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BEGIN:VEVENT
SUMMARY:Antonio Cauchi (Universitat Politècnica de Catalunya)
DTSTART:20210519T083000Z
DTEND:20210519T093000Z
DTSTAMP:20260404T094753Z
UID:RSVP/1
DESCRIPTION:Title: Algebraic cycles for the Siegel sixfold and the exceptional theta lift
from G2\nby Antonio Cauchi (Universitat Politècnica de Catalunya) as
part of Rendez-vous on special values and periods\n\n\nAbstract\nIn this
talk\, we will report some progress towards the Beilinson conjectures for
Shimura varieties associated to the symplectic group $\\mathrm{GSp}(6)$.
\nWe will describe a cohomological formula for the residue at $s=1$ of the
degree 8 spin $L$-function. We will then discuss an important family of c
uspidal automorphic representations for $\\mathrm{PGSp}(6)$ for which the
residue is non-zero and relate this to the existence of an algebraic cycle
coming from a Hilbert modular subvariety. This relation partially answers
a question of Gross and Savin on motives with Galois group of type $\\mat
hrm{G}2$. \nThis is joint work with Francesco Lemma and Joaquin Rodrigues
Jacinto.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukako Kezuka (Max-Planck-Institut für Mathematik)
DTSTART:20210519T100000Z
DTEND:20210519T110000Z
DTSTAMP:20260404T094753Z
UID:RSVP/2
DESCRIPTION:Title: On the non-triviality of the 2-part of the Tate-Shafarevich group\
nby Yukako Kezuka (Max-Planck-Institut für Mathematik) as part of Rendez-
vous on special values and periods\n\n\nAbstract\nThe conjecture of Birch
and Swinnerton-Dyer concerns a deep connection between the arithmetic of e
lliptic curves and the behaviour of their associated complex $L$-functions
at $s=1$. \nThe conjecture was formulated in the early 60's\, and much of
it remains mysterious today.\nIndeed\, the exact Birch-Swinnerton-Dyer fo
rmula remains unknown even for the classical family of elliptic curves $E$
of the form $x^3+y^3=N$\, where $N$ is a positive integer. \n\nIn this ta
lk\, I will study the "$p$-part" of the conjecture for these curves at sma
ll primes $p$. \nThese cases are often eschewed\, but they seem to make up
a most significant part of the full conjecture.\n\nFirst\, I will study t
he $3$-adic valuation of the algebraic part of their central $L$-values\,
and use it to show that the "analytic" order of the Tate-Shafarevich group
of $E$ is a perfect square for some $N$. \nIn the second part of the talk
\, I will explain how we can obtain the $3$-part of the Birch-Swinnerton-D
yer conjecture in certain special cases of $N$ where the rank of $E$ is kn
own to be equal to $0$ or $1$. For the $2$-part of the conjecture\, I will
explain a relation between the ideal class group of a corresponding cubic
field extension and the $2$-Selmer group of $E$. \nThis can be used to st
udy non-triviality of the $2$-part of the Tate-Shafarevich group of $E$\,
even when $E$ has rank $1$. \n\nThe second part of this talk is joint work
with Yongxiong Li.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Panetta (Université Paris Diderot)
DTSTART:20210519T123000Z
DTEND:20210519T133000Z
DTSTAMP:20260404T094753Z
UID:RSVP/3
DESCRIPTION:Title: Higher regulators and special values of the degree-eight L-function of
GSp(4)xGL(2)\nby Alex Panetta (Université Paris Diderot) as part of
Rendez-vous on special values and periods\n\n\nAbstract\nIn order to prove
Beilinson conjectures\, we link the image of an element through the Beili
nson regulator in the Deligne cohomology of the product of a Siegel variet
y and a modular curve respectively\, to the special value at $s = 1$ of th
e degree-eight $L$-function of $\\mathrm{GSp}(4) \\times \\mathrm{GL}(2)$
associated to a product of automorphic generic admissible cuspidal represe
ntations of $\\mathrm{GSp}(4)$ and $\\mathrm{GL}(2)$ respectively\, in the
case where this function is entire. \nIn this talk\, we will explain how
we can link these different objects using a linear form defined on the Del
igne cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Graham (University College London)
DTSTART:20210519T134500Z
DTEND:20210519T144500Z
DTSTAMP:20260404T094753Z
UID:RSVP/4
DESCRIPTION:Title: Euler systems and p-adic L-functions for conjugate self-dual represent
ations\nby Andrew Graham (University College London) as part of Rendez
-vous on special values and periods\n\n\nAbstract\nIn this talk\, I will d
escribe joint work with S.W.A. Shah on the construction of a split anticyc
lotomic Euler system for a large class of conjugate self-dual automorphic
representations admitting a Shalika model. \nThis Euler system arises from
special cycles on unitary Shimura varieties and the proof of the norm rel
ations amounts to a computation in local representation theory. \nI will a
lso describe the expected relation with $p$-adic $L$-functions (using the
machinery of higher Hida theory) and (expected) applications to the Bloch-
Kato conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Óscar Rivero (University of Warwick)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260404T094753Z
UID:RSVP/5
DESCRIPTION:Title: Eisenstein congruences and Euler systems\nby Óscar Rivero (Univer
sity of Warwick) as part of Rendez-vous on special values and periods\n\n\
nAbstract\nLet $f$ be a cuspidal eigenform of weight two\, and let $p$ be
a prime at which $f$ is congruent to an Eisenstein series. Beilinson const
ructed a class arising from the cup-product of two Siegel units and proved
a relationship with the first derivative of the $L$-series of $f$ at the
near central point $s=0$. I will motivate the study of congruences between
modular forms at the level of cohomology classes\, and will report on a j
oint work with Victor Rotger where we prove two congruence formulas relati
ng the Beilinson class with the arithmetic of circular units. The proofs m
ake use of delicate Galois properties satisfied by various integral lattic
es and exploits Perrin-Riou's\, Coleman's and Kato's work on the Euler sys
tems of circular units and Beilinson-Kato elements and\, most crucially\,
the work of Fukaya-Kato.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyu Zhang (Universität Duisburg-Essen)
DTSTART:20210520T083000Z
DTEND:20210520T093000Z
DTSTAMP:20260404T094753Z
UID:RSVP/6
DESCRIPTION:Title: p-part Bloch-Kato conjecture for Siegel modular forms of genus 2\n
by Xiaoyu Zhang (Universität Duisburg-Essen) as part of Rendez-vous on sp
ecial values and periods\n\n\nAbstract\nThe Bloch-Kato conjecture relates
the algebraic part of special $L$-values to the Selmer groups of the same
motive. \nIn this talk\, we study the $p$-part of this conjecture for a Si
egel modular form of genus $2$ and show\, under mild conditions on the ass
ociated Galois representation\, that the special value of the standard $L$
-function divided by an automorphic period is equal to the characteristic
ideal of the corresponding Selmer group\, up to $p$-units. \nThe proof rel
ies on some non-vanishing results of mod $p$ theta lifts from the orthogon
al group to the symplectic group.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (King's College London)
DTSTART:20210520T100000Z
DTEND:20210520T110000Z
DTSTAMP:20260404T094753Z
UID:RSVP/7
DESCRIPTION:Title: On a BSD-type formula for L-values of Artin twists of elliptic curves<
/a>\nby Hanneke Wiersema (King's College London) as part of Rendez-vous on
special values and periods\n\n\nAbstract\nIn this talk we discuss the pos
sible existence of a BSD-type formula for $L$-functions of elliptic curves
twisted by Artin representations. After outlining some expected propertie
s of these $L$-functions\, we present arithmetic consequences for the beha
viour of Tate–Shafarevich groups\, Selmer groups and rational points. We
illustrate these with some explicit examples. This is joint work with Vla
dimir Dokchitser and Robert Evans.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Gazda (Université Claude Bernard Lyon 1)
DTSTART:20210520T123000Z
DTEND:20210520T133000Z
DTSTAMP:20260404T094753Z
UID:RSVP/8
DESCRIPTION:Title: First Beilinson’s conjecture in function fields arithmetic\nby Q
uentin Gazda (Université Claude Bernard Lyon 1) as part of Rendez-vous on
special values and periods\n\n\nAbstract\nIn the mid 80’s\, Beilinson f
ormulated deep conjectures relating special values of $L$-functions to pie
ces of $K$-theory\, superseding at once the BSD conjecture and Deligne’s
conjecture. Beilinson's conjectures are fully expressed in the framework
of mixed motives\, which remains hypothetical. \n\nThis talk will be devot
ed to portray the analogous picture in the function fields setting\, using
so-called Goss $L$-values instead of classical $L$-values\, and mixed (un
iformizable) Anderson $A$-motives instead of Grothendieck's mixed motives.
After a recall of the classical conjectures\, we shall discuss and define
the analogue of motivic cohomology and regulators for function fields\, a
nd express the counterpart of Beilinson’s conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Hung Le (Université de Caen Normandie)
DTSTART:20210520T134500Z
DTEND:20210520T144500Z
DTSTAMP:20260404T094753Z
UID:RSVP/9
DESCRIPTION:Title: On identities for zeta values in Tate algebras\nby Huy Hung Le (Un
iversité de Caen Normandie) as part of Rendez-vous on special values and
periods\n\n\nAbstract\nZeta values in Tate algebras were introduced by Pel
larin in 2012. They are generalizations of Carlitz zeta values and play a
n increasingly important role in function field arithmetic. \n\nIn this ta
lk\, we will present some related conjectures proposed by Pellarin. \nThen
\, we will study the Bernoulli-type polynomials attached to these zeta val
ues. \nBy a combinatorial method\, we can also provide some explicit formu
las. \nWe will demonstrate how to use these results to prove a conjecture
of Pellarin on identities for zeta values in Tate algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Matthes (University of Oxford)
DTSTART:20210520T150000Z
DTEND:20210520T160000Z
DTSTAMP:20260404T094753Z
UID:RSVP/10
DESCRIPTION:Title: A new approach to multiple elliptic polylogarithms\nby Nils Matth
es (University of Oxford) as part of Rendez-vous on special values and per
iods\n\n\nAbstract\nMultiple polylogarithms may be viewed as the monodromy
of a certain "universal" unipotent differential equation on the projectiv
e line minus three points. This observation lies at the heart of their rel
ation to mixed Tate motives\, a point of view which brings powerful new to
ols to bear on the study of these functions and its special values.\n\nThe
goal of this talk is to describe an analogous picture for a once-puncture
d elliptic curve $E'$. In particular\, we obtain a new description of the
unipotent de Rham fundamental group of $E'$\, generalizing and improving o
n previous works of Levin-Racinet\, Brown-Levin\, Enriquez-Etingof\, and o
thers. Joint work in progress with Tiago J. Fonseca (Oxford).\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Zerbini (IPhT CEA-Saclay)
DTSTART:20210521T083000Z
DTEND:20210521T093000Z
DTSTAMP:20260404T094753Z
UID:RSVP/11
DESCRIPTION:Title: New modular forms from string theory\, and single-valued periods\
nby Federico Zerbini (IPhT CEA-Saclay) as part of Rendez-vous on special v
alues and periods\n\n\nAbstract\nI will introduce a class of modular forms
\, called modular graph functions\, which originate from the computation o
f Feynman integrals in string theory. \nModular graph functions generalise
real analytic Eisenstein series\, their expansion coefficients are multip
le zeta values\, and they are conjecturally related to the theory of singl
e-valued periods\, which I will briefly review. \nIn particular\, the expa
nsion coefficients are conjectured to belong to a small subalgebra of the
multiple zeta values whose elements are single-valued periods. \n\nI will
present a proof of this conjecture for the simplest kind of Feynman integr
als\, obtained in collaboration with Don Zagier. \nI will also mention how
modular graph functions are expected to be related to iterated extensions
of pure motives of modular forms\, and how one can attach $L$-functions t
o them.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Keilthy (Max-Planck-Institut für Mathematik)
DTSTART:20210521T100000Z
DTEND:20210521T110000Z
DTSTAMP:20260404T094753Z
UID:RSVP/12
DESCRIPTION:Title: Block graded relations among motivic multiple zeta values\nby Ada
m Keilthy (Max-Planck-Institut für Mathematik) as part of Rendez-vous on
special values and periods\n\n\nAbstract\nMultiple zeta values\, originall
y considered by Euler\, generalise the Riemann zeta function to multiple v
ariables.\n\nWhile values of the Riemann zeta function at odd positive int
egers are conjectured to be algebraically independent\, multiple zeta valu
es satisfy many algebraic and linear relations\, even forming a $\\mathbb{
Q}$-algebra. While families of well understood relations are known\, such
as the associator relations and double shuffle relations\, they only conje
cturally span all algebraic relations. Since multiple zeta values arise as
the periods of mixed Tate motives\, we obtain further algebraic structure
s\, which have been exploited to provide spanning sets by Brown. In this t
alk we will aim to define a new set of relations\, known to be complete in
low block degree.\n\nTo achieve this\, we will first review the necessary
algebraic set up\, focusing particularly on the motivic Lie algebra assoc
iated to the thrice punctured projective line. We then introduce a new fil
tration on the algebra of (motivic) multiple zeta values\, called the bloc
k filtration\, based on the work of Charlton. By considering the associate
d graded algebra\, we quickly obtain a new family of graded motivic relati
ons\, which can be shown to span all algebraic relations in low block degr
ee. We will also touch on some conjectural ungraded "lifts" of these relat
ions\, and if we have time\, compare to similar approaches using the depth
filtration.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahya Mehrabdollahei (Sorbonne Université)
DTSTART:20210521T123000Z
DTEND:20210521T133000Z
DTSTAMP:20260404T094753Z
UID:RSVP/13
DESCRIPTION:Title: Mahler measure of a family of exact polynomials\nby Mahya Mehrabd
ollahei (Sorbonne Université) as part of Rendez-vous on special values an
d periods\n\n\nAbstract\nI will present results around the Mahler measure
of a family of 2-variate exact polynomials. The closed formula for the Mah
ler measure of two-variable exact polynomials gives an expression of each
of these Mahler measures as a finite sum of the values of Dilogarithm at c
ertain roots of unity. \n\nThis allows to compute their values with any pr
ecision\, and to use the techniques of Riemann sums to compute the limit o
f this sequence of Mahler measures and an asymptotic expansion\, with a li
nk to a theorem of Boyd and Lawton.\nFinally\, for small values of d\, we
can relate these Mahler measures to values of special values of L-function
\, with a link with works of Boyd-Rodriguez Villegas and others.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (Universität Regensburg)
DTSTART:20210521T134500Z
DTEND:20210521T144500Z
DTSTAMP:20260404T094753Z
UID:RSVP/14
DESCRIPTION:Title: Twists of elliptic curves with CM\nby Eugenia Rosu (Universität
Regensburg) as part of Rendez-vous on special values and periods\n\n\nAbst
ract\nWe consider certain families of sextic twists $E_D$ of the elliptic
curve $y^2=x^3+1$ that are not defined over $\\mathbb{Q}$\, but over $\\ma
thbb{Q}[\\sqrt{-3}]$.\n\nWe compute a formula that relates the $L$-value $
L(E_D\, 1)$ to the square of a trace of a modular function at a CM point.
\nAssuming the Birch and Swinnerton-Dyer conjecture\, when the value above
is non-zero\, we should recover the order of the Tate-Shafarevich group\,
and under certain conditions we show that the value is indeed a square.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tamiozzo (Imperial College)
DTSTART:20210521T150000Z
DTEND:20210521T160000Z
DTSTAMP:20260404T094753Z
UID:RSVP/15
DESCRIPTION:Title: Torsion in the cohomology of Hilbert modular varieties (with a view t
owards Iwasawa theory)\nby Matteo Tamiozzo (Imperial College) as part
of Rendez-vous on special values and periods\n\n\nAbstract\nYiwen Zhou has
given a new construction of Kato's zeta element in local Iwasawa cohomolo
gy based on local-global compatibility between completed cohomology of mod
ular curves and the $p$-adic Langlands correspondence. After recalling thi
s construction\, we will discuss the proof of a vanishing theorem for coho
mology of Hilbert modular varieties which plays a key role in extending th
e above local-global compatibility result. This is joint work in progress
with Ana Caraiani.\n
LOCATION:https://stable.researchseminars.org/talk/RSVP/15/
END:VEVENT
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