BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jackson Morrow (UC Berkeley)
DTSTART:20220914T210000Z
DTEND:20220914T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/1
DESCRIPTION:Title: Boundedness of hyperbolic varieties\nby Jackson Morrow (UC Berk
eley) as part of UBC (online) Number Theory Seminar\n\n\nAbstract\nLet $C_
1$\, $C_2$ be smooth projective curves over an algebraically closed field
$K$ of characteristic zero. What is the behavior of the set of non-constan
t maps $C_1 \\to C_2$? Is it infinite\, finite\, or empty? It turns out th
at the answer to this question is determined by an invariant of curves cal
led the genus. In particular\, if $C_2$ has genus $g(C_2)\\geq 2$ (i.e.\,
$C_2$ is hyperbolic)\, then there are only finitely many non-constant morp
hisms $C_1 \\to C_2$ where $C_1$ is any curve\, and moreover\, the degree
of any map $C_1 \\to C_2$ is bounded linearly in $g(C_1)$ by the Riemann--
Hurwitz formula. \n\nIn this talk\, I will explain the above story and dis
cuss a higher dimensional generalization of this result. To this end\, I w
ill describe the conjectures of Demailly and Lang which predict a relation
ship between the geometry of varieties\, topological properties of Hom-sch
emes\, and the behavior of rational points on varieties. To conclude\, I w
ill sketch a proof of a variant of these conjectures\, which roughly says
that if $X/K$ is a hyperbolic variety\, then for every smooth projective c
urve $C/K$ of genus $g(C)\\geq 0$\, the degree of any map $C\\to X$ is bou
nded uniformly in $g(C)$.\n\nJoin Zoom Meeting\nhttps://ubc.zoom.us/j/6784
3190638?pwd=eUJsc1oyY2xhYnM4NmU3OW1sTEV2dz09\n\nMeeting ID: 678 4319 0638\
nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Liu (UC Santa Barbara)
DTSTART:20220921T210000Z
DTEND:20220921T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/2
DESCRIPTION:Title: p-adic L-functions for GSp(4)\\times GL(2)\nby Zheng Liu (UC Sa
nta Barbara) as part of UBC (online) Number Theory Seminar\n\n\nAbstract\n
For a cuspidal automorphic representation $\\Pi$ of GSp(4) and a cuspidal
automorphic representation $\\pi$ of GL(2)\, Furusawa's formula can be use
d to study the special values of the degree-eight $p$-adic $L$-function $L
(s\,\\Pi\\times\\pi)$. In this talk\, I will explain a construction of the
$p$-adic $L$-function for $\\Pi\\times\\pi$ by using Furusawa's formula a
nd a family of Eisenstein series. The construction includes choosing local
test sections at p and computing the corresponding local zeta integrals.\
n\nJoin Zoom Meeting\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYn
M4NmU3OW1sTEV2dz09\n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville (Universite de Montreal)
DTSTART:20220928T200000Z
DTEND:20220928T210000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/3
DESCRIPTION:Title: $K$-rational points on curves\nby Andrew Granville (Universite
de Montreal) as part of UBC (online) Number Theory Seminar\n\n\nAbstract\n
Mazur and Rubin's ``Diophantine stability'' program suggests asking\, for
a given curve $C$\, over what fields $K$ does $C$ have rational points\,
or at least to study the degrees of such $K$. We study this question for p
lanar curves $C$ from various perspectives and relate solvability to the s
hape of $C$'s Newton polygon (the real original one that Newton worked wit
h\, not a $p$-adic one which are frequently used in arithmetic geometry r
esearch). This is joint work with Lea Beneish\n\nZoom link:\nhttps://ubc.z
oom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3OW1sTEV2dz09\n\nMeeting ID: 6
78 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (Oklahoma State University)
DTSTART:20221005T210000Z
DTEND:20221005T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/4
DESCRIPTION:Title: Sato-Tate groups in higher dimensions\nby Melissa Emory (Oklaho
ma State University) as part of UBC (online) Number Theory Seminar\n\n\nAb
stract\nGiven an abelian variety over a number field\, its Sato-Tate group
is a compact Lie group\, and it is conjectured to control the distributio
n of Euler factors of the L-function of the abelian variety. In this talk
we will begin with a discussion on the Sato-Tate conjecture for elliptic c
urves and discuss work that computes the Sato-Tate groups of families of h
yperelliptic curves of arbitrarily high genus and discuss some open proble
ms in this area. This work is joint with H. Goodson and A. Peyrot.\n\nJoin
Zoom Meeting\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3O
W1sTEV2dz09\n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wanlin Li (Washington University\, St. Louis)
DTSTART:20221012T210000Z
DTEND:20221012T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/5
DESCRIPTION:Title: A generalization of Elkies' theorem\nby Wanlin Li (Washington U
niversity\, St. Louis) as part of UBC (online) Number Theory Seminar\n\n\n
Abstract\nElkies proved that for a fixed elliptic curve E defined over Q\,
there exist infinitely many primes at which the reductions of E are super
singular. In this talk\, we give the first generalization of Elkies' theor
em to curves of genus >2. We consider families of cyclic covers of the pro
jective line ramified at 4 points parametrized by a Shimura curve. This is
joint work in progress with Elena Mantovan\, Rachel Pries\, and Yunqing T
ang.\n\nZoom link:\nhttps://ubc.zoom.us/j/67936242498?pwd=ZDZOdzZTcDBpZ3d4
c1YvSUc5M1Z0QT09\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusheng Lee (Columbia University)
DTSTART:20221026T210000Z
DTEND:20221026T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/6
DESCRIPTION:Title: Arithmetic of theta liftings\nby Yusheng Lee (Columbia Universi
ty) as part of UBC (online) Number Theory Seminar\n\n\nAbstract\nWe discus
s the integrality of theta liftings of anti-cyclotomic characters to a def
inite unitary group $\\mathrm{U}(2)$ of two variables. This will allow us
to construct a Hida family of the theta liftings and relate the congruence
module of which to an anti-cyclotomic $p$-adic L-function. The result is
an input to Urban's construction of Euler systems.\n\nJoin Zoom Meeting\nh
ttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3OW1sTEV2dz09\n\nM
eeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Malettos (UBC Vancouver)
DTSTART:20221102T210000Z
DTEND:20221102T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/7
DESCRIPTION:by Simone Malettos (UBC Vancouver) as part of UBC (online) Num
ber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Males (University of Manitoba/ PIMS)
DTSTART:20221116T220000Z
DTEND:20221116T233000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/8
DESCRIPTION:Title: Asymptotics of combinatorial and topological objects via modular fo
rms\nby Joshua Males (University of Manitoba/ PIMS) as part of UBC (on
line) Number Theory Seminar\n\n\nAbstract\nThe use of modular forms in des
cribing the asymptotic behaviour of interesting objects goes back to the i
nvention of the Circle Method by Hardy and Ramanujan over 100 years ago. I
n this talk\, I'll describe several results in how we can use modular form
s and their relations to study newer objects\; in particular the distribut
ion over arithmetic progressions and bias in arithmetic progressions of ce
rtain combinatorial and topological objects. Finally\, I'll talk briefly a
bout some ongoing work that describes the asymptotic behaviour of a Nahm-t
ype sum which displays much more intricate behaviour than classical modula
r objects.\n\nParts of this talk will be based on works with various combi
nations of Kathrin Bringmann\, Giulia Cesana\, Will Craig\, Amanda Folsom\
, Ken Ono\, Larry Rolen\, and Matthias Storzer.\n\nMeeting ID: 678 4319 06
38\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Payman Eskandari (University of Winnipeg)
DTSTART:20221207T220000Z
DTEND:20221207T233000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/9
DESCRIPTION:by Payman Eskandari (University of Winnipeg) as part of UBC (o
nline) Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manami Roy (Fordham University)
DTSTART:20221019T210000Z
DTEND:20221019T223000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/10
DESCRIPTION:Title: Dimensions of spaces of Siegel cusp forms of degree 2\nby Mana
mi Roy (Fordham University) as part of UBC (online) Number Theory Seminar\
n\n\nAbstract\nComputing dimension formulas for the spaces of Siegel modul
ar forms of degree 2 is of great interest to many mathematicians. We will
start by discussing known results and methods in this context. The dimensi
ons of the spaces of Siegel cusp forms of non-squarefree levels are mostly
unavailable in the literature. This talk will present new dimension formu
las of Siegel cusp forms of degree 2\, weight k\, and level 4 for three co
ngruence subgroups. Our method relies on counting a particular set of cusp
idal automorphic representations of GSp(4) and exploring its connection to
dimensions of spaces of Siegel cusp forms of degree 2. This is recent wor
k (arXiv:2207.02747) with Ralf Schmidt and Shaoyun Yi.\n\nMeeting ID: 678
4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Schneider (University of Münster)
DTSTART:20221123T220000Z
DTEND:20221123T233000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/11
DESCRIPTION:by Peter Schneider (University of Münster) as part of UBC (on
line) Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Huang (UBC Vancouver)
DTSTART:20221130T220000Z
DTEND:20221130T233000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/12
DESCRIPTION:Title: Unit equations on quaternions\nby Yifeng Huang (UBC Vancouver)
as part of UBC (online) Number Theory Seminar\n\n\nAbstract\nA classical
theorem in number theory states that for any finitely generated subgroup $
\\Gamma$ of $\\mathbb{C}*$\, the "unit equation” $x+y=1$ has only finite
ly many solutions with $x\,y\\in \\Gamma$. One can view it as a statement
that relates addition and multiplication of complex numbers in a fundament
al way. Our main result (arXiv: 1910.13250) is an analog of this theorem o
n quaternions\, where the multiplication is no longer commutative. We then
explain its connection to iterations of self-maps on abelian varieties\,
and give a result about an orbit intersection problem as an application. T
he approach to our main result is based on the analysis of the Euclidean n
orm on quaternions\, and Baker’s estimate of linear combinations of loga
rithms. Time permitting\, I will sketch a proof focusing on how the diffic
ulties caused by noncommutativity are miraculously addressed in our case.\
n\nJoin Zoom Meeting\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYn
M4NmU3OW1sTEV2dz09\n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Knapp (University of Oregon)
DTSTART:20221214T220000Z
DTEND:20221214T233000Z
DTSTAMP:20260404T111245Z
UID:UBC_NTS/13
DESCRIPTION:Title: Bounds on the Number of Solutions to Thue’s Inequality\nby G
reg Knapp (University of Oregon) as part of UBC (online) Number Theory Sem
inar\n\n\nAbstract\nIn 1909\, Thue proved that when $F(x\,y) \\in \\mathbb
{Z}[x\,y]$ is irreducible\, homogeneous\, and has degree at least 3\, the
inequality $|F(x\,y)| \\leq h$ has finitely many integer-pair solutions fo
r any positive $h$. Because of this result\, the inequality $|F(x\,y)| \\
leq h$ is known as Thue’s Inequality and much work has been done to find
sharp bounds on the number of integer-pair solutions to Thue’s Inequali
ty. In this talk\, I will describe different techniques used by Baker\; M
ueller and Schmidt\; Saradha and Sharma\; Thomas\; and Akhtari and Bengoec
hea to make progress on this general problem. After that\, I will discuss
some improvements that can be made to a counting technique used in associ
ation with ``the gap principle’’ and how those improvements lead to be
tter bounds on the number of solutions to Thue’s Inequality.\n\nJoin Zoo
m Meeting\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3OW1sT
EV2dz09\n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://stable.researchseminars.org/talk/UBC_NTS/13/
END:VEVENT
END:VCALENDAR