BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marc Masdeu (Universitat Autònoma de Barcelona) DTSTART:20201203T143000Z DTEND:20201203T145000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/1 DESCRIPTION:Title: Quaternionic rigid meromorphic cocycles\nby Marc Masdeu (Unive rsitat Autònoma de Barcelona) as part of Computations with Arithmetic Gro ups\n\n\nAbstract\nRigid meromorphic cocycles were introduced by Darmon an d Vonk as a conjectural p-adic extension of the theory of singular moduli to real quadratic base fields. They are certain cohomology classes of $SL_ 2(\\mathbb{Z}[1/p])$ which can be evaluated at real quadratic irrationalit ies and the values thus obtained are conjectured to lie in algebraic exten sions of the base field.\n\nI will present joint work with X.Guitart and X .Xarles\, in which we generalize (and somewhat simplify) this construction to the setting where $SL_2(\\mathbb{Z}[1/p])$ is replaced by an order in an indefinite quaternion algebra over a totally real number field $F$. The se quaternionic cohomology classes can be evaluated at elements in almost totally complex extensions $K$ of $F$\, and we conjecture that the corresp onding values lie in algebraic extensions of $K$. I will show some new num erical evidence for this conjecture\, along with some interesting question s allowed by this flexibility.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Graham Ellis (National University of Ireland\, Galway) DTSTART:20201203T150000Z DTEND:20201203T152000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/2 DESCRIPTION:Title: An algorithm for computing Hecke operators\nby Graham Ellis (N ational University of Ireland\, Galway) as part of Computations with Arith metic Groups\n\n\nAbstract\nI will describe an approach to computing Hecke operators on the integral cuspidal cohomology of congruence subgroups of $SL_2(\\mathcal{O}_d)$ over various rings of quadratic integers $\\mathcal {O}_d$. The approach makes use of an explicit contracting homotopy on a cl assifying space for $SL_2(\\mathcal{O}_d)$. The approach\, which has been partially implemented\, is also relevant for computations on congruence su bgroups of $SL_m(\\mathbb{Z})$\, $m\\geq2$ (where it has been fully implem ented for $m=2$).\n LOCATION:https://researchseminars.org/talk/CompArithGroups/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Angelica Babei (Centre de recherches mathématiques) DTSTART:20201203T154500Z DTEND:20201203T160500Z DTSTAMP:20260419T110655Z UID:CompArithGroups/3 DESCRIPTION:Title: Zeros of period polynomials for Hilbert modular forms\nby Ange lica Babei (Centre de recherches mathématiques) as part of Computations w ith Arithmetic Groups\n\n\nAbstract\nThe study of period polynomials for c lassical modular forms has emerged due to their role in Eichler cohomology . In particular\, the Eichler-Shimura isomorphism gives a correspondence b etween cusp eigenforms and their period polynomials. The coefficients of p eriod polynomials also encode critical L-values for the associated modular form and thus contain rich arithmetic information. Recent works have cons idered the location of the zeros of period polynomials\, and it has been s hown that in various settings\, their zeros lie on a circle centered at th e origin. \n\nIn this talk\, I will describe joint work with Larry Rolen a nd Ian Wagner\, where we introduce period polynomials for Hilbert modular forms of level one and prove that their zeros lie on the unit circle. In p articular\, I will detail some of the computational tools we used in our p roof.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Breen (Clemson University) DTSTART:20201203T161500Z DTEND:20201203T163500Z DTSTAMP:20260419T110655Z UID:CompArithGroups/4 DESCRIPTION:Title: A trace formula for Hilbert modular forms\nby Benjamin Breen ( Clemson University) as part of Computations with Arithmetic Groups\n\n\nAb stract\nWe present an explicit trace formula for Hilbert modular forms. Th e Jacquet-Langlands correspondence relates spaces of Hilbert modular forms to spaces of quaternionic modular forms\; the latter being far more amena ble to computations. We discuss how to compute traces of Hecke operators o n spaces of quaternionic modular forms and provide explicit examples for s ome definite quaternion algebras.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Avner Ash (Boston College) DTSTART:20201203T170000Z DTEND:20201203T172000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/5 DESCRIPTION:Title: Cohomology of congruence subgroups of $SL_3(\\mathbb{Z})$ and real quadratic fields\nby Avner Ash (Boston College) as part of Computatio ns with Arithmetic Groups\n\n\nAbstract\nGiven the congruence subgroup $\\ Gamma=\\Gamma_0(N)$ of $SL_3(\\mathbb{Z})$ and the real quadratic field $E =\\mathbb{Q}(\\sqrt{d})$\, we compare the homology of $\\Gamma$ with coeff icients in the Steinberg modules of $E$ and $\\mathbb{Q}$. This leads to a connecting homomorphism whose image H is a "natural" (in particular Hecke -stable) subspace of $H^3(\\Gamma\,\\mathbb{Q})$. The units $O^\\times_E$ are the main ingredient in the construction of elements of $H$. We perform ed computations to determine $H$ for a variety of levels $N≤169$ and all $d≤10$. On the basis of the results we conjecture exactly what the imag e should be in general. This is joint work with Dan Yasaki.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Cecile Armana (Universite de Franche-Comte) DTSTART:20201208T143000Z DTEND:20201208T145000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/6 DESCRIPTION:Title: Sturm bounds for Drinfeld-type automorphic forms over function fie lds\nby Cecile Armana (Universite de Franche-Comte) as part of Computa tions with Arithmetic Groups\n\n\nAbstract\nSturm bounds say how many succ essive Fourier coefficients suffice to determine a modular form. For class ical modular forms\, they also provide bounds for the number of Hecke oper ators generating the Hecke algebra. I will present Sturm bounds for Drinfe ld-type automorphic forms over the function field $\\mathbb{F}_q(t)$. Thei r proof involve refinements of a fundamental domain for a corresponding Br uhat-Tits tree under the action of a congruence subgroup. This is a joint work with Fu-Tsun Wei.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Neil Dummigan (University of Sheffield) DTSTART:20201208T150000Z DTEND:20201208T152000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/7 DESCRIPTION:Title: Congruences involving non-parallel weight Hilbert modular forms\nby Neil Dummigan (University of Sheffield) as part of Computations with Arithmetic Groups\n\n\nAbstract\nWhen newforms are congruent\, the modulu s appears in a near-central adjoint $L$-value. When those newforms are com plex conjugates\, it actually appears in the other critical values too. Th e Bloch-Kato conjecture then demands non-zero elements of that order in th e associated Selmer groups. These are provided by conjectural congruences involving non-parallel weight Hilbert modular forms. An experimental examp le of such a congruence showed up following computations of algebraic modu lar forms for a definite orthogonal group\, for the genus of even unimodul ar lattices of rank $12$ over the golden ring.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Fang-Ting Tu (Louisiana State University) DTSTART:20201208T154500Z DTEND:20201208T160500Z DTSTAMP:20260419T110655Z UID:CompArithGroups/8 DESCRIPTION:Title: A Geometric Interpretation of a Whipple's ${}_7F_6$ Formula\nb y Fang-Ting Tu (Louisiana State University) as part of Computations with A rithmetic Groups\n\n\nAbstract\nThis talk is based on a joint work with We n-Ching Winnie Li and Ling Long. We consider hypergeometric motives corres ponding to a formula due to Whipple which relates certain hypergeometric v alues ${}_7F_6(1)$ and ${}_4F_3(1)$. From identities of hypergeometric cha racter sums\, we explain a special structure of the Galois representation behind Whipple's formula leading to a decomposition that can be described by Hecke eigenforms. In this talk\, I will use an example to demonstrate o ur approach and relate the hypergeometric values to periods of modular for ms.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark McConnell (Princeton University) DTSTART:20201208T161500Z DTEND:20201208T163500Z DTSTAMP:20260419T110655Z UID:CompArithGroups/9 DESCRIPTION:Title: Computing Hecke Operators for Arithmetic Subgroups of the Symplect ic Group\nby Mark McConnell (Princeton University) as part of Computat ions with Arithmetic Groups\n\n\nAbstract\nLet $\\Gamma$ be an arithmetic subgroup of $G = Sp(4\,\\mathbb{R})$. We will describe a new algorithm fo r computing the cohomology $H^i$ of the locally symmetric space $\\Gamma\\ backslash G/K$\, and the Hecke operators on this cohomology\, in all degre es $i$. This builds on recent work of Bob MacPherson and the author on co mputing the cohomology and Hecke operators on locally symmetric spaces for $SL(n\,\\mathbb{R})$. The computations for $SL$ use the well-tempered co mplex\, a contractible regular cell complex W on which arithmetic subgroup s of $SL$ act with only finitely many orbits of cells. For $Sp(4\,\\mathb b{R})$\, we define a certain subcomplex V of the first barycentric subdivi sion of W. This V is a contractible regular cell complex on which $\\Gamm a$ acts with only finitely many stabilizers of cells\, and it allows us to compute the Hecke operators. As a subcomplex\, V contains the symplectic well-rounded retract of MacPherson and the author (1993). The recent wor k for $Sp(4\,\\mathbb{R})$ is joint with Dylan Galt.\n LOCATION:https://researchseminars.org/talk/CompArithGroups/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathilde Gerbelli-Gauthier (Centre de Recherches Mathématiques) DTSTART:20201208T170000Z DTEND:20201208T172000Z DTSTAMP:20260419T110655Z UID:CompArithGroups/10 DESCRIPTION:Title: Limit multiplicity of non-tempered representations and endoscopy< /a>\nby Mathilde Gerbelli-Gauthier (Centre de Recherches Mathématiques) a s part of Computations with Arithmetic Groups\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CompArithGroups/10/ END:VEVENT END:VCALENDAR