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BEGIN:VEVENT
SUMMARY:Jessica Fintzen (University of Bonn)
DTSTART:20250924T220000Z
DTEND:20250924T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/1
DESCRIPTION:Title: Reduction to depth-zero for $\\bar{\\mathbb{Z}}[1/p]$-representati
ons of p-adic groups\nby Jessica Fintzen (University of Bonn) as part
of University of Utah Representation Theory / Number Theory Seminar\n\nLec
ture held in LCB 222.\n\nAbstract\nThe category of smooth complex represen
tations of p-adic groups decomposes into Bernstein blocks and by a joint r
esult with Adler\, Mishra and Ohara from August 2024 we know that under so
me minor tameness assumptions each Bernstein block is equivalent to a dept
h-zero Bernstein block\, which are the representations that correspond rou
ghly 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 L
anglands correspondence to their depth-zero counterpart that is often easi
er to solve or already known. For number theoretic applications one likes
to have a similar result when working with representations whose coefficie
nts 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 i
s any ring that contains all p-power roots of unity\, a fourth root of uni
ty and the inverse of a square-root of p\, for example\, R could be a fiel
d of characteristic 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 analogous to the result with complex coefficients (except for the “b
locks” being “larger”)\, the proof is of a very different nature. In
the complex setting the proof is achieved via type theory and an isomorph
ism of Hecke algebras\, which are techniques not available for general R-r
epresentations. We will sketch in the talk how we deal with the category o
f R-representations instead.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20250827T220000Z
DTEND:20250827T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/2
DESCRIPTION:Title: Boundedness of singularities (joint with AG seminar)\nby Cheny
ang Xu (Princeton) as part of University of Utah Representation Theory / N
umber Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\n(Joint with
Ziquan Zhuang) In this lecture\, I will explain our boundedness results fo
r klt singularities with normalized volume bounded\nfrom below by a positi
ve constant.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Peterson (Institut de Mathématiques de Jussieu)
DTSTART:20250910T220000Z
DTEND:20250910T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/3
DESCRIPTION:Title: The multitemporal wave equation on Bruhat–Tits buildings\nby
Carsten Peterson (Institut de Mathématiques de Jussieu) as part of Unive
rsity of Utah Representation Theory / Number Theory Seminar\n\nLecture hel
d in LCB 222.\n\nAbstract\nThe Satake isomorphism is an algebra isomorphis
m from the spherical Hecke algebra $H(G\, K)$ of a (adjoint) semisimple gr
oup over a non-archimedean local field to $W$-invariant elements in the gr
oup ring of the coweight lattice $P$. The multitemporal wave equation on t
he Bruhat–Tits building\, first introduced in the work of Anker–Rémy
–Trojan '23\, then corresponds to functions $G/K \\times P \\to \\mathb
b{C}$ such 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 t
he “time variable” $P$. \n\nIn this talk we shall motivate this equati
on\, largely by focusing on the rank one case\, and discuss several of its
properties such as existence and uniqueness of solutions\, finite speed o
f propagation\, conservation of energy\, scattering theory\, and the conne
ction with objects of central interest in representation theory such as Sc
hur polynomials and Kazhdan–Lusztig polynomials. This is based on joint
ongoing work with Jean–Philippe Anker\, Bertrand Rémy\, and Bartosz Tro
jan.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UC San Diego)
DTSTART:20251105T230000Z
DTEND:20251106T000000Z
DTSTAMP:20260404T094657Z
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
classical topic in modular forms is the computation of the Fourier coeffi
cients of the Eisenstein series for GL(2). Computing the Fourier coefficie
nts of Eisenstein series on higher rank groups has been more difficult. I
will describe a method to do this computation in some new cases: for certa
in Eisenstein series on groups of type D_4\, F_4\, and E_n. I will also d
escribe some arithmetic applications\, including to solving an "exceptiona
l" counting problem. This is joint work in progress with Bryan Hu\, Jenni
fer Johnson-Leung\, Finn McGlade\, and Manami Roy.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Utah)
DTSTART:20250917T220000Z
DTEND:20250917T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/5
DESCRIPTION:Title: The Minimal Denominator in Function Fields\nby Noy Soffer Aran
ov (Utah) as part of University of Utah Representation Theory / Number The
ory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nMeiss and Sanders pro
posed an 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 discuss the history of this problem and its generalizations\, as well
as the function field analogue of the minimal denominator problem and ope
n questions. This is based off the preprint https://arxiv.org/pdf/2501.001
71.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (University of East Anglia)
DTSTART:20251015T220000Z
DTEND:20251015T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/7
DESCRIPTION:Title: The universal Harish-Chandra j-function\nby Justin Trias (Univ
ersity of East Anglia) as part of University of Utah Representation Theory
/ Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nThe Hari
sh–Chandra μ-function plays a central role in the explicit Plancherel f
ormula for a p-adic group G. It arises as the normalising factor for the P
lancherel measure on the unitary dual of G\, and is defined through the th
eory of intertwining operators.\n\nIn this talk\, we show how to extend th
e construction of the μ-function—or more precisely its inverse\, the j-
function—to all finitely generated representations\, and over general co
efficient 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-func
tion.\nBeyond its role in harmonic analysis\, the universal j-function als
o encodes arithmetic information: it reflects aspects of the local Langlan
ds correspondence for classical groups\, via Mœglin’s criterion and its
connection to reducibility points of parabolically induced representation
s. Time permitting\, we will illustrate how this perspective applies to th
e study of the local Langlands correspondence in families. This is joint w
ork with Gil Moss.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Young (Utah State University)
DTSTART:20251112T230000Z
DTEND:20251113T000000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/8
DESCRIPTION:Title: $\\widehat{Z}$-invariants for Lie superalgebras\nby Matt Young
(Utah State University) as part of University of Utah Representation Theo
ry / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nThe go
al of this talk is to explain a representation theoretic approach to physi
cists' so-called $\\widehat{Z}$-invariants of $3$-manifolds\, as introduce
d by Gukov\, Pei\, Putrov and Vafa in the context of $3$d $\\mathcal{N}=2$
supersymmetric gauge theory. Specifically\, we use the representation the
ory quantum supergroups to construct non-semisimple analogues of the modul
ar tensor categories Reshetikhin\, Turaev\, Andersen and others. These cat
egories can in turn be used to construct quantum invariants of $3$-manifol
ds\, certain limits of which recover the $\\widehat{Z}$-invariants. I will
focus on specific examples and will not assume any familiarity with quant
um topology. Based on joint work with Francesco Costantino\, Matthew Harpe
r and Adam Robertson.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kim (Stanford University)
DTSTART:20251119T230000Z
DTEND:20251120T000000Z
DTSTAMP:20260404T094657Z
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 Representat
ion Theory / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract
\nIgusa stacks and the geometry of p-adic Shimura varieties\nAbstract: Igu
sa stacks are p-adic geometric objects introduced by\nMingjia Zhang that p
arametrize p-adic uniformizations of Shimura\nvarieties. In a joint work w
ith Daniels\, van Hoften\, and Zhang\, we\nconstructed Igusa stacks for Ho
dge type Shimura data and explained how\nit provides a natural bridge betw
een categorical local Langlands and\nthe cohomology of Shimura varieties.
I will discuss some geometric\ninput that goes into the construction of Ig
usa stacks\, and if time\npermits\, their cohomological applications.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shenghao Li (Maryland)
DTSTART:20260114T230000Z
DTEND:20260115T000000Z
DTSTAMP:20260404T094657Z
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
Representation Theory / Number Theory Seminar\n\nLecture held in LCB 222.
\n\nAbstract\nLet G be an unramified group over a p-adic field F\, and F_r
/F an unramified extension of degree r. Let H(G) (resp. H(G(F_r)) denote t
he Hecke algebra of G(F) (resp. G(F_r)). Roughly speaking\, we say two fun
ctions \\phi\\in H(G(F_r)) and f\\in H(G) are associated (or matching func
tions) if they have the same stable orbital integrals. One main question i
s: how can we construct matching functions? In 1986\, Kottwitz proved the
unit elements of some Hecke algebras are associated. In 1990\, Clozel defi
ned a base change map between spherical Hecke algebras and proved the two
functions corresponded by the base change map are associated. Later in 200
9 and 2012\, Haines generalized Clozel's result to centers of parahoric He
cke algebras and Bernstein centers of depth zero principal series block. I
n this talk\, we will briefly introduce the history and set up of base cha
nge fundamental lemma\, and focus on how we can generalize the result to g
eneral principal series blocks. This requires the concrete constructions o
f types for principal series blocks of unramified groups\, and some concre
te computations of root groups\, which might give some inspirations on fut
ure study on deeper level structures.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ekta Tiwari (Ottawa)
DTSTART:20260128T230000Z
DTEND:20260129T000000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/11
DESCRIPTION:Title: Seeing representations of a group through the lens of its maximal
compact subgroups\nby Ekta Tiwari (Ottawa) as part of University of U
tah Representation Theory / Number Theory Seminar\n\nLecture held in LCB 2
22.\n\nAbstract\nA classical problem in representation theory is to unders
tand how an irreducible representation of a group decomposes when restrict
ed to its subgroups. Such questions are commonly referred to as branching
problems.\n\nIn this talk\, we will explore the restriction of irreducible
smooth representations of the unramified quasi-split unitary group U(1\,1
) to its hyperspecial maximal compact subgroup K. We will present explicit
branching rules in this setting and discuss several applications that ari
se from having a concrete description of these restrictions.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kei Yuen Chan (The University of Hong Kong)
DTSTART:20260318T220000Z
DTEND:20260318T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/12
DESCRIPTION:Title: Branching laws for general linear groups over local fields\nb
y Kei Yuen Chan (The University of Hong Kong) as part of University of Uta
h Representation Theory / Number Theory Seminar\n\nLecture held in LCB 222
.\n\nAbstract\nBranching laws describe how a representation is decomposed
when restricted to some subgroups. For general linear groups over local fi
elds\, we have a complete Langlands classification for irreducible represe
ntations. This talk aims for describing components for algorithms in compu
ting quotient branching laws in terms of Langlands parameters for $\\mathr
m{GL}(\\mathbb Q_p)$\, and some examples computed by Basudev Pattanayak. I
f time permits\, I will describe some perspectives on real groups from usi
ng the Ciubotaru-Trapa functor for $\\mathbb R$\, and a generalization to
$\\mathbb C$ in a joint work with Daniel Wong (CUHK\, Shenzhen).\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kei Yuen Chan (The University of Hong Kong)
DTSTART:20260401T220000Z
DTEND:20260401T230000Z
DTSTAMP:20260404T094657Z
UID:UtahRTNT/13
DESCRIPTION:Title: Branching laws for general linear groups over local fields: Ranki
n-Selberg integrals and minimal multisegments\nby Kei Yuen Chan (The U
niversity of Hong Kong) as part of University of Utah Representation Theor
y / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nI will
continue my talk two weeks ago. The first part of my talk explains the Ran
kin-Selberg integrals from the work of Jacquet--Pieteski-Shapiro--Shalika
and an extension by Cogdell--Piatetski-Shapiro\, and the second part of my
talk explains a notion of minimal multisegments and connections to Bernst
ein-Zelevinsky derivatives.\n
LOCATION:https://stable.researchseminars.org/talk/UtahRTNT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Marcil (University of Oregon)
DTSTART:20260429T220000Z
DTEND:20260429T230000Z
DTSTAMP:20260404T094657Z
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://stable.researchseminars.org/talk/UtahRTNT/14/
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