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BEGIN:VEVENT
SUMMARY:Tom Weston (Univ. Masschusetts Amherst)
DTSTART:20220120T230000Z
DTEND:20220121T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/2
DESCRIPTION:Title: Explicit Reciprocity Laws and Iwasawa Theory for Mo
dular Forms\nby Tom Weston (Univ. Masschusetts Amherst) as part of Iwa
sawa theory Virtual Seminar\n\n\nAbstract\nA conjecture of Mazur and Tate
predicts that analytic theta elements of\nmodular forms\, which encode spe
cial values of L-functions\, should lie in\nthe Fitting ideal of their Sel
mer groups over cyclotomic extensions. In\nthis talk we outline a proof o
f this conjecture (up to scaling) for\np-power cyclotomic extensions in th
e case that the modular form is\nnon-ordinary at p. The key tool is a gen
eral local construction of\ncohomology classes via the p-adic local Langla
nds correspondence. This\nis joint work with Matthew Emerton and Robert P
ollack.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Muller (Universite Laval)
DTSTART:20220127T230000Z
DTEND:20220128T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/3
DESCRIPTION:Title: Class Groups and fine Selmer Groups\nby Kathari
na Muller (Universite Laval) as part of Iwasawa theory Virtual Seminar\n\n
\nAbstract\nStarting from a result by Lim-Murty relating classical Iwasawa
invariants of fine Selmer groups and $p$-class groups over the cyclotomic
$\\mathbb{Z}_p$-extension\, we investigate generalizations of this result
s for multiple $\\mathbb{Z}_p$-extensions and uniform p-adic Lie-extension
s. If time allows we will also discuss a density result for the weak Leopo
ldt conjecture. This is joined work with Sören Kleine.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Delbourgo (University of Waikato)
DTSTART:20220203T230000Z
DTEND:20220204T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/4
DESCRIPTION:Title: L-invariants attached to the symmetric square repre
sentation\nby Daniel Delbourgo (University of Waikato) as part of Iwas
awa theory Virtual Seminar\n\n\nAbstract\nThe p-adic L-function attached t
o the symmetric square of a modular\nform vanishes at certain critical twi
sts\, even though the complex\nL-function does not. We'll survey what is k
nown about the first\nderivative of this p-adic L-function\, and then desc
ribe an algorithm\nto compute the first derivative for non-CM elliptic cur
ves. This talk\nshould hopefully be accessible to graduate students in num
ber theory.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylan Gajek-Leonard (Univ. Massachusetts Amherst)
DTSTART:20220210T230000Z
DTEND:20220211T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/5
DESCRIPTION:Title: Iwasawa Invariants of Modular Forms with $a_p=0$\nby Rylan Gajek-Leonard (Univ. Massachusetts Amherst) as part of Iwasawa
theory Virtual Seminar\n\n\nAbstract\nMazur-Tate elements provide a conve
nient method to study the\nanalytic Iwasawa theory of p-nonordinary modula
r forms\, where the\nassociated p-adic L-functions have unbounded coeffici
ents. The Iwasawa\ninvariants of Mazur-Tate elements are well-understood i
n the case of\nweight two modular forms\, where they can be related to the
growth of\np-Selmer groups and decompositions of the p-adic L-function. A
t higher\nweights\, less is known. By constructing certain lifts to the fu
ll Iwasawa\nalgebra\, we compute the Iwasawa invariants of Mazur-Tate elem
ents for\nhigher weight modular forms with $a_p=0$ in terms of the plus/mi
nus\ninvariants of the p-adic L-function. Combined with results of\nPollac
k-Weston\, this forces a relation between plus/minus (and Sprung's\nsharp
/flat) invariants at weights 2 and p+1.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debanjana Kundu (University of British Columbia)
DTSTART:20220217T230000Z
DTEND:20220218T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/6
DESCRIPTION:Title: Fine Selmer Groups and Duality\nby Debanjana Ku
ndu (University of British Columbia) as part of Iwasawa theory Virtual Sem
inar\n\n\nAbstract\nIn Iwasawa Theory of $p$-adic Representations (1989)\,
R. Greenberg developed an Iwasawa theory for $p$-ordinary motives. In pa
rticular\, he showed that the $p$-Selmer group over the cyclotomic $\\math
bb{Z}_p$ extension satisfies an algebraic functional equation. In the inte
rvening years\, this strategy has been extended by several authors to prov
e functional equations in other settings. After discussing the history of
these results\, I will report on joint work with J. Hatley\, A. Lei\, and
J.Ray where we take the first steps in trying to prove an algebraic functi
onal equation for the fine Selmer group.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Cauchi (Concordia University)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/7
DESCRIPTION:Title: On refined conjectures of Birch and Swinnerton-Dyer
type in the Rankin-Selberg setting\nby Antonio Cauchi (Concordia Univ
ersity) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nIn the la
te 80's\, Mazur and Tate proposed conjectures on the structure\nof the Fit
ting ideals of Selmer groups over number fields of elliptic curves\nover Q
. These conjectures are aimed to refine Birch and Swinnerton-Dyer type\nco
njectures over number fields as well as the Iwasawa main conjectures over
the\ncyclotomic $\\mathbb{Z}_p$-tower of Q. Results in this direction hav
e been obtained by Kim\nand Kurihara\, who studied the Fitting ideals over
finite sub-extensions of the\ncyclotomic $\\mathbb{Z}_p$-extension of Q.\
n\nIn this talk\, I will describe results analogous to theirs on the Fitti
ng ideals\nover the finite layers of the cyclotomic $\\mathbb{Z}_p$-extens
ion of Q of Selmer groups\nattached to the Rankin-Selberg convolution of t
wo modular forms f and g. In the\ncase where f corresponds to an elliptic
curve E/Q and g to a two-dimensional\nodd irreducible Artin representatio
n with splitting field F\, I will explain how\nour results give an upper b
ound of the dimension of the g-isotypic component of\nthe Mordell-Weil gro
up of E over the finite layers of the cyclotomic\n$\\mathbb{Z}_p$-extensio
n of F. This is joint work with Antonio Lei.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART:20220303T230000Z
DTEND:20220304T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/8
DESCRIPTION:Title: Selmer classes on CM elliptic curves of rank 2\
nby Francesc Castella (UC Santa Barbara) as part of Iwasawa theory Virtual
Seminar\n\n\nAbstract\nLet E be an elliptic curve over Q\, and let p be a
prime of good ordinary reduction for E. Following the pioneering work of
Skinner (and independently Wei Zhang) from about 8 years ago\, there is a
growing number of results in the direction of a p-converse to a theorem of
Gross-Zagier and Kolyvagin\, showing that if the p-adic Selmer group of E
is 1-dimensional\, then a Heegner point on E has infinite order. In this
talk\, I'll report on the proof of an analogue of Skinner's result in the
rank 2 case\, in which Heegner points are replaced by certain generalized
Kato classes introduced by Darmon-Rotger. For E without CM\, such an analo
gue was obtained in an earlier work with M.-L. Hsieh\, and in this talk I'
ll focus on the CM case\, whose proof uses a different set of ideas.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabella Negrini (McGill University)
DTSTART:20220310T230000Z
DTEND:20220311T000000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/9
DESCRIPTION:Title: A Shimura-Shintani correspondence for rigid analyti
c cocycles\nby Isabella Negrini (McGill University) as part of Iwasawa
theory Virtual Seminar\n\n\nAbstract\nIn their paper Singular moduli for
real quadratic fields: a rigid\n analytic approach\, Darmon and Vonk intro
duced rigid meromorphic cocycles\,\n i.e. elements of $H^1(SL_2(\\mathbb{Z
}[1/p])\, M^x)$ where $M^x$ is the multiplicative\n group of rigid meromor
phic functions on the p-adic upper-half plane.\n Their values at RM points
belong to narrow ring class fields of real\n quadratic fields and behave
analogously to CM values of modular functions\n on $SL_2(\\mathbb{Z})\\bac
kslash H$. In this talk\, I will present some progress towards\n developin
g a Shimura-Shintani correspondence in this setting.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lei (Universite Laval)
DTSTART:20220317T220000Z
DTEND:20220317T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/10
DESCRIPTION:Title: Asymptotic formula for Tate--Shafarevich groups of
$p$-supersingular elliptic curves over anticyclotomic extensions\nby
Antonio Lei (Universite Laval) as part of Iwasawa theory Virtual Seminar\n
\n\nAbstract\nLet $p\\ge 5$ be a prime number and $E/\\mathbf{Q}$ an ellip
tic curve with good supersingular reduction at $p$. Under the generalized
Heegner hypothesis\, we investigate the $p$-primary subgroups of the Tate-
-Shafarevich groups of $E$ over number fields contained inside the anticyc
lotomic $\\mathbf{Z}_p$-extension of an imaginary quadratic field where $p
$ splits. This is joint work with Meng Fai Lim and Katharina Mueller.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20220324T220000Z
DTEND:20220324T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/11
DESCRIPTION:Title: Kolyvagin's conjecture\, bipartite Euler systems\,
and higher congruences of modular forms\nby Naomi Sweeting (Harvard)
as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nFor an elliptic c
urve E\, Kolyvagin used Heegner points to construct special Galois cohomo
logy classes valued in the torsion points of E. Under the conjecture that
not all of these classes vanish\, he showed that they encode the Selmer ra
nk of E. I will explain a proof of new cases of this conjecture that build
s on prior work of Wei Zhang. The proof naturally leads to a generalizatio
n of Kolyvagin's work in a complimentary "definite" setting\, where Heegne
r points are replaced by special values of a quaternionic modular form. I'
ll also explain an "ultrapatching" formalism which simplifies the Selmer g
roup arguments required for the proof.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Washington (University of Maryland)
DTSTART:20220331T220000Z
DTEND:20220331T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/12
DESCRIPTION:Title: Musings on $\\mu$\nby Lawrence Washington (Uni
versity of Maryland) as part of Iwasawa theory Virtual Seminar\n\n\nAbstra
ct\nIwasawa showed how to produce examples of $\\mathbb{Z}_p$-extensions w
here the mu-invariant (for class groups) is nonzero\, and this method also
yields extensions\nwhere the $\\ell$-part of the class group is unbounded
\, where $\\ell$ is a prime different from $p$. I'll review this construct
ion and some related computations and then discuss\nsome ideas on whether
this completely accounts for the behavior of the class number.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART:20220407T220000Z
DTEND:20220407T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/13
DESCRIPTION:Title: Partial classicality of Hilbert modular forms\
nby Chi-Yun Hsu (UCLA) as part of Iwasawa theory Virtual Seminar\n\n\nAbst
ract\nModular forms are global sections of certain line bundles on the mod
ular curve\, while p-adic overconvergent modular forms are defined only ov
er a strict neighborhood of the ordinary locus. The philosophy of classica
lity theorems is that when the p-adic valuation of $U_p$-eigenvalue is sma
ll compared to the weight (called a small slope condition)\, an overconver
gent $U_p$-eigenform is automatically classical\, namely\, it can be exten
ded to the whole modular curve. In the case of Hilbert modular forms\, the
re are the partially classical forms which are defined over a strict neigh
borhood of a “partially ordinary locus”. Modifying Kassaei’s method
of analytic continuation\, we show that under a weaker small slope conditi
on\, an overconvergent form is automatically partially classical.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Rosso (Concordia University)
DTSTART:20220414T220000Z
DTEND:20220414T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/14
DESCRIPTION:Title: Overconvergent Eichler--Shimura morphism for famil
ies of Siegel modular forms\nby Giovanni Rosso (Concordia University)
as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nClassical results
of Eichler and Shimura decompose the cohomology of certain\nlocal systems
on the modular curve in terms of holomorphic and anti-holomorphic\nmodula
r forms. A similar result has been proved by Faltings' for the etale\ncoho
mology of the modular curve and Falting's result has been partly\ngenerali
sed to Coleman families by Andreatta-Iovita-Stevens.\nIn this talk\, based
on joint work with Hansheng Diao and Ju-Feng Wu\, I will\nexplain how one
constructs a morphism from the overconvergent cohomology of\n$GSp_{2g}$ t
o the space of families of Siegel modular forms. This can be seen as a\nfi
rst step in an Eichler-Shimura decomposition for overconvergent cohomology
\nand involves a new definition of the sheaf of overconvergent Siegel modu
lar\nforms using the Hodge--Tate map at infinite level. If time allows it\
, I'll\nexplain how one can hope to use higher Coleman theory to find a co
mplete\nanalogue of the classical Eichler--Shimura decomposition in small
slope.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cedric Dion (Laval)
DTSTART:20220421T220000Z
DTEND:20220421T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/15
DESCRIPTION:Title: Arithmetic statistics for 2-bridge links\nby C
edric Dion (Laval) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract
\nLet p be a fixed odd prime number. A famous theorem due to Iwasawa gives
a formula for the rate of growth of the p-class group when the fields var
y in a $\\mathbb{Z}_p$-extension of a number field. In this talk\, based o
n joint work with Anwesh Ray\, we study the topological analogue of Iwasaw
a theory for knots or\, more generally\, for links which are disjoint unio
n of knots. In this setting\, one can show that the lambda-invariant assoc
iated to a $\\mathbb{Z}_p$-cover of a link with at least 2 components is a
lways greater than 0. We give explicit formulae to detect when the case $\
\mu=0$ and $\\lambda=1$ do occur\, at least in the case of 2 and 3-compone
nts links. We then study the proportion of 2-components links for which $\
\mu=0$ and $\\lambda=1$ when the links are parametrized in Schubert normal
form. Backed by numerical evidence\, we conjecture that $\\mu=0$ for 100%
of such links.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Vallieres (California State U\, Chico)
DTSTART:20220428T220000Z
DTEND:20220428T230000Z
DTSTAMP:20260422T225920Z
UID:iwasawa_theory_virtual_seminar/16
DESCRIPTION:Title: On some theorems in graph theory analogous to past
results in Iwasawa theory\nby Daniel Vallieres (California State U\,
Chico) as part of Iwasawa theory Virtual Seminar\n\n\nAbstract\nIn the 195
0s\, Iwasawa proved his celebrated theorem on the growth of\nthe p-part of
the class number in Zp-extensions of number fields. The growth\nof the q
-part\, where q is another rational prime distinct from p\, was studied\nb
y Washington and Sinnott among others. In this talk\, we will explain our
work\nin obtaining analogous results in graph theory for the number of sp
anning trees\nin some infinite towers of graphs analogous to $\\mathbb{Z}_
p$-extensions of number fields.\nPart of this work is joint with Kevin McG
own and part of this work is joint\nwith Antonio Lei.\n
LOCATION:https://researchseminars.org/talk/iwasawa_theory_virtual_seminar/
16/
END:VEVENT
END:VCALENDAR