T000000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/9
DESCRIPTION:Title: Igusa stacks and the geometry of p-adic Shimura varieties\nby Daniel
Kim (Stanford University) as part of University of Utah Representation The
ory / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nIgusa
stacks and the geometry of p-adic Shimura varieties\nAbstract: Igusa stac
ks are p-adic geometric objects introduced by\nMingjia Zhang that parametr
ize p-adic uniformizations of Shimura\nvarieties. In a joint work with Dan
iels\, van Hoften\, and Zhang\, we\nconstructed Igusa stacks for Hodge typ
e Shimura data and explained how\nit provides a natural bridge between cat
egorical local Langlands and\nthe cohomology of Shimura varieties. I will
discuss some geometric\ninput that goes into the construction of Igusa sta
cks\, and if time\npermits\, their cohomological applications.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shenghao Li (Maryland)
DTSTART:20260114T230000Z
DTEND:20260115T000000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/10
DESCRIPTION:Title: Base change fundamental lemma for Bernstein centers of principal series
blocks\nby Shenghao Li (Maryland) as part of University of Utah Repres
entation Theory / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbs
tract\nLet G be an unramified group over a p-adic field F\, and F_r/F an u
nramified extension of degree r. Let H(G) (resp. H(G(F_r)) denote the Heck
e algebra of G(F) (resp. G(F_r)). Roughly speaking\, we say two functions
\\phi\\in H(G(F_r)) and f\\in H(G) are associated (or matching functions)
if they have the same stable orbital integrals. One main question is: how
can we construct matching functions? In 1986\, Kottwitz proved the unit el
ements of some Hecke algebras are associated. In 1990\, Clozel defined a b
ase change map between spherical Hecke algebras and proved the two functio
ns corresponded by the base change map are associated. Later in 2009 and 2
012\, Haines generalized Clozel's result to centers of parahoric Hecke alg
ebras and Bernstein centers of depth zero principal series block. In this
talk\, we will briefly introduce the history and set up of base change fun
damental lemma\, and focus on how we can generalize the result to general
principal series blocks. This requires the concrete constructions of types
for principal series blocks of unramified groups\, and some concrete comp
utations of root groups\, which might give some inspirations on future stu
dy on deeper level structures.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ekta Tiwari (Ottawa)
DTSTART:20260128T230000Z
DTEND:20260129T000000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/11
DESCRIPTION:Title: Seeing representations of a group through the lens of its maximal compac
t subgroups\nby Ekta Tiwari (Ottawa) as part of University of Utah Rep
resentation Theory / Number Theory Seminar\n\nLecture held in LCB 222.\n\n
Abstract\nA classical problem in representation theory is to understand ho
w an irreducible representation of a group decomposes when restricted to i
ts subgroups. Such questions are commonly referred to as branching problem
s.\n\nIn this talk\, we will explore the restriction of irreducible smooth
representations of the unramified quasi-split unitary group U(1\,1) to it
s hyperspecial maximal compact subgroup K. We will present explicit branch
ing rules in this setting and discuss several applications that arise from
having a concrete description of these restrictions.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kei Yuen Chan (The University of Hong Kong)
DTSTART:20260318T220000Z
DTEND:20260318T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/12
DESCRIPTION:Title: Branching laws for general linear groups over local fields\nby Kei Y
uen Chan (The University of Hong Kong) as part of University of Utah Repre
sentation Theory / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAb
stract\nBranching laws describe how a representation is decomposed when re
stricted to some subgroups. For general linear groups over local fields\,
we have a complete Langlands classification for irreducible representation
s. This talk aims for describing components for algorithms in computing qu
otient branching laws in terms of Langlands parameters for $\\mathrm{GL}(\
\mathbb Q_p)$\, and some examples computed by Basudev Pattanayak. If time
permits\, I will describe some perspectives on real groups from using the
Ciubotaru-Trapa functor for $\\mathbb R$\, and a generalization to $\\math
bb C$ in a joint work with Daniel Wong (CUHK\, Shenzhen).\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kei Yuen Chan (The University of Hong Kong)
DTSTART:20260401T220000Z
DTEND:20260401T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/13
DESCRIPTION:Title: Branching laws for general linear groups over local fields: Rankin-Selbe
rg integrals and minimal multisegments\nby Kei Yuen Chan (The Universi
ty of Hong Kong) as part of University of Utah Representation Theory / Num
ber Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nI will continu
e my talk two weeks ago. The first part of my talk explains the Rankin-Sel
berg integrals from the work of Jacquet--Pieteski-Shapiro--Shalika and an
extension by Cogdell--Piatetski-Shapiro\, and the second part of my talk e
xplains a notion of minimal multisegments and connections to Bernstein-Zel
evinsky derivatives.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Marcil (University of Oregon)
DTSTART:20260429T220000Z
DTEND:20260429T230000Z
DTSTAMP:20260422T225825Z
UID:UtahRTNT/14
DESCRIPTION:by David Marcil (University of Oregon) as part of University o
f Utah Representation Theory / Number Theory Seminar\n\nLecture held in LC
B 222.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/14/
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