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BEGIN:VEVENT
SUMMARY:Stella Sue Gastineau (Boston College)
DTSTART:20200520T220000Z
DTEND:20200520T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/1
DESCRIPTION:Title: Diving into the shallow end\nby Stella Sue Gastineau (
Boston College) as part of University of Oregon Number Theory Seminar\n\n\
nAbstract\nIn 2013\, Reeder-Yu gave a construction of supercuspidal repres
entations by starting with stable characters coming from the shallowest de
pth of the Moy-Prasad filtration. In this talk\, we will be diving deeper
—but not too deep. In doing so\, we will construct examples of supercusp
idal representations coming from a larger class of "shallow" characters. U
sing methods similar to Reeder-Yu\, we can begin to make predictions about
the Langlands parameters for these representations.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (University of California\, Los Angeles)
DTSTART:20200527T220000Z
DTEND:20200527T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/2
DESCRIPTION:Title: Construction of Euler Systems for $\\mathrm{GSp}_4×\\math
rm{GL}_2$\nby Chi-Yun Hsu (University of California\, Los Angeles) as
part of University of Oregon Number Theory Seminar\n\n\nAbstract\nAn Euler
system is a collection of norm-compatible first Galois cohomology classes
with the Galois groups varying over cyclotomic fields. By constructing an
Euler system\, one can bound the Selmer group of Galois representations.
We construct Euler systems for the Galois representations coming from auto
morphic representations of $\\mathrm{GSp}_4×\\mathrm{GL}_2$. The strategy
follows the work of Loeffler-Zerbes-Skinner in the case of $\\mathrm{GSp}
_4$\, using automorphic input to show norm compatibility. This is a work i
n progress with Zhaorong Jin and Ryotaro Sakamoto.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christelle Vincent (University of Vermont)
DTSTART:20200603T220000Z
DTEND:20200603T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/3
DESCRIPTION:Title: On the equidistribution of joint shapes of rings and their
resolvents\nby Christelle Vincent (University of Vermont) as part of
University of Oregon Number Theory Seminar\n\n\nAbstract\nIn her thesis\,
Piper H showed that "shapes of number fields" are "equidistributed" under
certain mild and expected conditions. The proof uses Bhargava's parametriz
ation of cubic\, quartic\, and quintic rings\, which itself works by attac
hing to each such ring one or more "resolvent ring" and parametrizing ring
s with a choice of resolvent.\n\nA natural question then arises: Are the s
hapes of a ring and its resolvent independent of one another\; in other wo
rds is the ordered pair of shapes equidistributed too? What if we replace
rings and a choice of resolvent ring with fields and their resolvent field
s?\n\nIn this talk we will introduce the notion of the shape of a ring or
number field\, briefly define what we mean by equidistribution in this con
text\, and describe the resolvent ring of a quartic ring. We will then giv
e a glimpse of the difficulties in extending a result about rings and thei
r resolvents to fields and their resolvents. This is joint work with Piper
H.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Webster (University of Oregon)
DTSTART:20201021T180000Z
DTEND:20201021T190000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/4
DESCRIPTION:Title: The p-adic Mehta Integral\nby Joe Webster (University
of Oregon) as part of University of Oregon Number Theory Seminar\n\n\nAbst
ract\nThe Mehta integral is the canonical partition function for 1-dimensi
onal log-Coulomb gas in a harmonic potential well. Mehta and Dyson showed
that it also determines the joint probability densities for the eigenvalue
s of Gaussian random matrix ensembles\, and Bombieri later found its expli
cit form. We introduce the p-adic analogue of the Mehta integral as the ca
nonical partition function for a p-adic log-Coulomb gas\, discuss its unde
rlying combinatorial structure\, and find its explicit formula and domain.
\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (Harvard)
DTSTART:20201104T190000Z
DTEND:20201104T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/5
DESCRIPTION:by Yujie Xu (Harvard) as part of University of Oregon Number T
heory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (University of Chicago)
DTSTART:20201111T190000Z
DTEND:20201111T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/6
DESCRIPTION:Title: Cohomology of Arithmetic Groups and Endoscopy\nby Math
ilde Gerbelli-Gauthier (University of Chicago) as part of University of Or
egon Number Theory Seminar\n\n\nAbstract\nHow fast do Betti numbers grow i
n a congruence tower of compact arithmetic manifolds? The dimension of the
middle degree of cohomology is proportional to the volume of the manifold
\, but away from the middle the growth is known to be sub-linear in the vo
lume. I will explain how automorphic representations and the phenomenon of
endoscopy provide a framework to understand and quantify this slow growth
. Specifically\, I will discuss how to obtain some explicit bounds in the
case of unitary groups using Arthur's stable trace formula.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (University of Toronto)
DTSTART:20201118T190000Z
DTEND:20201118T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/7
DESCRIPTION:Title: A multiplicity one theorem for general spin groups\nby
Melissa Emory (University of Toronto) as part of University of Oregon Num
ber Theory Seminar\n\n\nAbstract\nA classical problem in representation th
eory is how a\nrepresentation of a group decomposes when restricted to a s
ubgroup. In the\n1990s\, Gross-Prasad formulated an intriguing conjecture
regarding the\nrestriction of representations\, also known as branching la
ws\, of special\northogonal groups. Gan\, Gross and Prasad extended this
conjecture\, now\nknown as the local Gan-Gross-Prasad (GGP) conjecture\, t
o the remaining\nclassical groups. There are many ingredients needed to pr
ove a local GGP\nconjecture. In this talk\, we will focus on the first in
gredient: a\nmultiplicity at most one theorem. Aizenbud\, Gourevitch\, Ral
lis and\nSchiffmann proved a multiplicity (at most) one theorem for restri
ctions of\nirreducible representations of certain p-adic classical groups
and\nWaldspurger proved the same theorem for the special orthogonal groups
. We\nwill discuss work that establishes a multiplicity (at most) one theo
rem\nfor restrictions of irreducible representations for a non-classical g
roup\,\nthe general spin group. This is joint work with Shuichiro Takeda.\
n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aycock (University of Oregon)
DTSTART:20201125T190000Z
DTEND:20201125T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/8
DESCRIPTION:Title: Overconvergent Differential Operators Acting on Modular Fo
rms.\nby Jon Aycock (University of Oregon) as part of University of Or
egon Number Theory Seminar\n\n\nAbstract\nIn the 1970's\, Katz used Damere
ll's formula to construct p-adic L-functions for CM fields by interpolatin
g differential operators. However\, these operators were only defined over
the ordinary locus\, leading to restrictions on p. Recently\, a geometric
theory of overconvergent modular forms has given a way around these restr
ictions. I will describe how to do this in the case of modular forms\, and
then give a brief template for the Hilbert case.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananth Shankar (University of Wisconsin)
DTSTART:20201202T190000Z
DTEND:20201202T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/9
DESCRIPTION:Title: A finiteness criterion for 2-dimensional representations o
f surface groups\nby Ananth Shankar (University of Wisconsin) as part
of University of Oregon Number Theory Seminar\n\n\nAbstract\nLet C be a a
complex algebraic curve of genus $\\geq 1$\, and let $\\pi$ be its fundame
ntal group. Let $\\rho: \\pi\\rightarrow \\GL_2(\\C)$ be a semisimple 2-di
mensional representation\, such that $\\rho(\\alpha)$ has finite order for
every simple closed loop $\\alpha.$ We will prove that $\\rho$ has finite
image. If time permits\, we will mention applications of this result to t
he Grothendieck-Katz p-curvature conjecture. This is joint work with Anand
Patel and Junho Peter Whang.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART:20210217T190000Z
DTEND:20210217T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/10
DESCRIPTION:Title: Rational points on twist families of curves\nby Ari S
hnidman (Hebrew University of Jerusalem) as part of University of Oregon N
umber Theory Seminar\n\n\nAbstract\nA curve C of genus g > 1 has finite au
tomorphism group G. If C is defined over a number field F\, we consider a
twist family of C\, which is a family of curves over F each of which is is
omorphic C over the algebraic closure of F. For example\, the family C_d
: x^6 + y^6 = d is a family of twists of the degree 6 fermat curve C_1. In
this talk\, I'll present some results which show that for various twist f
amilies\, a large proportion of twists have very few F-rational points. F
or example\, we can show that C_d(Q) is empty for at least 66% of integers
d. Our proofs generally have two steps: bound the average rank of the Jac
obian using a 3-descent\, and then apply Chabauty-like methods to bound th
e number of rational points when the rank is small.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Razan Taha (Purdue University)
DTSTART:20210303T190000Z
DTEND:20210303T200000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/11
DESCRIPTION:Title: p-adic Measures for Reciprocals of L-functions of Totally
Real Fields\nby Razan Taha (Purdue University) as part of University
of Oregon Number Theory Seminar\n\n\nAbstract\nIn 2014\, Gelbart\, Miller\
, Panchishkin\, and Shahidi introduced an analog to part of the Langlands-
Shahidi method by constructing certain p-adic L-functions using the non-co
nstant Fourier coefficients of Eisenstein series. In this talk\, we extend
their work to totally real number fields. We construct p-adic measures wh
ich interpolate the special values of p-adic L-functions of a totally real
field K at negative integers. These measures are defined by analyzing the
non-constant terms of partial Eisenstein series of the Hilbert modular gr
oup.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Mundy (Columbia University)
DTSTART:20210510T220000Z
DTEND:20210510T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/12
DESCRIPTION:Title: The Skinner--Urban method and the symmetric cube Bloch--K
ato conjecture\nby Sam Mundy (Columbia University) as part of Universi
ty of Oregon Number Theory Seminar\n\n\nAbstract\nThe Skinner--Urban metho
d is a general method which can be used to construct nontrivial elements i
n the Bloch--Kato Selmer groups attached to certain Galois representations
. After giving a historical overview of the method as well as techniques w
hich preceded it\, I will briefly explain how it can be used to construct
nontrivial elements in the Selmer group for the symmetric cube of the Galo
is representation attached to a level 1 modular form\, under certain stand
ard conjectures. This will take us through the theory of automorphic forms
and Galois representations for the exceptional group G_2.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (University of Luxembourg)
DTSTART:20210524T210000Z
DTEND:20210524T220000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/13
DESCRIPTION:Title: Revisiting the modularity of the abelian surfaces of cond
uctor 277\nby Lassina Dembélé (University of Luxembourg) as part of
University of Oregon Number Theory Seminar\n\n\nAbstract\nThere is an isog
eny class of semistable abelian surfaces $A$ with good reduction outside $
277$ and $End_Q(A) = \\Z$. The modularity (or paramodularity) of this clas
se was proved by a team of six people: Armand Brumer\, Ariel Pacetti\, Cri
s Poor\, Gonzalo Tornaria\, John Voight and David Yuen. They did so by usi
ng the so-called Faltings-Serre method. This was the first known case of t
he paramodularity conjecture. In this work in progress\, I will discuss ho
w to (re-)prove the modularity of these surfaces by directly applying defo
rmation theory. This could be seen as an explicit approach to deformation
theory.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gil Moss (University of Utah)
DTSTART:20210426T220000Z
DTEND:20210426T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/14
DESCRIPTION:Title: Moduli of Langlands parameters\nby Gil Moss (Universi
ty of Utah) as part of University of Oregon Number Theory Seminar\n\n\nAbs
tract\nThe local Langlands correspondence connects representation of p-adi
c groups to Langlands parameters\, which are certain representations of Ga
lois groups of local fields. In recent work with Dat\, Helm\, and Kurinczu
k\, we have shown that Langlands parameters\, when viewed through the righ
t lens\, occur naturally within a moduli space over Z[1/p]\, and we can sa
y some things about the geometry of this moduli space. This geometry shoul
d be reflected in the representation theory of p-adic groups\, on the othe
r side of the local Langlands correspondence. The "local Langlands in fami
lies" conjecture describes the moduli space of Langlands parameters in ter
ms of the center of the category of representations of the p-adic group--
it was established for GL(n) in 2018. The goal of the talk is to give an o
verview of this picture\, including current work in-progress\, with some d
iscussion of the relation with recent work of Zhu and Fargues-Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Williams (RWTH Aachen)
DTSTART:20210503T203000Z
DTEND:20210503T213000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/15
DESCRIPTION:Title: Borcherds products and a ring of Hermitian modular forms<
/a>\nby Brandon Williams (RWTH Aachen) as part of University of Oregon Num
ber Theory Seminar\n\n\nAbstract\nWe will compute the ring of modular form
s for the group U(2\, 2) over the integers in Q(\\sqrt{-7}). The main tool
is Borcherds products and their application to Hermitian modular forms du
e to Dern.\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lowry-Duda (ICERM)
DTSTART:20210517T220000Z
DTEND:20210517T230000Z
DTSTAMP:20260404T095030Z
UID:UOregonNTSeminar/16
DESCRIPTION:Title: Visualizing modular forms\nby David Lowry-Duda (ICERM
) as part of University of Oregon Number Theory Seminar\n\n\nAbstract\nWe
investigate ways to visualize modular forms. A good visualization of\na mo
dular form should reveal some of the highly symmetric structure of\nthe mo
dular form. But different methods of visualization shine different\nspotli
ghts on the modular form. In this talk\, we examine different\nmethods of
making and studying these visualizations. Further\, we'll\nexamine both cl
assical and non-classical modular forms in a variety of\ndifferent visuali
zations. There will be lots and lots of pictures!\n
LOCATION:https://stable.researchseminars.org/talk/UOregonNTSeminar/16/
END:VEVENT
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