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Spring Semester 2016

Date / Time Speaker Title Location
4 March 2016
14:15-15:15 		Dr. Margaret Bilu
Université Paris Sud Orsay
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Number Theory Seminar

Title Motivic Euler products
Speaker, Affiliation Dr. Margaret Bilu, Université Paris Sud Orsay
Date, Time 4 March 2016, 14:15-15:15
Location HG G 43
Abstract The Grothendieck group of varieties over a field k is the quotient of the free abelian group on the set of isomorphism classes of varieties by the so-called cut-and-paste relations. It also has a ring structure coming from the product of varieties over the field k. In this talk I am going to show how certain power series with coefficients in this ring may be endowed with an Euler product decomposition. This will in particular apply to Kapranov's zeta function of a variety, which is a motivic version of the Hasse-Weil zeta function. I will finish by discussing a possible application of these Euler products to the geometric analogue of Manin's conjecture for equivariant compactifications of vector groups, through the study of motivic height zeta functions.
Motivic Euler productsread_more
HG G 43
11 March 2016
14:15-15:15 		Anna Cadoret
École Polytechnique, Palaiseau
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Number Theory Seminar

Title Geometric monodromy - semi simplicity and maximality
Speaker, Affiliation Anna Cadoret, École Polytechnique, Palaiseau
Date, Time 11 March 2016, 14:15-15:15
Location HG G 43
Abstract Let X be a connected scheme, smooth and separated over an algebraic ally closed field k of characteristic p, let f:Y-> X be a smooth proper morphism and x a geometric point on X. We show that the tensor invariants of bounded length d of the etale fundamental group \pi_1(X) acting on the \'etale cohomology groups H^*(Y_x,\F_l) are the reduction modulo-l of the tensor invariants of \pi_1(X,x) acting on H^*(Y_x,\Z_l) for l large enough depending on f:Y-> X, d. We use this result to discuss semisimplicity and maximality issues about the image of \pi_1(X,x) on H^*(Y_x,\Z_l). This is a joint work with Chun-Yin Hui and Akio Tamagawa.
Geometric monodromy - semi simplicity and maximality read_more
HG G 43
18 March 2016
14:15-15:15 		Prof. Dr. Paul Nelson
ETH Zurich, Switzerland
Details

Number Theory Seminar

Title Average and worst case behavior of automorphic forms on quaternion algebra
Speaker, Affiliation Prof. Dr. Paul Nelson, ETH Zurich, Switzerland
Date, Time 18 March 2016, 14:15-15:15
Location HG G 43
Average and worst case behavior of automorphic forms on quaternion algebra
HG G 43
* 8 April 2016
14:00-15:00 		Prof. Dr. Nigel Boston
University of Wisconsin at Madison and FIM
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Number Theory Seminar

Title Non-abelian Cohen-Lenstra heuristics
Speaker, Affiliation Prof. Dr. Nigel Boston, University of Wisconsin at Madison and FIM
Date, Time 8 April 2016, 14:00-15:00
Location HG G 43
Non-abelian Cohen-Lenstra heuristics
HG G 43
29 April 2016
14:15-14:55 		Nikolas Kuhn
ETH Zürich
Details

Number Theory Seminar

Title Finding Endomorphisms of a Drinfeld Module
Speaker, Affiliation Nikolas Kuhn, ETH Zürich
Date, Time 29 April 2016, 14:15-14:55
Location HG G 43
Finding Endomorphisms of a Drinfeld Module
HG G 43
29 April 2016
15:05-15:45 		Jennifer-Jayne Jakob
ETH Zürich
Details

Number Theory Seminar

Title Good Reduction of Postcritically Finite Quadratic Morphisms
Speaker, Affiliation Jennifer-Jayne Jakob, ETH Zürich
Date, Time 29 April 2016, 15:05-15:45
Location HG G 43
Good Reduction of Postcritically Finite Quadratic Morphisms
HG G 43
6 May 2016
14:15-15:15 		Prof. Dr. Hélène Esnault
Freie Universität Berlin
Details

Number Theory Seminar

Title Connections in characteristic zero and in positive characteristic
Speaker, Affiliation Prof. Dr. Hélène Esnault, Freie Universität Berlin
Date, Time 6 May 2016, 14:15-15:15
Location HG G 43
Abstract The p-curvature conjecture predicts that a connection in characteristic zero is isotrivial (almost) all its p-curvatures vanish. We make a (much) stronger assumption in order to be able to derive some properties of the connection. Joint work with Mark Kisin.
Connections in characteristic zero and in positive characteristicread_more
HG G 43
13 May 2016
14:15-15:15 		Ezra Waxman
Tel Aviv University
Details

Number Theory Seminar

Title The Distribution of Slopes of Gaussian Primes for the Rational Function Field
Speaker, Affiliation Ezra Waxman, Tel Aviv University
Date, Time 13 May 2016, 14:15-15:15
Location HG G 43
Abstract Hecke proved that the Gaussian primes are equidistributed across sectors of the complex plane, by making use of (infinite) Hecke characters and their associated L-functions. In this talk I will present a function field analogue to this result, by making use of "super even" characters and their associated L-functions. By applying a recent result of N. Katz concerning the equidistribution of super even characters, I will also provide a result for the variance of function field Gaussian primes across sectors; a computation whose analogue in number fields is unknown beyond a trivial regime.
The Distribution of Slopes of Gaussian Primes for the Rational Function Fieldread_more
HG G 43
20 May 2016
14:15-15:15 		Steve Kudla
University of Toronto
Details

Number Theory Seminar

Title Borcherds forms near the boundary
Speaker, Affiliation Steve Kudla, University of Toronto
Date, Time 20 May 2016, 14:15-15:15
Location HG G 43
Abstract Borcherds’ regularized theta lift gives rise to a remarkable family of meromorphic automorphic forms for orthogonal groups of rational quadratic spaces of signature (m,2). In particular, these forms have a explicitly given divisor and product formulas, convergent in the neighborhood of each point boundary component. In this talk, I will explain another collection of product formulas for a Borcherds form. These exist under the assumption that the rational quadratic space admits isotropic planes, and each is convergent in a neighborhood of a curve boundary component. The Fourier-Jacobi expansion of the Borcherds form and its vanishing order at the corresponding divisor in the toridal compactification can be read off from the second product formula. I will then discuss how these results are used in joint work with Bruinier, Howard, Rapoport and Yang on modularity of generating series for special divisors on unitary Shimura varieties.
Borcherds forms near the boundaryread_more
HG G 43
27 May 2016
14:15-15:15 		Djordje Milićević
Bryn Mawr College
Details

Number Theory Seminar

Title p-adic analytic twists, modularity, and strong subconvexity
Speaker, Affiliation Djordje Milićević, Bryn Mawr College
Date, Time 27 May 2016, 14:15-15:15
Location HG G 43
Abstract One of the principal analytic questions about automorphic L-functions are the so-called subconvex estimates on the size of their critical values, deeply arithmetic both in proofs and in the often spectacular consequences. In this talk, we will present our recent subconvexity bound for the central value of the L-function associated to a fixed cuspidal newform f twisted by a Dirichlet character chi of a high prime power conductor. From an adelic viewpoint, the analogy between this so-called "depth aspect" and the familiar t-aspect is particularly natural, as one is focusing on ramification at one (finite or infinite) place at a time. We prove our results by exhibiting strong cancellation between the Hecke eigenvalues of f and the values of chi, which act as twists by exponentials with a p-adically analytic phase. Among the tools, we develop p-adic counterparts to Farey dissection and van der Corput estimates for exponential sums. This is joint work with Valentin Blomer.
p-adic analytic twists, modularity, and strong subconvexityread_more
HG G 43
* 14 July 2016
14:15-15:15 		Prof. Dr. Andre Reznikov
Bar-Ilan University
Details

Number Theory Seminar

Title Hyperbolic lattice points counting and bounds on various Fourier coefficients of Maass forms
Speaker, Affiliation Prof. Dr. Andre Reznikov, Bar-Ilan University
Date, Time 14 July 2016, 14:15-15:15
Location HG G 43
Abstract We discuss how effective lattice points counting could be used in order to bound non-trivially unipotent/hyperbolic/spherical Fourier coefficients of a fixed Maass form. While the resulting exponents in our method are far from the best known, the method is soft and appeals only to L^2-theory.
Hyperbolic lattice points counting and bounds on various Fourier coefficients of Maass formsread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: Özlem Imamoglu, Peter Simon Jossen, Emmanuel Kowalski, Paul Nelson, Richard Pink, Evelina Viada, Gisbert Wüstholz

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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