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BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard University)
DTSTART;VALUE=DATE-TIME:20210922T221000Z
DTEND;VALUE=DATE-TIME:20210922T231000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/1
DESCRIPTION:Title: Heegner points and patched Euler systems in anticyclotomic Iwasawa t
heory\nby Naomi Sweeting (Harvard University) as part of UBC Number th
eory seminar\n\n\nAbstract\nThis talk will report on recent work proving n
ew cases of the\nHeegner Point Main Conjecture of Perrin-Riou. I'll explai
n the statement of\nthe conjecture and the method of patched bipartite Eul
er systems used in\nthe proof. This method reduces the HPMC to a main conj
ecture of Bertolini\nand Darmon "at infinite level"\, which can be resolve
d using the work of\nSkinner-Urban along with a deformation-theoretic inpu
t following methods of\nFakhruddin-Khare-Patrikis. One consequence of the
results is an improved\np-converse theorem to the work of Gross-Zagier and
Kolyvagin: p-Selmer rank\none implies analytic rank one.\n\nPlease sign u
p for the talk using the link https://ubc.zoom.us/meeting/register/u5Yrfu2
sqTkoH9AqIzq7m7896a2yg2A6BlSe and the zoom link will be sent to your maili
ng address.\n
LOCATION:https://researchseminars.org/talk/number_theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Beneish (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210915T220000Z
DTEND;VALUE=DATE-TIME:20210915T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/2
DESCRIPTION:Title: Fields generated by points on superelliptic curves\nby Lea Benei
sh (UC Berkeley) as part of UBC Number theory seminar\n\n\nAbstract\nWe gi
ve an asymptotic lower bound on the number of field\nextensions generated
by algebraic points on superelliptic curves over\n$\\mathbb{Q}$ with fixed
degree $n$\, discriminant bounded by $X$\, and Galois\nclosure $S_n$. For
$C$ a fixed curve given by an affine equation $y^m =\nf(x)$ where $m \\ge
q 2$ and $deg f(x) = d \\geq m$\, we find that for all\ndegrees $n$ divisi
ble by $gcd(m\, d)$ and sufficiently large\, the number of\nsuch fields is
asymptotically bounded below by $X^{c_n}$ \, where $c_n$ goes to\n$1/m^2$
as $n$ goes to $\\infty$. This bound is determined explicitly by\nparamet
erizing $x$ and $y$ by rational functions\, counting specializations\,\nan
d accounting for multiplicity. We then give geometric heuristics\nsuggesti
ng that for $n$ not divisible by $gcd(m\, d)$\, degree $n$ points\nmay be
less abundant than those for which $n$ is divisible by $gcd(m\, d)$.\nName
ly\, we discuss the obvious geometric sources from which we expect to\nfin
d points on $C$ and discuss the relationship between these sources and\nou
r parametrization. When one a priori has a point on $C$ of degree not\ndiv
isible by $gcd(m\, d)$\, we argue that a similar counting argument\napplie
s. As a proof of concept we show in the case that $C$ has a rational\npoin
t that our methods can be extended to bound the number of fields\ngenerate
d by a degree $n$ point of $C$\, regardless of divisibility of $n$\nby $gc
d(m\, d)$. This talk is based on joint work with Christopher Keyes.\n\nPle
ase sign up for the talk using the link https://ubc.zoom.us/meeting/regist
er/u5Yrfu2sqTkoH9AqIzq7m7896a2yg2A6BlSe and the zoom link will be sent to
your mailing address.\n
LOCATION:https://researchseminars.org/talk/number_theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20211013T220000Z
DTEND;VALUE=DATE-TIME:20211013T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/3
DESCRIPTION:Title: Arithmetic statistics and diophantine stability for elliptic curves<
/a>\nby Anwesh Ray (University of British Columbia) as part of UBC Number
theory seminar\n\n\nAbstract\nIn 2017\, B. Mazur and K. Rubin introduced t
he notion of diophantine stability for a variety defined over a number fie
ld. Given an elliptic curve E defined over the rationals and a prime numbe
r p\, E is said to be diophantine stable at p if there are abundantly many
p-cyclic extensions $L/\\mathbb{Q}$ such that $E(L)=E(\\mathbb{Q})$. In p
articular\, this means that given any integer $n>0$\, there are infinitely
many cyclic extensions with Galois group $\\mathbb{Z}/p^n\\mathbb{Z}$\, s
uch that $E(L)=E(\\mathbb{Q})$. It follows from more general results of Ma
zur-Rubin that $E$ is diophantine stable at a positive density set of prim
es p.\n\nIn this talk\, I will discuss diophantine stability of average fo
r pairs $(E\,p)$\, where $E$ is a non-CM elliptic curve and $p\\geq 11$ is
a prime number at which $E$ has good ordinary reduction. First\, I will f
ix the elliptic curve and vary the prime. In this context\, it is shown th
at diophantine stability is a consequence of certain properties of Selmer
groups studied in Iwasawa theory. Statistics for Iwasawa invariants were s
tudied recently (in joint work with collaborators). As an application\, on
e shows that if the Mordell Weil rank of E is zero\, then\, $E$ is diophan
tine stable at $100\\%$ of primes $p$. One also shows that standard conjec
tures (like rank distribution) imply that for any prime $p\\geq 11$\, a po
sitive density set of elliptic curves (ordered by height) is diophantine s
table at $p$. I will also talk about related results for stability and gro
wth of the p-primary part of the Tate-Shafarevich group in cyclic p-extens
ions.\n
LOCATION:https://researchseminars.org/talk/number_theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (Ohio State University)
DTSTART;VALUE=DATE-TIME:20211020T220000Z
DTEND;VALUE=DATE-TIME:20211020T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/4
DESCRIPTION:Title: Counting elliptic curves with rational N-isogeny\nby Soumya Sank
ar (Ohio State University) as part of UBC Number theory seminar\n\n\nAbstr
act\nThe classical problem of counting elliptic curves with a rational\nN-
isogeny can be phrased in terms of counting rational points on certain mod
uli\nstacks of elliptic curves. Counting points on stacks poses various ch
allenges\,\nand I will discuss these along with a few ways to overcome the
m. I will also\ntalk about the theory of heights on stacks developed in re
cent work of\nEllenberg\, Satriano and Zureick-Brown and use it to count e
lliptic curves with\nan N-isogeny for certain N. The talk assumes no prior
knowledge of stacks and\nis based on joint work with Brandon Boggess.\n
LOCATION:https://researchseminars.org/talk/number_theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20210929T221000Z
DTEND;VALUE=DATE-TIME:20210929T231000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/5
DESCRIPTION:Title: Heegner points and generalised Kato classes\nby Francesc Castell
a (UC Santa Barbara) as part of UBC Number theory seminar\n\n\nAbstract\nF
or an elliptic curve $E/\\mathbb{Q}$ and a fixed prime $p$\, a\ncelebrated
"$p$-converse" to a theorem of Kolyvagin takes the form of the\nimplicati
on: If the $p^\\infty$ Selmer group of $E$ has\n$\\mathbb{Z}_p$-corank one
\, then a certain Heegner is non-torsion. The\nGross-Zagier formula then a
llows one to conclude that $E$ has analytic rank\none. Following the pione
ering work of Skinner and Wei Zhang\, a growing\nnumber of results are kno
wn in the direction of this $p$-converse. In this\ntalk\, I'll describe th
e proof of a result in the same spirit for elliptic\ncurves of rank two\,
in which Heegner points are replaced by certain\ngeneralised Kato classes
introduced by Darmon and Rotger. The talk is based\non joint work with M.-
L. Hsieh.\n
LOCATION:https://researchseminars.org/talk/number_theory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artane Siad (IAS/Princeton)
DTSTART;VALUE=DATE-TIME:20211027T220000Z
DTEND;VALUE=DATE-TIME:20211027T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/6
DESCRIPTION:by Artane Siad (IAS/Princeton) as part of UBC Number theory se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (U Oregon)
DTSTART;VALUE=DATE-TIME:20211201T230000Z
DTEND;VALUE=DATE-TIME:20211202T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/7
DESCRIPTION:by Ellen Eischen (U Oregon) as part of UBC Number theory semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylan Gajek-Leonard (UMass Amherst)
DTSTART;VALUE=DATE-TIME:20211006T220000Z
DTEND;VALUE=DATE-TIME:20211006T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/8
DESCRIPTION:Title: Iwasawa Invariants of Modular Forms with $a_p=0$\nby Rylan Gajek
-Leonard (UMass Amherst) as part of UBC Number theory seminar\n\n\nAbstrac
t\nMazur-Tate elements provide a convenient method to study the\nanalytic
Iwasawa theory of p-nonordinary modular forms\, where the\nassociated p-ad
ic L-functions tend to have unbounded coefficients. The\nIwasawa invariant
s of Mazur-Tate elements are well-understood in the case\nof weight 2 modu
lar forms\, where they can be related to the growth of\np-Selmer groups an
d decompositions of the p-adic L-function. At higher\nweights\, less is kn
own. By constructing certain lifts to the full Iwasawa\nalgebra\, we compu
te the Iwasawa invariants of Mazur-Tate elements for\nhigher weight modula
r forms with $a_p=0$ in terms of the plus/minus\ninvariants of the p-adic
L-function. Combined with results of\nPollack-Weston\, this forces a relat
ion between the plus/minus invariants\nat weights 2 and p+1.\n
LOCATION:https://researchseminars.org/talk/number_theory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hoi Yip (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20211117T230000Z
DTEND;VALUE=DATE-TIME:20211118T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/9
DESCRIPTION:by Chi Hoi Yip (University of British Columbia) as part of UBC
Number theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Garcia-Fritz (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20211103T220000Z
DTEND;VALUE=DATE-TIME:20211103T230000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/10
DESCRIPTION:by Natalia Garcia-Fritz (Pontificia Universidad Católica de C
hile) as part of UBC Number theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashay Burungale (Caltech/UT Austin)
DTSTART;VALUE=DATE-TIME:20211124T230000Z
DTEND;VALUE=DATE-TIME:20211125T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/11
DESCRIPTION:by Ashay Burungale (Caltech/UT Austin) as part of UBC Number t
heory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prajeet Bajpai (UBC)
DTSTART;VALUE=DATE-TIME:20211208T230000Z
DTEND;VALUE=DATE-TIME:20211209T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/12
DESCRIPTION:by Prajeet Bajpai (UBC) as part of UBC Number theory seminar\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Hartmann (UPenn)
DTSTART;VALUE=DATE-TIME:20211215T230000Z
DTEND;VALUE=DATE-TIME:20211216T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/13
DESCRIPTION:by Julia Hartmann (UPenn) as part of UBC Number theory seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbey Bourdon (Wake Forest University)
DTSTART;VALUE=DATE-TIME:20211220T230000Z
DTEND;VALUE=DATE-TIME:20211221T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/14
DESCRIPTION:by Abbey Bourdon (Wake Forest University) as part of UBC Numbe
r theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heidi Goodson (Brooklyn College)
DTSTART;VALUE=DATE-TIME:20220112T230000Z
DTEND;VALUE=DATE-TIME:20220113T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/15
DESCRIPTION:by Heidi Goodson (Brooklyn College) as part of UBC Number theo
ry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State University)
DTSTART;VALUE=DATE-TIME:20220119T230000Z
DTEND;VALUE=DATE-TIME:20220120T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/16
DESCRIPTION:by Preston Wake (Michigan State University) as part of UBC Num
ber theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220126T230000Z
DTEND;VALUE=DATE-TIME:20220127T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/17
DESCRIPTION:by Melissa Emory (University of Toronto) as part of UBC Number
theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Lalin (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20220209T230000Z
DTEND;VALUE=DATE-TIME:20220210T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/18
DESCRIPTION:by Matilde Lalin (Université de Montréal) as part of UBC Num
ber theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Isham (Colgate University)
DTSTART;VALUE=DATE-TIME:20220202T230000Z
DTEND;VALUE=DATE-TIME:20220203T000000Z
DTSTAMP;VALUE=DATE-TIME:20211022T090807Z
UID:number_theory/19
DESCRIPTION:by Kelly Isham (Colgate University) as part of UBC Number theo
ry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/number_theory/19/
END:VEVENT
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