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:20260404T111135Z UID:NTUniPD/1 DESCRIPTION:Title: Algebraicity of polyquadratic plectic points\nby Lennart Gehrma nn (Universität Duisburg-Essen) as part of Number Theory Seminars at Univ ersità degli Studi di Padova\n\n\nAbstract\nHeegner points play an import ant role in our understanding of the arithmetic of modular elliptic curves . These points\, that arise from CM points on Shimura curves\, control the Mordell-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 employed to generalize the definition of Heegner points to quadratic exte nsions that are not necessarily CM. Numerical evidence strongly supports t he belief that these so-called Stark-Heegner points completely control the Mordell-Weil group of elliptic curves of rank 1. In this talk I will repo rt on a plectic generalizations of Stark-Heegner points. Inspired by Nekov ar and Scholl's conjectures\, these points are expected to control Mordell -Weil groups of higher rank elliptic curves. I will give strong evidence f or this expectation in the case of polyquadratic CM fields. This is joint work with Michele Fornea.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Pengo (École normale supérieure de Lyon) DTSTART:20220317T104500Z DTEND:20220317T114500Z DTSTAMP:20260404T111135Z UID:NTUniPD/2 DESCRIPTION:Title: Limits of Mahler measures and (successively) exact polynomials\ nby Riccardo Pengo (École normale supérieure de Lyon) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nMahler 's measure is a height function of fundamental importance in Diophantine g eometry\, protagonist of a celebrated problem posed by Lehmer. The work of Boyd has shown that Lehmer's problem can be approached by studying Mahler measures of multivariate polynomials\, and that the latter are often link ed to special values of $L$-functions. In this seminar\, I will talk about a generalization of the work of Boyd\, obtained jointly with François Br unault\, Antonin Guilloux and Mahya Mehrabdollahei\, in which we find a cl ass of sequences of polynomials whose Mahler measures converge. Furthermor e\, we provide an explicit upper bound for the error term\, and an asympto tic expansion for a particular family of polynomials\, whose terms share a ll the peculiar property of being "exact". If time permits\, I will explai n more in detail this notion of exactness\, and talk about a generalizatio n of it (the notion of "successive exactness")\, studied jointly with Fran çois Brunault\, which is related to a certain "weight loss" of the $L$-fu nctions whose special values are conjecturally related to the Mahler measu re of the polynomial in question.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Marrama (Centre de Mathématiques Laurent Schwartz\, École Polytechnique) DTSTART:20220331T094500Z DTEND:20220331T104500Z DTSTAMP:20260404T111135Z UID:NTUniPD/3 DESCRIPTION:Title: Filtrations of Barsotti-Tate groups via Harder-Narasimhan theory.\nby Andrea Marrama (Centre de Mathématiques Laurent Schwartz\, École Polytechnique) as part of Number Theory Seminars at Università degli Stud i di Padova\n\n\nAbstract\nLet $p$ be a prime number and let $R$ be a comp lete valuation ring of rank one and mixed characteristic $(0\,p)$.\nGiven a Barsotti-Tate group $H$ over $R$\, its $p$-power-torsion parts possess a natural "Harder-Narasimhan" filtration\, introduced by Fargues in analogy with the theory of vector bundles over a smooth projective curve over an algebraically closed field.\nOne may wonder when these filtrations build u p to a filtration of the whole Barsotti-Tate group $H$.\nI will present so me sufficient conditions in this direction\, especially in the case that t he endomorphisms 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 Bijakowski.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Battistoni (Università degli Studi di Milano) DTSTART:20220324T104500Z DTEND:20220324T114500Z DTSTAMP:20260404T111135Z UID:NTUniPD/4 DESCRIPTION:Title: Arithmetic equivalence for number fields and global function fields .\nby Francesco Battistoni (Università degli Studi di Milano) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstr act\nTwo number fields $K$ and $L$ are said to be arithmetically equivalen t if\, for almost every prime number $p$\, the factorizations of $p$ in th e 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 finit e extensions of a function field $F(T)$\, where $F$ is a finite field.\nIn this talk we discuss the concept of arithmetic equivalence in both contex ts\, focusing on the similarities and the differences between the two case s. In particular\, we will show a group-theoretic analogue of the problem and we will explain the relation between arithmetic equivalence and equali ty of certain zeta functions (the classical Dedekind zeta function for num ber fields\, a more complicated function for function fields). Finally\, w e will show how to produce examples of equivalent but not isomorphic field s in both contexts.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Óscar Rivero (Warwick University) DTSTART:20220414T094500Z DTEND:20220414T104500Z DTSTAMP:20260404T111135Z UID:NTUniPD/5 DESCRIPTION:Title: Anticyclotomic Euler systems and diagonal cycles\nby Óscar Riv ero (Warwick University) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nIn this talk\, I will discuss joint w ork with Raul Alonso and Francesc Castella where we construct an anticyclo tomic Euler system for the Rankin$-$Selberg convolutions of two modular fo rms\, using $p$-adic families of generalized Gross$-$Kudla$-$Schoen diagon al cycles. As applications of this construction\, we prove new cases of th e Bloch$-$Kato conjecture in analytic rank zero (and results towards new c ases in analytic rank one)\, and a divisibility towards an Iwasawa main co njecture. If time permits\, I will also consider the case of the symmetric square of a modular form\, where the key ingredient is a factorization fo rmula for the triple product $p$-adic $L$-function.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tamiozzo (Imperial College London) DTSTART:20220428T094500Z DTEND:20220428T104500Z DTSTAMP:20260404T111135Z UID:NTUniPD/6 DESCRIPTION:Title: Geodesics on modular surfaces and functional transcendence\nby Matteo Tamiozzo (Imperial College London) as part of Number Theory Seminar s at Università degli Studi di Padova\n\n\nAbstract\nThe approach to the André-Oort conjecture suggested by Pila-Zannier relies on the study of (c omplex) subvarieties of Shimura varieties (and their universal cover) from the viewpoint of functional transcendence. I will first recall the main r esults of this theory in the simplest case of the product of two modular c urves. I will then deduce analogous theorems for real subvarieties of a mo dular curve seen as a real algebraic surface.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Giada Grossi (LAGA\, Université Sorbonne Paris Nord) DTSTART:20220407T094500Z DTEND:20220407T104500Z DTSTAMP:20260404T111135Z 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\nA bstract\nI will discuss work in progress with F. Castella and C. Skinner o n the anticyclotomic and cyclotomic Iwasawa main conjectures at Eisenstein primes $p$\, generalising our earlier paper with J. Lee and the results o f Greenberg and Vatsal. As a consequence\, we obtain new results on the p- part of the Birch-Swinnerton-Dyer conjecture.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Cauchi (Concordia University (Montreal)) DTSTART:20220609T101500Z DTEND:20220609T111500Z DTSTAMP:20260404T111135Z UID:NTUniPD/8 DESCRIPTION:Title: Quaternionic diagonal cycles and instances of the Birch and Swinner ton-Dyer conjecture for elliptic curves over totally real fields.\nby Antonio Cauchi (Concordia University (Montreal)) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nIn the early nineties\, Kato’s Euler system of Beilinson elements and the theory of H eegner points revolutionised the arithmetic of (modular) elliptic curves o ver 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 generalised 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 t he work and collective effort of Bertolini\, Darmon\, Rotger\, Seveso\, an d Venerucci\, has proven to be a fertile environment for proving new insta nces of the Birch and Swinnerton-Dyer conjecture for elliptic curves over the rationals. The aim of this talk is to discuss joint work in progress w ith Daniel Barrera\, Santiago Molina\, and Victor Rotger on the generalisa tion of the theory of diagonal cycles to quaternionic Shimura curves over totally real number fields $F$ and its application to extending Kato’s r esult for twists of elliptic curves $E/F$ by Hecke characters of $F$ of fi nite order.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksander Horawa (University of Michigan) DTSTART:20220422T130000Z DTEND:20220422T140000Z DTSTAMP:20260404T111135Z UID:NTUniPD/10 DESCRIPTION:Title: Motivic action on coherent cohomology of Hilbert modular varieties \nby Aleksander Horawa (University of Michigan) as part of Number Theo ry Seminars at Università degli Studi di Padova\n\n\nAbstract\nA surprisi ng property of the cohomology of locally symmetric spaces is that\nHecke o perators can act on multiple cohomological degrees with the same\neigenval ues. We will discuss this phenomenon for the coherent cohomology of\nline bundles on modular curves and\, more generally\, Hilbert modular\nvarietie s. We propose an arithmetic explanation: a hidden degree-shifting\naction of a certain motivic cohomology group (the Stark unit group). This\nextend s the conjectures of Venkatesh\, Prasanna\, and Harris to Hilbert\nmodular varieties.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tamiozzo (Imperial College London) DTSTART:20220429T130500Z DTEND:20220429T140500Z DTSTAMP:20260404T111135Z UID:NTUniPD/11 DESCRIPTION:Title: Perfectoid Jacquet-Langlands correspondence and the cohomology of Hilbert modular varieties\nby Matteo Tamiozzo (Imperial College London ) as part of Number Theory Seminars at Università degli Studi di Padova\n \n\nAbstract\nThe work of Tian-Xiao on the Goren-Oort stratification for q uaternionic Shimura varieties provides a geometric incarnation of the Jacq uet-Langlands correspondence\, and leads to a geometric approach to level raising of quaternionic automorphic forms. I will describe a perfectoid ve rsion of Tian-Xiao's result\, and explain how it can be used\, joint with geometric properties of the Hodge-Tate period map\, to prove vanishing the orems for the cohomology of quaternionic Shimura varieties with torsion co efficients. This is joint work with Ana Caraiani.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Bullach (King’s College London) DTSTART:20220512T094500Z DTEND:20220512T104500Z DTSTAMP:20260404T111135Z UID:NTUniPD/12 DESCRIPTION:Title: Dirichlet $L$-series at $s = 0$ and the scarcity of Euler systems< /a>\nby Dominik Bullach (King’s College London) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nIn 1989 Cole man made a distribution-theoretic conjecture which predicts that every Eul er system `for $\\Q$' should essentially be cyclotomic in nature. In this talk I will discuss work joint with Burns\, Daoud and Seo which not only a llows us to prove Coleman's Conjecture but also provides an elementary int erpretation of\, and thereby more direct strategy to proving\, the equivar iant Tamagawa 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 field s.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Fornea (Columbia University) DTSTART:20220629T090000Z DTEND:20220629T100000Z DTSTAMP:20260404T111135Z UID:NTUniPD/13 DESCRIPTION:Title: Plectic Jacobians and Hodge theory\nby Michele Fornea (Columbi a University) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nGehrmann\, Guitart\, Masdeu and myself recently proposed\, and gave evidence for\, plectic generalizations of Stark-Heegne r points. The construction is p-adic\, cohomological\, and unfortunately l acking a satisfying geometric interpretation. Nevertheless\, we formulated precise conjectures on the algebraicity of plectic points and their signi ficance for the arithmetic of higher rank elliptic curves.\nIn this talk I will report on work in progress on the Archimedean side of the story wher e geometry has a prominent role:\nI will describe a collection of complex tori — called plectic Jacobians — associated with the plectic Hodge s tructure appearing in the middle degree cohomology of Hilbert modular vari eties. Interestingly\, the Oda-Yoshida conjecture can be used to prove tha t plectic Jacobians are modular abelian varieties defined over $\\overline {\\mathbb{Q}}$. Moreover\, the existence of exotic Abel-Jacobi morphisms ( mapping zero-cycles to plectic Jacobians) further highlights the arithmeti c appeal of the construction.\n LOCATION:https://stable.researchseminars.org/talk/NTUniPD/13/ END:VEVENT END:VCALENDAR