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BEGIN:VEVENT
SUMMARY:Jackie Lang (Oxford)
DTSTART:20201105T140000Z
DTEND:20201105T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/1
DESCRIPTION:Title: Eisenstein congruences at prime-square level\nby Jackie Lang (Ox
ford) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nC
ongruences between modular forms have been studied by many mathematicians\
, starting with some observations of Ramanujan. They have been exploited
by number theorists in the last 50 years to prove many deep arithmetic fac
ts. We will give a survey of examples of these congruences and some of th
eir arithmetic applications. Having established the historical context\,
we will discuss some work in progress with Preston Wake where we study Eis
enstein congruences at prime-square level. We will end with an applicatio
n to proving nontriviality of class groups of a family of number fields.\n
\nPasscode: The 3-digit prime numerator of Riemann zeta at -11\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Wuthrich (Nottingham)
DTSTART:20201112T140000Z
DTEND:20201112T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/2
DESCRIPTION:Title: Integrality of twisted L-values of elliptic curves\nby Chris Wut
hrich (Nottingham) as part of Dublin Algebra and Number Theory Seminar\n\n
\nAbstract\nIn the context of the generalised Birch and Swinnerton-Dyer co
njecture\, one considers the value at $s=1$ of the L-function of an ellipt
ic curve $E/\\mathbb{Q}$ twisted by a Dirichlet character $\\chi$. When no
rmalised with a period\, one obtains an algebraic number $\\mathscr{L}(E\,
\\chi)$. In joint work with Hanneke Wiersema\, we determine under what con
ditions $\\mathscr{L}(E\,\\chi)$ is an algebraic integer.\n\nPasscode: The
3-digit prime numerator of Riemann zeta at -11\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Williams (Warwick)
DTSTART:20201119T140000Z
DTEND:20201119T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/3
DESCRIPTION:Title: p-adic L-functions in higher dimensions\nby Christopher Williams
(Warwick) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstra
ct\nThere are lots of theorems and conjectures relating special values of
complex analytic L-functions to arithmetic data\; for example\, celebrated
examples include the class number formula and the BSD conjecture. These c
onjectures predict a surprising (complex) bridge between the fields of ana
lysis and arithmetic. However\, these conjectures are extremely difficult
to prove. Most recent progress has come from instead trying to build analo
gous $p$-adic bridges\, constructing a $p$-adic version of the $L$-functio
n and relating it to $p$-adic arithmetic data via "Iwasawa main conjecture
s". From the $p$-adic bridge\, one can deduce special cases of the complex
bridge\; this strategy has\, for example\, led to the current state-of-th
e-art results towards the BSD conjecture.\n\nEssential in this strategy is
the construction of a $p$-adic L-function. In this talk I will give an in
troduction to $p$-adic L-functions\, focusing first on the $p$-adic analog
ue of the Riemann zeta function (the case of ${\\rm GL}_1$)\, then describ
ing what one expects in a more general setting. At the end of the talk I w
ill state some recent results from joint work with Daniel Barrera and Mlad
en Dimitrov on the construction of $p$-adic L-functions for certain automo
rphic representations of ${\\rm GL}_{2n}$.\n\nPasscode: The 3-digit prime
numerator of Riemann zeta at -11\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (King's College London)
DTSTART:20201126T140000Z
DTEND:20201126T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/4
DESCRIPTION:Title: Symmetric power functoriality for modular forms\nby James Newton
(King's College London) as part of Dublin Algebra and Number Theory Semin
ar\n\n\nAbstract\nOne prediction of the Langlands program is that all 'rea
sonable' L-functions should arise from automorphic forms. For example\, th
e modularity theorem of Wiles\, Breuil\, Conrad\, Diamond and Taylor ident
ifies the Hasse-Weil L-function of an elliptic curve defined over the rati
onals with the L-function of a modular form. More generally\, the symmetri
c power L-functions of elliptic curves should be the L-functions of higher
rank automorphic forms. This prediction is closely related to the arithme
tic of the elliptic curve (e.g. the Sato-Tate conjecture). I will discuss
this circle of ideas\, including some recent work with Jack Thorne in whic
h we prove automorphy of these symmetric power L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State)
DTSTART:20210211T140000Z
DTEND:20210211T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/6
DESCRIPTION:Title: Tame derivatives and the Eisenstein ideal\nby Preston Wake (Mich
igan State) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstr
act\nAs was made famous by Mazur\, the mod-5 Galois representation associa
ted to the elliptic curve $X_0(11)$ is reducible. Less famously\, but also
noted by Mazur\, the mod-25 Galois representation is reducible. We'll exp
lain why this mod-5 reducibility is to be expected\, but why this mod-25 r
educibility is surprising. We'll also discuss the analytic and algebraic s
ignificance of the characters that appear in the mod-25 representation.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART:20210225T140000Z
DTEND:20210225T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/7
DESCRIPTION:Title: Partial classicality of Hilbert modular forms\nby Chi-Yun Hsu (U
CLA) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nOv
erconvergent Hilbert modular forms are defined over a strict neighborhood
of the ordinary locus of the Hilbert modular variety. The philosophy of cl
assicality theorems is that when the valuation of $U_p$-eigenvalues are sm
all enough (called a small slope condition)\, an overconvergent Hecke eige
nform is automatically classical\, namely\, it can be defined over the who
le Hilbert modular variety. On the other hand\, we can define partially cl
assical forms as forms defined over a strict neighborhood of a “partiall
y ordinary locus”. We show that under a weaker small slope condition\, a
n overconvergent form is automatically partially classical. We adapt Kassa
ei’s method of analytic continuation.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Vigni (University of Genoa)
DTSTART:20210401T130000Z
DTEND:20210401T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/8
DESCRIPTION:Title: On Shafarevich–Tate groups and analytic ranks in Hida families of
modular forms\nby Stefano Vigni (University of Genoa) as part of Dubl
in Algebra and Number Theory Seminar\n\n\nAbstract\nShafarevich-Tate group
s and analytic ranks (that is\, vanishing orders of L-functions) play a ma
jor role in the study of the arithmetic of elliptic curves\, abelian varie
ties\, and more generally higher (even) weight modular forms. In this talk
\, I will describe results on the behaviour of these arithmetic invariants
when the modular forms they are attached to vary in a so-called Hida fami
ly. In particular\, our results provide some evidence for a conjecture of
\nGreenberg predicting that the analytic ranks of even weight modular form
s in a Hida family should be as small as allowed by the functional equatio
n\, with at most finitely many exceptions.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chan-Ho Kim (KIAS)
DTSTART:20210128T140000Z
DTEND:20210128T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/9
DESCRIPTION:Title: Refined applications of Kato's Euler systems\nby Chan-Ho Kim (KI
AS) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nIn
modern number theory\, one of the most interesting goals is to understand
the arithmetic meaning of special values of L-functions of various arithme
tic objects (e.g. Birch and Swinnerton-Dyer conjecture and Bloch-Kato's Ta
magawa number conjecture). Iwasawa theory is the most successful way at pr
esent to achieve this aim\, and many important results are based on the th
eory of Euler systems. We will discuss more refined applications of Kato's
Euler systems for modular forms beyond their standard applications.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Roehrig (Universität zu Köln)
DTSTART:20210204T140000Z
DTEND:20210204T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/10
DESCRIPTION:Title: Siegel theta series for indefinite quadratic forms\nby Christin
a Roehrig (Universität zu Köln) as part of Dublin Algebra and Number The
ory Seminar\n\n\nAbstract\nIn this talk\, we will give an insight into the
field of Siegel modular forms. As they occur as a generalization of ellip
tic modular forms\, some results can be transferred from the well-known th
eory developed for these functions. We examine a result by Vignéras\, wh
o showed that there is a quite simple way to determine whether a certain t
heta-series admits modular transformation properties. To be more specific\
, she showed that solving a differential equation of second order serves a
s a criterion for modularity. We generalize this result for Siegel theta-s
eries.\n\nIn order to do so\, we construct Siegel theta-series for indefin
ite quadratic forms by considering functions that solve an $n\\times n$-sy
stem of partial differential equations. These functions do not only give e
xamples of Siegel theta-series\, but we can even determine a basis of Sch
wartz functions that generate series which transform like modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukako Kezuka (MPI (Bonn))
DTSTART:20210422T130000Z
DTEND:20210422T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/11
DESCRIPTION:Title: Tamagawa number divisibility of central L-values\nby Yukako Kez
uka (MPI (Bonn)) as part of Dublin Algebra and Number Theory Seminar\n\n\n
Abstract\nIn this talk\, I will report on some recent progress on the conj
ecture of Birch and Swinnerton-Dyer for elliptic curves $E$ of the form $x
^3+y^3=N$ for cube-free positive integers $N$. They are cubic twists of th
e Fermat elliptic curve $x^3+y^3=1$\, and admit complex multiplication by
the ring of integers of $\\mathbb{Q}(\\sqrt{-3})$. First\, I will explain
the Tamagawa number divisibility satisfied by the central $L$-values\, and
exhibit a curious relation between the $3$-part of the Tate$-$Shafarevich
group of $E$ and the number of prime divisors of $N$ which are inert in $
\\mathbb{Q}(\\sqrt{-3})$. I will then explain my joint work with Yongxiong
Li\, studying in more detail the cases when $N=2p$ or $2p^2$ for an odd p
rime number $p$ congruent to $2$ or $5$ modulo $9$. For these curves\, we
establish the $3$-part of the Birch$-$Swinnerton-Dyer conjecture and a rel
ation between the ideal class group of $\\mathbb{Q}(\\sqrt[3]{p})$ and the
$2$-Selmer group of $E$\, which can be used to study non-triviality of th
e $2$-part of their Tate$-$Shafarevich group.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simeon Ball (UPC)
DTSTART:20210325T153000Z
DTEND:20210325T163000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/12
DESCRIPTION:Title: Additive codes over finite fields\nby Simeon Ball (UPC) as part
of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nIf $A$ is an a
belian group then we define an additive code to be a code $C$ with the pro
perty that for all $u\,v \\in C$\, we have $u+v \\in C$. If $A$ is a finit
e field then $C$ is linear over some subfield of $A$\, so we take $A={\\ma
thbb F}_{q^h}$ and assume that $C$ is linear over ${\\mathbb F}_q$.\n\nI w
ill spend the first part of the talk talking about the geometry of linear\
, additive and quantum stabiliser codes. \n\nThe second part of the talk (
joint work with Michel Lavrauw and Guillermo Gamboa) will concern additive
MDS codes. An {\\em MDS code} $C$ is a subset of $A^n$ of size $|A|^k$ in
which any two elements of $C$ differ in at least $n-k+1$ coordinates. In
other words\, the minimum (Hamming) distance $d$ between any two elements
of $C$ is $n-k+1$. \n\n\n\nThe trivial upper bound on the length $n$ of a
$k$-dimensional additive MDS code over ${\\mathbb F}_{q^h}$ is\n$$\nn \\le
qslant q^h+k-1.\n$$\n\n\nThe classical example of an MDS code is the Reed-
Solomon code\, which is the evaluation code of all polynomials of degree a
t most $k-1$ over ${\\mathbb F}_{q^h}$. The Reed-Solomon code is linear ov
er ${\\mathbb F}_{q^h}$ and has length $q^h+1$.\n\nThe MDS conjecture stat
es (excepting two specific cases) that an MDS code has length at most $q^h
+1$. In other words\, there are no better MDS codes than the Reed-Solomon
codes.\n\nWe use geometrical and computational techniques to classify all
additive MDS codes over ${\\mathbb F}_{q^h}$ for $q^h \\in \\{4\,8\,9\\}$.
We also classify the longest additive MDS codes over ${\\mathbb F}_{16}$
which are linear over ${\\mathbb F}_4$. These classifications not only ver
ify the MDS conjecture for additive codes in these cases but also confirm
there are no additive non-linear MDS codes that perform as well as their l
inear counterparts. \n\nIn this talk\, I will cover the main geometrical t
heorem that allows us to obtain this classification and compare these clas
sifications with the classifications of {\\bf all} MDS codes of alphabets
of size at most $8$\, obtained previously by Alderson (2006)\, Kokkala\, K
rotov and Östergård (2015) and Kokkala and Östergård (2016).\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Garvan (University of Florida)
DTSTART:20210304T140000Z
DTEND:20210304T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/13
DESCRIPTION:Title: The spt and unimodal sequence conjectures\nby Frank Garvan (Uni
versity of Florida) as part of Dublin Algebra and Number Theory Seminar\n\
n\nAbstract\nIn 2012 Bryson\, Ono\, Pitman\, and Rhoades showed how the ge
nerating functions\nfor certain strongly unimodal sequences are related to
quantum modular\nand mock modular forms. They proved some parity results
and conjectured\nsome mod 4 congruences for the coefficients of these gene
rating functions.\nIn 2016 Kim\, Lim and Lovejoy obtained similar results
for odd-balanced\nunimodal sequences and made similar mod 4 conjectures. I
n 2017\nthe speaker made some similar conjectures for the Andrews spt-func
tion.\n \n \nIn this talk\, we outline how to prove these conjectures.\nTh
is involves a connection between the Hurwitz class number function\nand Ra
manujan's mock theta functions.\n \nThis is joint work with Rong Chen (Sha
nghai).\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giada Grossi (Paris 13)
DTSTART:20210408T130000Z
DTEND:20210408T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/14
DESCRIPTION:Title: The p-part of BSD for rational elliptic curves at Eisenstein primes
\nby Giada Grossi (Paris 13) as part of Dublin Algebra and Number Theo
ry Seminar\n\n\nAbstract\nLet $E$ be an elliptic curve over the rationals
and $p$ an odd prime such that E admits a rational $p$-isogeny satisfying
some assumptions. In joint work with F. Castella\, J. Lee\, and C. Skinner
\, we study the anticyclotomic Iwasawa theory for $E/K$ for some suitable
quadratic imaginary field $K$. I will give a general introduction to Iwasa
wa theory and to how it can be used to obtain results about the Birch--Swi
nnerton-Dyer conjecture. In particular\, I will talk about how our results
\, combined with complex and $p$-adic Gross-Zagier formulae\, allow us to
prove a $p$-converse to the theorem of Gross--Zagier and Kolyvagin and the
$p$-part of the Birch--Swinnerton-Dyer formula in analytic rank 1 for ell
iptic curves as above.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Moree (MPI Bonn)
DTSTART:20210923T130000Z
DTEND:20210923T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/15
DESCRIPTION:Title: Euler-Kronecker constants and cusp forms\nby Pieter Moree (MPI
Bonn) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nR
amanujan\, in a manuscript not published during his lifetime\, made a very
precise conjecture for how many integers $n\\le x$ the Ramanujan tau func
tion $\\tau(n)$ is not divisible by 691 (and likewise for some other prime
s). The $\\tau(n)$ are the Fourier coefficients of the Delta function\, wh
ich is a cusp form for the full modular group. Rankin proved that Ramanuja
n's claim is asymptotically correct. However\, the speaker showed in 2004
that the second-order behavior predicted by Ramanujan does not match reali
ty. The proof makes use of high precision computation of constants akin to
the Euler-Mascheroni constant called Euler-Kronecker constants.\n\nRecent
ly the author\, joint with Ciolan and Languasco\, studied the analogue of
Ramanujan's conjecture for the exceptional primes\, as classified by Serre
and Swinnerton-Dyer\, for the 5 cups forms akin to the Delta function for
which the space of cusp forms is 1-dimensional. The tool for this is a hi
gh-precision evaluation of the number of integers $n\\le x$ for which a p
rescribed integer $q$ does not divide the $k$th sum of divisors function\,
sharpening earlier work of Rankin and Scourfield. In my talk\, I will rep
ort on generalities on Euler-Kronecker constants and the above work\, with
ample of historical material.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Bayer-Fluckiger (EPFL)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/16
DESCRIPTION:Title: Isometries of lattices\, knot theory and K3 surfaces\nby Eva Ba
yer-Fluckiger (EPFL) as part of Dublin Algebra and Number Theory Seminar\n
\n\nAbstract\nWe give necessary and sufficient conditions for an integral
polynomial to be the characteristic polynomial of an isometry of some even
\, unimodular lattice of given signature. This result has applications in
knot theory (existence of knots with given Alexander polynomial and Milnor
signatures) as well as to K3 surfaces (existence of K3 surfaces having an
automorphism with given dynamical degree).\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jehanne Dousse (CNRS\, Lyon)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/17
DESCRIPTION:Title: Cylindric partitions\, q-difference equations and Rogers-Ramanujan
type identities\nby Jehanne Dousse (CNRS\, Lyon) as part of Dublin Alg
ebra and Number Theory Seminar\n\n\nAbstract\nCylindric partitions\, which
were introduced by Gessel and Krattenthaler in 1997\, can be seen as gene
ralisations of integer partitions involving periodicity conditions. Since
the 1980s and the founding work of Lepowsky and Wilson on Rogers-Ramanujan
identities\, several connections between characters of Lie algebras and p
artition identities have emerged. In particular\, Andrews\, Schilling and
Warnaar discovered in 1998 a family of partition identities related to ch
aracters of A_2. Recently\, Corteel and Welsh established a q-difference
equation satisfied by generating functions for cylindric partitions and us
ed it to reprove the A_2 Rogers-Ramanujan identities of Andrews\, Schillin
g and Warnaar. We build on this technique to discover and prove a new fami
ly of A_2 Rogers-Ramanujan identities and give explicitly positive express
ions for certain characters. \nThis is joint work with Sylvie Corteel and
Ali Uncu.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuma Mizuno (Chiba University)
DTSTART:20211118T120000Z
DTEND:20211118T130000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/18
DESCRIPTION:Title: Nahm's problem and cluster algebras\nby Yuma Mizuno (Chiba Univ
ersity) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\
nNahm\, Terhoeven\, and Zagier studied the intersection of the set of q-hy
pergeometric series and the set of modular functions\, and they found that
the problem of finding an element of this intersection is related to the
dilogarithm function and algebraic K-theory. In this talk\, I will explain
this problem is also related to the periodicity of T-systems (and Y-syste
ms)\, which are difference equations that appear in the theory of cluster
algebras. I will give a systematic construction of q-hypergeometric series
that are expected to be modular using the theory of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UCSB)
DTSTART:20211202T140000Z
DTEND:20211202T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/19
DESCRIPTION:Title: Iwasawa theory of elliptic curves at Eisenstein primes\nby Fran
cesc Castella (UCSB) as part of Dublin Algebra and Number Theory Seminar\n
\n\nAbstract\nIn an influential paper from 2000\, Greenberg and Vatsal int
roduced a method for studying the cyclotomic Iwasawa theory of elliptic cu
rves E over Q at Eisenstein primes (i.e.\, primes p for which E admits a r
ational p-isogeny). Combined with Kato's work\, their results had importan
t implications towards the Birch and Swinnerton-Dyer conjecture in rank 0.
In this talk\, I will try to convey the main ideas of their method\, and
then move on to explain recent joint work with G. Grossi and C. Skinner (p
artly in progress) in which we develop the method of Greenberg-Vatsal in t
he anti-cyclotomic setting\, leading to new applications towards the Birch
and Swinnerton-Dyer conjecture in rank 1.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Ahlgren (UIUC)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/20
DESCRIPTION:Title: Congruences for the partition function\nby Scott Ahlgren (UIUC)
as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nThe pa
rtition function p(n) counts the number of ways to break a natural number
n into parts. The arithmetic properties of this function have been the top
ic of intensive study for many years. Much of the interest (and the diffic
ulty) in this problem arises from the fact that values of the partition f
unction are given by the coefficients of a weakly holomorphic modular form
of half-integral weight. I’ll describe some recent work with Olivia Be
ckwith and Martin Raum\, and with Patrick Allen and Shiang Tang which goes
a long way towards explaining exactly when congruences for the partition
function can occur. The main tools are techniques from the theory of modu
lar forms\, Galois representations\, and analytic number theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahesh Kakde (IISc)
DTSTART:20211125T140000Z
DTEND:20211125T150000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/21
DESCRIPTION:Title: On the Brumer-Stark conjecture\nby Mahesh Kakde (IISc) as part
of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nThe talk will s
tart with an introduction to Stark’s conjectures. We will then specialis
e to the situation of Brumer-Stark conjecture and its various refinements.
I will then sketch a proof of the conjecture. This is joint work with Sam
it Dasgupta.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Sprang (Universität Duisburg-Essen)
DTSTART:20211007T130000Z
DTEND:20211007T140000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/22
DESCRIPTION:Title: Algebraicity of critical Hecke L-values\nby Johannes Sprang (Un
iversität Duisburg-Essen) as part of Dublin Algebra and Number Theory Sem
inar\n\n\nAbstract\nIn 1735\, Euler discovered his well-known formula for
the values of the Riemann zeta function at the positive even integers. In
particular\, Euler's result shows that all these values are rational up to
multiplication with a particular period\, here the period is a power of 2
πi. Conjecturally this is expected to hold for all critical L-values of m
otives. In this talk\, we will focus on L-functions of number fields. In t
he first part of the talk\, we will discuss the 'critical' and 'non-critic
al' L-values exemplary for the Riemann zeta function. Afterwards\, we will
head on to more general number fields and explain a joint result with Gu
ido Kings on the algebraicity of critical Hecke L-values for totally imagi
nary fields up to explicit periods.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Medvedovsky (Boston University)
DTSTART:20211013T143000Z
DTEND:20211013T153000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/23
DESCRIPTION:Title: Counting modular forms with fixed mod-$p$ Galois representation and
Atkin-Lehner-at-$p$ eigenvalue\nby Anna Medvedovsky (Boston Universit
y) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nWork
in progress joint with Samuele Anni and Alexandru Ghitza. For $N$ prime t
o $p$\, we count the number of classical modular forms of level $Np$ and w
eight $k$ with fixed mod-$p$ Galois representation and Atkin-Lehner-at-$p$
sign\, generalizing both recent results of Martin generalizing work of Wa
katsuki and Yamauchi (no residual representation constraint) and the $\\ov
erline{\\rho}$-dimension-counting formulas of Bergdall-Pollack and Jochnow
itz. Working with the Atkin-Lehner involution typically requires inverting
$p$\, which naturally complicates investigations modulo $p$. To resolve t
his tension\, we use the trace formula to establish up-to-semisimplifcatio
n isomorphisms between certain mod-$p$ Hecke modules (namely\, refinements
of the weight-filtration graded pieces $W_k$) by exhibiting ever-deeper c
ongruences between traces of prime-power Hecke operators acting on charact
eristic-zero Hecke modules. This last technique\, relying on our refinemen
t of a special case of Brauer-Nesbitt\, is new\, purely algebraic\, and ma
y well be of independent interest. We will begin with this algebra theorem
\, then discuss the classical Atkin-Lehner dimension split\, and only then
move on to our refined dimension-counting results.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazuto Ota (Osaka University)
DTSTART:20220127T100000Z
DTEND:20220127T110000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/24
DESCRIPTION:Title: On Iwasawa theory for CM elliptic curves at inert primes\nby Ka
zuto Ota (Osaka University) as part of Dublin Algebra and Number Theory Se
minar\n\n\nAbstract\n!! Note the unusual time !!\n\nI will report on joint
work with Ashay Burungale and Shinichi Kobayashi on anticyclotomic Iwasaw
a theory for CM elliptic curves at inert primes. A key result is a structu
re theorem of local units predicted by Rubin\, which leads to new developm
ents in supersingular Iwasawa theory such as a Bertolini-Darmon-Prasanna s
tyle formula for Rubin’s anticyclotomic p-adic L-function. In this talk\
, I will explain the conjecture of Rubin and such a development.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon)
DTSTART:20220407T160000Z
DTEND:20220407T170000Z
DTSTAMP:20260404T094542Z
UID:UCDANT/25
DESCRIPTION:Title: Some congruences and consequences in number theory and beyond\n
by Ellen Eischen (University of Oregon) as part of Dublin Algebra and Numb
er Theory Seminar\n\n\nAbstract\nIn the mid-1800s\, Kummer observed some s
triking congruences between certain values of the Riemann zeta function\,
which have important consequences in algebraic number theory\, in particul
ar for unique factorization in certain rings. In spite of its potential\,
this topic lay mostly dormant for nearly a century until it was revived by
Iwasawa in the mid-1950s. Since then\, advances in arithmetic geometry an
d number theory (in particular\, for modular forms\, certain analytic func
tions that play a central role in number theory) have enabled substantial
extension to congruences in the context of other arithmetically significan
t data\, and this has remained an active area of research. In this talk\,
I will survey old and new tools for studying such congruences. I will conc
lude by introducing some unexpected challenges that arise when one tries t
o take what would seem like immediate next steps beyond the current state
of the art.\n
LOCATION:https://stable.researchseminars.org/talk/UCDANT/25/
END:VEVENT
END:VCALENDAR