BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lennart Gehrmann (Universität Duisburg-Essen) DTSTART:20220310T104500Z DTEND:20220310T114500Z DTSTAMP:20260422T225825Z UID:NTUniPD/1 DESCRIPTION:Title: Algebraicity of polyquadratic plectic points\nby Lennart Gehrmann (Uni versität Duisburg-Essen) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nHeegner points play an important rol e in our understanding of the arithmetic of modular elliptic curves. These points\, that arise from CM points on Shimura curves\, control the Mordel l-Weil group of elliptic curves of rank 1. The work of Bertolini\, Darmon and their schools has shown that p-adic methods can be successfully employ ed to generalize the definition of Heegner points to quadratic extensions that are not necessarily CM. Numerical evidence strongly supports the beli ef that these so-called Stark-Heegner points completely control the Mordel l-Weil group of elliptic curves of rank 1. In this talk I will report on a plectic generalizations of Stark-Heegner points. Inspired by Nekovar and Scholl's conjectures\, these points are expected to control Mordell-Weil g roups of higher rank elliptic curves. I will give strong evidence for this expectation in the case of polyquadratic CM fields. This is joint work wi th Michele Fornea.\n LOCATION:https://researchseminars.org/talk/NTUniPD/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Pengo (École normale supérieure de Lyon) DTSTART:20220317T104500Z DTEND:20220317T114500Z DTSTAMP:20260422T225825Z UID:NTUniPD/2 DESCRIPTION:Title: Limits of Mahler measures and (successively) exact polynomials\nby Ric cardo Pengo (École normale supérieure de Lyon) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nMahler's meas ure is a height function of fundamental importance in Diophantine geometry \, protagonist of a celebrated problem posed by Lehmer. The work of Boyd h as shown that Lehmer's problem can be approached by studying Mahler measur es of multivariate polynomials\, and that the latter are often linked to s pecial values of $L$-functions. In this seminar\, I will talk about a gene ralization of the work of Boyd\, obtained jointly with François Brunault\ , Antonin Guilloux and Mahya Mehrabdollahei\, in which we find a class of sequences of polynomials whose Mahler measures converge. Furthermore\, we provide an explicit upper bound for the error term\, and an asymptotic exp ansion for a particular family of polynomials\, whose terms share all the peculiar property of being "exact". If time permits\, I will explain more in detail this notion of exactness\, and talk about a generalization of it (the notion of "successive exactness")\, studied jointly with François B runault\, which is related to a certain "weight loss" of the $L$-functions whose special values are conjecturally related to the Mahler measure of t he polynomial in question.\n LOCATION:https://researchseminars.org/talk/NTUniPD/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Marrama (Centre de Mathématiques Laurent Schwartz\, École Polytechnique) DTSTART:20220331T094500Z DTEND:20220331T104500Z DTSTAMP:20260422T225825Z UID:NTUniPD/3 DESCRIPTION:Title: Filtrations of Barsotti-Tate groups via Harder-Narasimhan theory.\nby Andrea Marrama (Centre de Mathématiques Laurent Schwartz\, École Polytec hnique) as part of Number Theory Seminars at Università degli Studi di Pa dova\n\n\nAbstract\nLet $p$ be a prime number and let $R$ be a complete va luation ring of rank one and mixed characteristic $(0\,p)$.\nGiven a Barso tti-Tate group $H$ over $R$\, its $p$-power-torsion parts possess a natura l "Harder-Narasimhan" filtration\, introduced by Fargues in analogy with t he theory of vector bundles over a smooth projective curve over an algebra ically closed field.\nOne may wonder when these filtrations build up to a filtration of the whole Barsotti-Tate group $H$.\nI will present some suff icient conditions in this direction\, especially in the case that the endo morphisms of $H$ contain the ring of integers of a finite extension of $\\ mathbb{Q}_p$.\nThis is partly based on a joint work with Stéphane Bijakow ski.\n LOCATION:https://researchseminars.org/talk/NTUniPD/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Battistoni (Università degli Studi di Milano) DTSTART:20220324T104500Z DTEND:20220324T114500Z DTSTAMP:20260422T225825Z UID:NTUniPD/4 DESCRIPTION:Title: Arithmetic equivalence for number fields and global function fields.\n by Francesco Battistoni (Università degli Studi di Milano) as part of Num ber Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nTw o number fields $K$ and $L$ are said to be arithmetically equivalent if\, for almost every prime number $p$\, the factorizations of $p$ in the rings of integers of $K$ and $L$ are analogous (in a precise sense that will be explained). A completely similar definition can be given for finite exten sions of a function field $F(T)$\, where $F$ is a finite field.\nIn this t alk we discuss the concept of arithmetic equivalence in both contexts\, fo cusing on the similarities and the differences between the two cases. In p articular\, we will show a group-theoretic analogue of the problem and we will explain the relation between arithmetic equivalence and equality of c ertain zeta functions (the classical Dedekind zeta function for number fie lds\, a more complicated function for function fields). Finally\, we will show how to produce examples of equivalent but not isomorphic fields in bo th contexts.\n LOCATION:https://researchseminars.org/talk/NTUniPD/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Óscar Rivero (Warwick University) DTSTART:20220414T094500Z DTEND:20220414T104500Z DTSTAMP:20260422T225825Z UID:NTUniPD/5 DESCRIPTION:Title: Anticyclotomic Euler systems and diagonal cycles\nby Óscar Rivero (Wa rwick University) as part of Number Theory Seminars at Università degli S tudi di Padova\n\n\nAbstract\nIn this talk\, I will discuss joint work wit h Raul Alonso and Francesc Castella where we construct an anticyclotomic E uler system for the Rankin$-$Selberg convolutions of two modular forms\, u sing $p$-adic families of generalized Gross$-$Kudla$-$Schoen diagonal cycl es. As applications of this construction\, we prove new cases of the Bloch $-$Kato conjecture in analytic rank zero (and results towards new cases in analytic rank one)\, and a divisibility towards an Iwasawa main conjectur e. If time permits\, I will also consider the case of the symmetric square of a modular form\, where the key ingredient is a factorization formula f or the triple product $p$-adic $L$-function.\n LOCATION:https://researchseminars.org/talk/NTUniPD/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tamiozzo (Imperial College London) DTSTART:20220428T094500Z DTEND:20220428T104500Z DTSTAMP:20260422T225825Z UID:NTUniPD/6 DESCRIPTION:Title: Geodesics on modular surfaces and functional transcendence\nby Matteo Tamiozzo (Imperial College London) as part of Number Theory Seminars at Un iversità degli Studi di Padova\n\n\nAbstract\nThe approach to the André- Oort conjecture suggested by Pila-Zannier relies on the study of (complex) subvarieties of Shimura varieties (and their universal cover) from the vi ewpoint of functional transcendence. I will first recall the main results of this theory in the simplest case of the product of two modular curves. I will then deduce analogous theorems for real subvarieties of a modular c urve seen as a real algebraic surface.\n LOCATION:https://researchseminars.org/talk/NTUniPD/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Giada Grossi (LAGA\, Université Sorbonne Paris Nord) DTSTART:20220407T094500Z DTEND:20220407T104500Z DTSTAMP:20260422T225825Z UID:NTUniPD/7 DESCRIPTION:Title: (Anti)cyclotomic main conjectures for elliptic curves at Eisenstein primes .\nby Giada Grossi (LAGA\, Université Sorbonne Paris Nord) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract \nI will discuss work in progress with F. Castella and C. Skinner on the a nticyclotomic and cyclotomic Iwasawa main conjectures at Eisenstein primes $p$\, generalising our earlier paper with J. Lee and the results of Green berg and Vatsal. As a consequence\, we obtain new results on the p-part of the Birch-Swinnerton-Dyer conjecture.\n LOCATION:https://researchseminars.org/talk/NTUniPD/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Cauchi (Concordia University (Montreal)) DTSTART:20220609T101500Z DTEND:20220609T111500Z DTSTAMP:20260422T225825Z UID:NTUniPD/8 DESCRIPTION:Title: Quaternionic diagonal cycles and instances of the Birch and Swinnerton-Dye r conjecture for elliptic curves over totally real fields.\nby Antonio Cauchi (Concordia University (Montreal)) as part of Number Theory Seminar s at Università degli Studi di Padova\n\n\nAbstract\nIn the early ninetie s\, Kato’s Euler system of Beilinson elements and the theory of Heegner points revolutionised the arithmetic of (modular) elliptic curves over the rationals. For instance\, the former led Kato to proving instances of the Birch and Swinnerton-Dyer conjecture for twists of elliptic curves over $ \\Q$ by finite order characters. While the theory of Heegner points was ge neralised to elliptic curves $E/F$ defined over totally real number fields \, Kato’s result has not found its natural extension to twists of $E/F$ yet. More recently\, the theory of diagonal cycles\, arising from the work and collective effort of Bertolini\, Darmon\, Rotger\, Seveso\, and Vener ucci\, has proven to be a fertile environment for proving new instances of the Birch and Swinnerton-Dyer conjecture for elliptic curves over the rat ionals. The aim of this talk is to discuss joint work in progress with Dan iel Barrera\, Santiago Molina\, and Victor Rotger on the generalisation of the theory of diagonal cycles to quaternionic Shimura curves over totally real number fields $F$ and its application to extending Kato’s result f or twists of elliptic curves $E/F$ by Hecke characters of $F$ of finite or der.\n LOCATION:https://researchseminars.org/talk/NTUniPD/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksander Horawa (University of Michigan) DTSTART:20220422T130000Z DTEND:20220422T140000Z DTSTAMP:20260422T225825Z UID:NTUniPD/10 DESCRIPTION:Title: Motivic action on coherent cohomology of Hilbert modular varieties\nb y Aleksander Horawa (University of Michigan) as part of Number Theory Semi nars at Università degli Studi di Padova\n\n\nAbstract\nA surprising prop erty of the cohomology of locally symmetric spaces is that\nHecke operator s can act on multiple cohomological degrees with the same\neigenvalues. We will discuss this phenomenon for the coherent cohomology of\nline bundles on modular curves and\, more generally\, Hilbert modular\nvarieties. We p ropose an arithmetic explanation: a hidden degree-shifting\naction of a ce rtain motivic cohomology group (the Stark unit group). This\nextends the c onjectures of Venkatesh\, Prasanna\, and Harris to Hilbert\nmodular variet ies.\n LOCATION:https://researchseminars.org/talk/NTUniPD/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tamiozzo (Imperial College London) DTSTART:20220429T130500Z DTEND:20220429T140500Z DTSTAMP:20260422T225825Z UID:NTUniPD/11 DESCRIPTION:Title: Perfectoid Jacquet-Langlands correspondence and the cohomology of Hilbert modular varieties\nby Matteo Tamiozzo (Imperial College London) as pa rt of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbs tract\nThe work of Tian-Xiao on the Goren-Oort stratification for quaterni onic Shimura varieties provides a geometric incarnation of the Jacquet-Lan glands correspondence\, and leads to a geometric approach to level raising of quaternionic automorphic forms. I will describe a perfectoid version o f Tian-Xiao's result\, and explain how it can be used\, joint with geometr ic properties of the Hodge-Tate period map\, to prove vanishing theorems f or the cohomology of quaternionic Shimura varieties with torsion coefficie nts. This is joint work with Ana Caraiani.\n LOCATION:https://researchseminars.org/talk/NTUniPD/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Bullach (King’s College London) DTSTART:20220512T094500Z DTEND:20220512T104500Z DTSTAMP:20260422T225825Z UID:NTUniPD/12 DESCRIPTION:Title: Dirichlet $L$-series at $s = 0$ and the scarcity of Euler systems\nby Dominik Bullach (King’s College London) as part of Number Theory Semina rs at Università degli Studi di Padova\n\n\nAbstract\nIn 1989 Coleman mad e a distribution-theoretic conjecture which predicts that every Euler syst em `for $\\Q$' should essentially be cyclotomic in nature. In this talk I will discuss work joint with Burns\, Daoud and Seo which not only allows u s to prove Coleman's Conjecture but also provides an elementary interpreta tion of\, and thereby more direct strategy to proving\, the equivariant Ta magawa Number Conjecture (eTNC) for Dirichlet $L$-series at $s = 0$. As a concrete application we obtain an unconditional proof of the `minus part' of the eTNC over finite abelian CM extensions of totally real fields.\n LOCATION:https://researchseminars.org/talk/NTUniPD/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Fornea (Columbia University) DTSTART:20220629T090000Z DTEND:20220629T100000Z DTSTAMP:20260422T225825Z UID:NTUniPD/13 DESCRIPTION:Title: Plectic Jacobians and Hodge theory\nby Michele Fornea (Columbia Unive rsity) as part of Number Theory Seminars at Università degli Studi di Pad ova\n\n\nAbstract\nGehrmann\, Guitart\, Masdeu and myself recently propose d\, and gave evidence for\, plectic generalizations of Stark-Heegner point s. The construction is p-adic\, cohomological\, and unfortunately lacking a satisfying geometric interpretation. Nevertheless\, we formulated precis e conjectures on the algebraicity of plectic points and their significance for the arithmetic of higher rank elliptic curves.\nIn this talk I will r eport on work in progress on the Archimedean side of the story where geome try has a prominent role:\nI will describe a collection of complex tori — called plectic Jacobians — associated with the plectic Hodge struct ure appearing in the middle degree cohomology of Hilbert modular varieties . Interestingly\, the Oda-Yoshida conjecture can be used to prove that ple ctic Jacobians are modular abelian varieties defined over $\\overline{\\ma thbb{Q}}$. Moreover\, the existence of exotic Abel-Jacobi morphisms (mappi ng zero-cycles to plectic Jacobians) further highlights the arithmetic app eal of the construction.\n LOCATION:https://researchseminars.org/talk/NTUniPD/13/ END:VEVENT END:VCALENDAR