BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antonio Cauchi (Universitat Politècnica de Catalunya) DTSTART:20210519T083000Z DTEND:20210519T093000Z DTSTAMP:20260422T212752Z UID:RSVP/1 DESCRIPTION:Title: Alg ebraic cycles for the Siegel sixfold and the exceptional theta lift from G 2\nby Antonio Cauchi (Universitat Politècnica de Catalunya) as part o f 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 wi ll 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 cuspidal 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 ques tion of Gross and Savin on motives with Galois group of type $\\mathrm{G}2 $. \nThis is joint work with Francesco Lemma and Joaquin Rodrigues Jacinto .\n LOCATION:https://researchseminars.org/talk/RSVP/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yukako Kezuka (Max-Planck-Institut für Mathematik) DTSTART:20210519T100000Z DTEND:20210519T110000Z DTSTAMP:20260422T212752Z UID:RSVP/2 DESCRIPTION:Title: On the non-triviality of the 2-part of the Tate-Shafarevich group\nby Yuk ako Kezuka (Max-Planck-Institut für Mathematik) as part of Rendez-vous on special values and periods\n\n\nAbstract\nThe conjecture of Birch and Swi nnerton-Dyer concerns a deep connection between the arithmetic of elliptic 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 rem ains mysterious today.\nIndeed\, the exact Birch-Swinnerton-Dyer formula r emains 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 talk\, I will study the "$p$-part" of the conjecture for these curves at small prim es $p$. \nThese cases are often eschewed\, but they seem to make up a most significant part of the full conjecture.\n\nFirst\, I will study the $3$- 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 wi ll explain how we can obtain the $3$-part of the Birch-Swinnerton-Dyer con jecture in certain special cases of $N$ where the rank of $E$ is known to be equal to $0$ or $1$. For the $2$-part of the conjecture\, I will explai n 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 study non -triviality of the $2$-part of the Tate-Shafarevich group of $E$\, even wh en $E$ has rank $1$. \n\nThe second part of this talk is joint work with Y ongxiong Li.\n LOCATION:https://researchseminars.org/talk/RSVP/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Panetta (Université Paris Diderot) DTSTART:20210519T123000Z DTEND:20210519T133000Z DTSTAMP:20260422T212752Z UID:RSVP/3 DESCRIPTION:Title: Hig her 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 Beilin son conjectures\, we link the image of an element through the Beilinson re gulator in the Deligne cohomology of the product of a Siegel variety and a modular curve respectively\, to the special value at $s = 1$ of the degre e-eight $L$-function of $\\mathrm{GSp}(4) \\times \\mathrm{GL}(2)$ associa ted to a product of automorphic generic admissible cuspidal representation s of $\\mathrm{GSp}(4)$ and $\\mathrm{GL}(2)$ respectively\, in the case w here this function is entire. \nIn this talk\, we will explain how we can link these different objects using a linear form defined on the Deligne co homology.\n LOCATION:https://researchseminars.org/talk/RSVP/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Graham (University College London) DTSTART:20210519T134500Z DTEND:20210519T144500Z DTSTAMP:20260422T212752Z UID:RSVP/4 DESCRIPTION:Title: Eul er systems and p-adic L-functions for conjugate self-dual representations< /a>\nby Andrew Graham (University College London) as part of Rendez-vous o n special values and periods\n\n\nAbstract\nIn this talk\, I will describe joint work with S.W.A. Shah on the construction of a split anticyclotomic Euler system for a large class of conjugate self-dual automorphic represe ntations admitting a Shalika model. \nThis Euler system arises from specia l cycles on unitary Shimura varieties and the proof of the norm relations amounts to a computation in local representation theory. \nI will also des cribe the expected relation with $p$-adic $L$-functions (using the machine ry of higher Hida theory) and (expected) applications to the Bloch-Kato co njecture.\n LOCATION:https://researchseminars.org/talk/RSVP/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Óscar Rivero (University of Warwick) DTSTART:20210519T150000Z DTEND:20210519T160000Z DTSTAMP:20260422T212752Z UID:RSVP/5 DESCRIPTION:Title: Eis enstein congruences and Euler systems\nby Óscar Rivero (University of Warwick) as part of Rendez-vous on special values and periods\n\n\nAbstra ct\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 constructed a class arising from the cup-product of two Siegel units and proved a rela tionship with the first derivative of the $L$-series of $f$ at the near ce ntral point $s=0$. I will motivate the study of congruences between modula r forms at the level of cohomology classes\, and will report on a joint wo rk with Victor Rotger where we prove two congruence formulas relating the Beilinson class with the arithmetic of circular units. The proofs make use of delicate Galois properties satisfied by various integral lattices and exploits Perrin-Riou's\, Coleman's and Kato's work on the Euler systems of circular units and Beilinson-Kato elements and\, most crucially\, the wor k of Fukaya-Kato.\n LOCATION:https://researchseminars.org/talk/RSVP/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaoyu Zhang (Universität Duisburg-Essen) DTSTART:20210520T083000Z DTEND:20210520T093000Z DTSTAMP:20260422T212752Z UID:RSVP/6 DESCRIPTION:Title: p-p art Bloch-Kato conjecture for Siegel modular forms of genus 2\nby Xiao yu Zhang (Universität Duisburg-Essen) as part of Rendez-vous on special v alues and periods\n\n\nAbstract\nThe Bloch-Kato conjecture relates the alg ebraic 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 Siegel mo dular form of genus $2$ and show\, under mild conditions on the associated Galois representation\, that the special value of the standard $L$-functi on divided by an automorphic period is equal to the characteristic ideal o f the corresponding Selmer group\, up to $p$-units. \nThe proof relies on some non-vanishing results of mod $p$ theta lifts from the orthogonal grou p to the symplectic group.\n LOCATION:https://researchseminars.org/talk/RSVP/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanneke Wiersema (King's College London) DTSTART:20210520T100000Z DTEND:20210520T110000Z DTSTAMP:20260422T212752Z UID:RSVP/7 DESCRIPTION:Title: On a BSD-type formula for L-values of Artin twists of elliptic curves\nby Hanneke Wiersema (King's College London) as part of Rendez-vous on specia l values and periods\n\n\nAbstract\nIn this talk we discuss the possible e xistence of a BSD-type formula for $L$-functions of elliptic curves twiste d by Artin representations. After outlining some expected properties of th ese $L$-functions\, we present arithmetic consequences for the behaviour o f Tate–Shafarevich groups\, Selmer groups and rational points. We illust rate these with some explicit examples. This is joint work with Vladimir D okchitser and Robert Evans.\n LOCATION:https://researchseminars.org/talk/RSVP/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Quentin Gazda (Université Claude Bernard Lyon 1) DTSTART:20210520T123000Z DTEND:20210520T133000Z DTSTAMP:20260422T212752Z UID:RSVP/8 DESCRIPTION:Title: Fir st Beilinson’s conjecture in function fields arithmetic\nby Quentin Gazda (Université Claude Bernard Lyon 1) as part of Rendez-vous on specia l values and periods\n\n\nAbstract\nIn the mid 80’s\, Beilinson formulat ed deep conjectures relating special values of $L$-functions to pieces of $K$-theory\, superseding at once the BSD conjecture and Deligne’s conjec ture. Beilinson's conjectures are fully expressed in the framework of mixe d motives\, which remains hypothetical. \n\nThis talk will be devoted to p ortray the analogous picture in the function fields setting\, using so-cal led Goss $L$-values instead of classical $L$-values\, and mixed (uniformiz able) Anderson $A$-motives instead of Grothendieck's mixed motives. After a recall of the classical conjectures\, we shall discuss and define the an alogue of motivic cohomology and regulators for function fields\, and expr ess the counterpart of Beilinson’s conjectures.\n LOCATION:https://researchseminars.org/talk/RSVP/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Huy Hung Le (Université de Caen Normandie) DTSTART:20210520T134500Z DTEND:20210520T144500Z DTSTAMP:20260422T212752Z UID:RSVP/9 DESCRIPTION:Title: On identities for zeta values in Tate algebras\nby Huy Hung Le (Universit é de Caen Normandie) as part of Rendez-vous on special values and periods \n\n\nAbstract\nZeta values in Tate algebras were introduced by Pellarin i n 2012. They are generalizations of Carlitz zeta values and play an incre asingly important role in function field arithmetic. \n\nIn this talk\, we will present some related conjectures proposed by Pellarin. \nThen\, we w ill study the Bernoulli-type polynomials attached to these zeta values. \n By a combinatorial method\, we can also provide some explicit formulas. \n We will demonstrate how to use these results to prove a conjecture of Pell arin on identities for zeta values in Tate algebras.\n LOCATION:https://researchseminars.org/talk/RSVP/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Matthes (University of Oxford) DTSTART:20210520T150000Z DTEND:20210520T160000Z DTSTAMP:20260422T212752Z UID:RSVP/10 DESCRIPTION:Title: A new approach to multiple elliptic polylogarithms\nby Nils Matthes (Uni versity of Oxford) as part of Rendez-vous on special values and periods\n\ n\nAbstract\nMultiple polylogarithms may be viewed as the monodromy of a c ertain "universal" unipotent differential equation on the projective line minus three points. This observation lies at the heart of their relation t o mixed Tate motives\, a point of view which brings powerful new tools to bear on the study of these functions and its special values.\n\nThe goal o f this talk is to describe an analogous picture for a once-punctured ellip tic curve $E'$. In particular\, we obtain a new description of the unipote nt de Rham fundamental group of $E'$\, generalizing and improving on previ ous works of Levin-Racinet\, Brown-Levin\, Enriquez-Etingof\, and others. Joint work in progress with Tiago J. Fonseca (Oxford).\n LOCATION:https://researchseminars.org/talk/RSVP/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Zerbini (IPhT CEA-Saclay) DTSTART:20210521T083000Z DTEND:20210521T093000Z DTSTAMP:20260422T212752Z UID:RSVP/11 DESCRIPTION:Title: Ne w modular forms from string theory\, and single-valued periods\nby Fed erico Zerbini (IPhT CEA-Saclay) as part of Rendez-vous on special values a nd periods\n\n\nAbstract\nI will introduce a class of modular forms\, call ed modular graph functions\, which originate from the computation of Feynm an integrals in string theory. \nModular graph functions generalise real a nalytic Eisenstein series\, their expansion coefficients are multiple zeta values\, and they are conjecturally related to the theory of single-value d periods\, which I will briefly review. \nIn particular\, the expansion c oefficients are conjectured to belong to a small subalgebra of the multipl e zeta values whose elements are single-valued periods. \n\nI will present a proof of this conjecture for the simplest kind of Feynman integrals\, o btained in collaboration with Don Zagier. \nI will also mention how modula r graph functions are expected to be related to iterated extensions of pur e motives of modular forms\, and how one can attach $L$-functions to them. \n LOCATION:https://researchseminars.org/talk/RSVP/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Keilthy (Max-Planck-Institut für Mathematik) DTSTART:20210521T100000Z DTEND:20210521T110000Z DTSTAMP:20260422T212752Z UID:RSVP/12 DESCRIPTION:Title: Bl ock graded relations among motivic multiple zeta values\nby Adam Keilt hy (Max-Planck-Institut für Mathematik) as part of Rendez-vous on special values and periods\n\n\nAbstract\nMultiple zeta values\, originally consi dered by Euler\, generalise the Riemann zeta function to multiple variable s.\n\nWhile values of the Riemann zeta function at odd positive integers a re conjectured to be algebraically independent\, multiple zeta values sati sfy many algebraic and linear relations\, even forming a $\\mathbb{Q}$-alg ebra. While families of well understood relations are known\, such as the associator relations and double shuffle relations\, they only conjecturall y span all algebraic relations. Since multiple zeta values arise as the pe riods of mixed Tate motives\, we obtain further algebraic structures\, whi ch have been exploited to provide spanning sets by Brown. In this talk we will aim to define a new set of relations\, known to be complete in low bl ock degree.\n\nTo achieve this\, we will first review the necessary algebr aic set up\, focusing particularly on the motivic Lie algebra associated t o the thrice punctured projective line. We then introduce a new filtration on the algebra of (motivic) multiple zeta values\, called the block filtr ation\, based on the work of Charlton. By considering the associated grade d algebra\, we quickly obtain a new family of graded motivic relations\, w hich can be shown to span all algebraic relations in low block degree. We will also touch on some conjectural ungraded "lifts" of these relations\, and if we have time\, compare to similar approaches using the depth filtra tion.\n LOCATION:https://researchseminars.org/talk/RSVP/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahya Mehrabdollahei (Sorbonne Université) DTSTART:20210521T123000Z DTEND:20210521T133000Z DTSTAMP:20260422T212752Z UID:RSVP/13 DESCRIPTION:Title: Ma hler measure of a family of exact polynomials\nby Mahya Mehrabdollahei (Sorbonne Université) as part of Rendez-vous on special values and perio ds\n\n\nAbstract\nI will present results around the Mahler measure of a fa mily of 2-variate exact polynomials. The closed formula for the Mahler mea sure of two-variable exact polynomials gives an expression of each of thes e Mahler measures as a finite sum of the values of Dilogarithm at certain roots of unity. \n\nThis allows to compute their values with any precision \, and to use the techniques of Riemann sums to compute the limit of this sequence of Mahler measures and an asymptotic expansion\, with a link to a theorem of Boyd and Lawton.\nFinally\, for small values of d\, we can rel ate 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://researchseminars.org/talk/RSVP/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugenia Rosu (Universität Regensburg) DTSTART:20210521T134500Z DTEND:20210521T144500Z DTSTAMP:20260422T212752Z UID:RSVP/14 DESCRIPTION:Title: Tw ists of elliptic curves with CM\nby Eugenia Rosu (Universität Regensb urg) as part of Rendez-vous on special values and periods\n\n\nAbstract\nW e 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 $\\mathbb{Q} [\\sqrt{-3}]$.\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. \nAssum ing the Birch and Swinnerton-Dyer conjecture\, when the value above is non -zero\, we should recover the order of the Tate-Shafarevich group\, and un der certain conditions we show that the value is indeed a square.\n LOCATION:https://researchseminars.org/talk/RSVP/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tamiozzo (Imperial College) DTSTART:20210521T150000Z DTEND:20210521T160000Z DTSTAMP:20260422T212752Z UID:RSVP/15 DESCRIPTION:Title: To rsion in the cohomology of Hilbert modular varieties (with a view towards Iwasawa theory)\nby Matteo Tamiozzo (Imperial College) as part of Rend ez-vous on special values and periods\n\n\nAbstract\nYiwen Zhou has given a new construction of Kato's zeta element in local Iwasawa cohomology base d on local-global compatibility between completed cohomology of modular cu rves and the $p$-adic Langlands correspondence. After recalling this const ruction\, we will discuss the proof of a vanishing theorem for cohomology of Hilbert modular varieties which plays a key role in extending the above local-global compatibility result. This is joint work in progress with An a Caraiani.\n LOCATION:https://researchseminars.org/talk/RSVP/15/ END:VEVENT END:VCALENDAR