BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jackie Lang (Oxford)
DTSTART;VALUE=DATE-TIME:20201105T140000Z
DTEND;VALUE=DATE-TIME:20201105T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/1
DESCRIPTION:Title: E
isenstein congruences at prime-square level\nby Jackie Lang (Oxford) a
s part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nCongruen
ces between modular forms have been studied by many mathematicians\, start
ing with some observations of Ramanujan. They have been exploited by numb
er theorists in the last 50 years to prove many deep arithmetic facts. We
will give a survey of examples of these congruences and some of their ari
thmetic applications. Having established the historical context\, we will
discuss some work in progress with Preston Wake where we study Eisenstein
congruences at prime-square level. We will end with an application to pr
oving nontriviality of class groups of a family of number fields.\n\nPassc
ode: The 3-digit prime numerator of Riemann zeta at -11\n
LOCATION:https://researchseminars.org/talk/UCDANT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Wuthrich (Nottingham)
DTSTART;VALUE=DATE-TIME:20201112T140000Z
DTEND;VALUE=DATE-TIME:20201112T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/2
DESCRIPTION:Title: I
ntegrality of twisted L-values of elliptic curves\nby Chris Wuthrich (
Nottingham) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstr
act\nIn the context of the generalised Birch and Swinnerton-Dyer conjectur
e\, one considers the value at $s=1$ of the L-function of an elliptic curv
e $E/\\mathbb{Q}$ twisted by a Dirichlet character $\\chi$. When normalise
d with a period\, one obtains an algebraic number $\\mathscr{L}(E\,\\chi)$
. In joint work with Hanneke Wiersema\, we determine under what conditions
$\\mathscr{L}(E\,\\chi)$ is an algebraic integer.\n\nPasscode: The 3-digi
t prime numerator of Riemann zeta at -11\n
LOCATION:https://researchseminars.org/talk/UCDANT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Williams (Warwick)
DTSTART;VALUE=DATE-TIME:20201119T140000Z
DTEND;VALUE=DATE-TIME:20201119T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/3
DESCRIPTION:Title: p
-adic L-functions in higher dimensions\nby Christopher Williams (Warwi
ck) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nThe
re are lots of theorems and conjectures relating special values of complex
analytic L-functions to arithmetic data\; for example\, celebrated exampl
es include the class number formula and the BSD conjecture. These conjectu
res predict a surprising (complex) bridge between the fields of analysis a
nd arithmetic. However\, these conjectures are extremely difficult to prov
e. Most recent progress has come from instead trying to build analogous $p
$-adic bridges\, constructing a $p$-adic version of the $L$-function and r
elating it to $p$-adic arithmetic data via "Iwasawa main conjectures". Fro
m the $p$-adic bridge\, one can deduce special cases of the complex bridge
\; this strategy has\, for example\, led to the current state-of-the-art r
esults towards the BSD conjecture.\n\nEssential in this strategy is the co
nstruction of a $p$-adic L-function. In this talk I will give an introduct
ion to $p$-adic L-functions\, focusing first on the $p$-adic analogue of t
he Riemann zeta function (the case of ${\\rm GL}_1$)\, then describing wha
t one expects in a more general setting. At the end of the talk I will sta
te some recent results from joint work with Daniel Barrera and Mladen Dimi
trov on the construction of $p$-adic L-functions for certain automorphic r
epresentations of ${\\rm GL}_{2n}$.\n\nPasscode: The 3-digit prime numerat
or of Riemann zeta at -11\n
LOCATION:https://researchseminars.org/talk/UCDANT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (King's College London)
DTSTART;VALUE=DATE-TIME:20201126T140000Z
DTEND;VALUE=DATE-TIME:20201126T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/4
DESCRIPTION:Title: S
ymmetric power functoriality for modular forms\nby James Newton (King'
s College London) as part of Dublin Algebra and Number Theory Seminar\n\n\
nAbstract\nOne prediction of the Langlands program is that all 'reasonable
' L-functions should arise from automorphic forms. For example\, the modul
arity theorem of Wiles\, Breuil\, Conrad\, Diamond and Taylor identifies t
he Hasse-Weil L-function of an elliptic curve defined over the rationals w
ith the L-function of a modular form. More generally\, the symmetric power
L-functions of elliptic curves should be the L-functions of higher rank a
utomorphic forms. This prediction is closely related to the arithmetic of
the elliptic curve (e.g. the Sato-Tate conjecture). I will discuss this ci
rcle of ideas\, including some recent work with Jack Thorne in which we pr
ove automorphy of these symmetric power L-functions.\n
LOCATION:https://researchseminars.org/talk/UCDANT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State)
DTSTART;VALUE=DATE-TIME:20210211T140000Z
DTEND;VALUE=DATE-TIME:20210211T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/6
DESCRIPTION:Title: T
ame derivatives and the Eisenstein ideal\nby Preston Wake (Michigan St
ate) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nAs
was made famous by Mazur\, the mod-5 Galois representation associated 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 explain wh
y this mod-5 reducibility is to be expected\, but why this mod-25 reducibi
lity is surprising. We'll also discuss the analytic and algebraic signific
ance of the characters that appear in the mod-25 representation.\n
LOCATION:https://researchseminars.org/talk/UCDANT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART;VALUE=DATE-TIME:20210225T140000Z
DTEND;VALUE=DATE-TIME:20210225T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/7
DESCRIPTION:Title: P
artial classicality of Hilbert modular forms\nby Chi-Yun Hsu (UCLA) as
part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nOverconve
rgent Hilbert modular forms are defined over a strict neighborhood of the
ordinary locus of the Hilbert modular variety. The philosophy of classical
ity theorems is that when the valuation of $U_p$-eigenvalues are small eno
ugh (called a small slope condition)\, an overconvergent Hecke eigenform i
s automatically classical\, namely\, it can be defined over the whole Hilb
ert modular variety. On the other hand\, we can define partially classical
forms as forms defined over a strict neighborhood of a “partially ordin
ary locus”. We show that under a weaker small slope condition\, an overc
onvergent form is automatically partially classical. We adapt Kassaei’s
method of analytic continuation.\n
LOCATION:https://researchseminars.org/talk/UCDANT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Vigni (University of Genoa)
DTSTART;VALUE=DATE-TIME:20210401T130000Z
DTEND;VALUE=DATE-TIME:20210401T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/8
DESCRIPTION:Title: O
n Shafarevich–Tate groups and analytic ranks in Hida families of modula
r forms\nby Stefano Vigni (University of Genoa) as part of Dublin Alge
bra and Number Theory Seminar\n\n\nAbstract\nShafarevich-Tate groups and a
nalytic ranks (that is\, vanishing orders of L-functions) play a major rol
e in the study of the arithmetic of elliptic curves\, abelian varieties\,
and more generally higher (even) weight modular forms. In this talk\, I wi
ll describe results on the behaviour of these arithmetic invariants when t
he modular forms they are attached to vary in a so-called Hida family. In
particular\, our results provide some evidence for a conjecture of \nGreen
berg predicting that the analytic ranks of even weight modular forms in a
Hida family should be as small as allowed by the functional equation\, wit
h at most finitely many exceptions.\n
LOCATION:https://researchseminars.org/talk/UCDANT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chan-Ho Kim (KIAS)
DTSTART;VALUE=DATE-TIME:20210128T140000Z
DTEND;VALUE=DATE-TIME:20210128T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/9
DESCRIPTION:Title: R
efined applications of Kato's Euler systems\nby Chan-Ho Kim (KIAS) 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 ari
thmetic meaning of special values of L-functions of various arithmetic obj
ects (e.g. Birch and Swinnerton-Dyer conjecture and Bloch-Kato's Tamagawa
number conjecture). Iwasawa theory is the most successful way at present t
o achieve this aim\, and many important results are based on the theory of
Euler systems. We will discuss more refined applications of Kato's Euler
systems for modular forms beyond their standard applications.\n
LOCATION:https://researchseminars.org/talk/UCDANT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Roehrig (Universität zu Köln)
DTSTART;VALUE=DATE-TIME:20210204T140000Z
DTEND;VALUE=DATE-TIME:20210204T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/10
DESCRIPTION:Title:
Siegel theta series for indefinite quadratic forms\nby Christina Roehr
ig (Universität zu Köln) as part of Dublin Algebra and Number Theory Sem
inar\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 elliptic mod
ular forms\, some results can be transferred from the well-known theory de
veloped for these functions. We examine a result by Vignéras\, who showe
d that there is a quite simple way to determine whether a certain theta-se
ries admits modular transformation properties. To be more specific\, she s
howed that solving a differential equation of second order serves as a cri
terion for modularity. We generalize this result for Siegel theta-series.\
n\nIn order to do so\, we construct Siegel theta-series for indefinite qua
dratic forms by considering functions that solve an $n\\times n$-system of
partial differential equations. These functions do not only give examples
of Siegel theta-series\, but we can even determine a basis of Schwartz f
unctions that generate series which transform like modular forms.\n
LOCATION:https://researchseminars.org/talk/UCDANT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukako Kezuka (MPI (Bonn))
DTSTART;VALUE=DATE-TIME:20210422T130000Z
DTEND;VALUE=DATE-TIME:20210422T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/11
DESCRIPTION:Title:
Tamagawa number divisibility of central L-values\nby Yukako Kezuka (MP
I (Bonn)) as part of Dublin Algebra and Number Theory Seminar\n\nInteracti
ve livestream: https://ucd-ie.zoom.us/j/5963025149\n\nAbstract\nIn this ta
lk\, I will report on some recent progress on the conjecture of Birch and
Swinnerton-Dyer for elliptic curves $E$ of the form $x^3+y^3=N$ for cube-f
ree positive integers $N$. They are cubic twists of the Fermat elliptic cu
rve $x^3+y^3=1$\, 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 r
elation between the $3$-part of the Tate$-$Shafarevich group of $E$ and th
e 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 mo
re detail the cases when $N=2p$ or $2p^2$ for an odd prime number $p$ cong
ruent to $2$ or $5$ modulo $9$. For these curves\, we establish the $3$-pa
rt of the Birch$-$Swinnerton-Dyer conjecture and a relation between the id
eal class group of $\\mathbb{Q}(\\sqrt[3]{p})$ and the $2$-Selmer group of
$E$\, which can be used to study non-triviality of the $2$-part of their
Tate$-$Shafarevich group.\n
LOCATION:https://researchseminars.org/talk/UCDANT/11/
URL:https://ucd-ie.zoom.us/j/5963025149
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simeon Ball (UPC)
DTSTART;VALUE=DATE-TIME:20210325T153000Z
DTEND;VALUE=DATE-TIME:20210325T163000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/12
DESCRIPTION:Title:
Additive codes over finite fields\nby Simeon Ball (UPC) as part of Dub
lin Algebra and Number Theory Seminar\n\n\nAbstract\nIf $A$ is an abelian
group then we define an additive code to be a code $C$ with the property t
hat for all $u\,v \\in C$\, we have $u+v \\in C$. If $A$ is a finite field
then $C$ is linear over some subfield of $A$\, so we take $A={\\mathbb F}
_{q^h}$ and assume that $C$ is linear over ${\\mathbb F}_q$.\n\nI will spe
nd the first part of the talk talking about the geometry of linear\, addit
ive and quantum stabiliser codes. \n\nThe second part of the talk (joint w
ork with Michel Lavrauw and Guillermo Gamboa) will concern additive MDS co
des. 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 w
ords\, 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 $k$-dim
ensional additive MDS code over ${\\mathbb F}_{q^h}$ is\n$$\nn \\leqslant
q^h+k-1.\n$$\n\n\nThe classical example of an MDS code is the Reed-Solomon
code\, which is the evaluation code of all polynomials of degree at most
$k-1$ over ${\\mathbb F}_{q^h}$. The Reed-Solomon code is linear over ${\\
mathbb F}_{q^h}$ and has length $q^h+1$.\n\nThe MDS conjecture states (exc
epting 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 additiv
e MDS codes over ${\\mathbb F}_{q^h}$ for $q^h \\in \\{4\,8\,9\\}$. We als
o classify the longest additive MDS codes over ${\\mathbb F}_{16}$ which a
re linear over ${\\mathbb F}_4$. These classifications not only verify the
MDS conjecture for additive codes in these cases but also confirm there a
re no additive non-linear MDS codes that perform as well as their linear c
ounterparts. \n\nIn this talk\, I will cover the main geometrical theorem
that allows us to obtain this classification and compare these classificat
ions with the classifications of {\\bf all} MDS codes of alphabets of size
at most $8$\, obtained previously by Alderson (2006)\, Kokkala\, Krotov a
nd Östergård (2015) and Kokkala and Östergård (2016).\n
LOCATION:https://researchseminars.org/talk/UCDANT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Garvan (University of Florida)
DTSTART;VALUE=DATE-TIME:20210304T140000Z
DTEND;VALUE=DATE-TIME:20210304T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/13
DESCRIPTION:Title:
The spt and unimodal sequence conjectures\nby Frank Garvan (University
of Florida) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbst
ract\nIn 2012 Bryson\, Ono\, Pitman\, and Rhoades showed how the generatin
g functions\nfor certain strongly unimodal sequences are related to quantu
m modular\nand mock modular forms. They proved some parity results and con
jectured\nsome mod 4 congruences for the coefficients of these generating
functions.\nIn 2016 Kim\, Lim and Lovejoy obtained similar results for odd
-balanced\nunimodal sequences and made similar mod 4 conjectures. In 2017\
nthe speaker made some similar conjectures for the Andrews spt-function.\n
\n \nIn this talk\, we outline how to prove these conjectures.\nThis invo
lves a connection between the Hurwitz class number function\nand Ramanujan
's mock theta functions.\n \nThis is joint work with Rong Chen (Shanghai).
\n
LOCATION:https://researchseminars.org/talk/UCDANT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giada Grossi (Paris 13)
DTSTART;VALUE=DATE-TIME:20210408T130000Z
DTEND;VALUE=DATE-TIME:20210408T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T102104Z
UID:UCDANT/14
DESCRIPTION:Title:
The p-part of BSD for rational elliptic curves at Eisenstein primes\nb
y Giada Grossi (Paris 13) as part of Dublin Algebra and Number Theory Semi
nar\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 as
sumptions. In joint work with F. Castella\, J. Lee\, and C. Skinner\, we s
tudy the anticyclotomic Iwasawa theory for $E/K$ for some suitable quadrat
ic imaginary field $K$. I will give a general introduction to Iwasawa theo
ry and to how it can be used to obtain results about the Birch--Swinnerton
-Dyer conjecture. In particular\, I will talk about how our results\, comb
ined 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 $p$-pa
rt of the Birch--Swinnerton-Dyer formula in analytic rank 1 for elliptic c
urves as above.\n
LOCATION:https://researchseminars.org/talk/UCDANT/14/
END:VEVENT
END:VCALENDAR