Departement Mathematik

Number theory seminar

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Frühjahrssemester 2016

Datum / Zeit Referent:in Titel Ort
4. März 2016
14:15-15:15 		Dr. Margaret Bilu
Université Paris Sud Orsay
Details

Number Theory Seminar

Titel Motivic Euler products
Referent:in, Affiliation Dr. Margaret Bilu, Université Paris Sud Orsay
Datum, Zeit 4. März 2016, 14:15-15:15
Ort 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. März 2016
14:15-15:15 		Anna Cadoret
École Polytechnique, Palaiseau
Details

Number Theory Seminar

Titel Geometric monodromy - semi simplicity and maximality
Referent:in, Affiliation Anna Cadoret, École Polytechnique, Palaiseau
Datum, Zeit 11. März 2016, 14:15-15:15
Ort 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. März 2016
14:15-15:15 		Prof. Dr. Paul Nelson
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Average and worst case behavior of automorphic forms on quaternion algebra
Referent:in, Affiliation Prof. Dr. Paul Nelson, ETH Zurich, Switzerland
Datum, Zeit 18. März 2016, 14:15-15:15
Ort 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
Details

Number Theory Seminar

Titel Non-abelian Cohen-Lenstra heuristics
Referent:in, Affiliation Prof. Dr. Nigel Boston, University of Wisconsin at Madison and FIM
Datum, Zeit 8. April 2016, 14:00-15:00
Ort 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

Titel Finding Endomorphisms of a Drinfeld Module
Referent:in, Affiliation Nikolas Kuhn, ETH Zürich
Datum, Zeit 29. April 2016, 14:15-14:55
Ort 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

Titel Good Reduction of Postcritically Finite Quadratic Morphisms
Referent:in, Affiliation Jennifer-Jayne Jakob, ETH Zürich
Datum, Zeit 29. April 2016, 15:05-15:45
Ort HG G 43
Good Reduction of Postcritically Finite Quadratic Morphisms
HG G 43
6. Mai 2016
14:15-15:15 		Prof. Dr. Hélène Esnault
Freie Universität Berlin
Details

Number Theory Seminar

Titel Connections in characteristic zero and in positive characteristic
Referent:in, Affiliation Prof. Dr. Hélène Esnault, Freie Universität Berlin
Datum, Zeit 6. Mai 2016, 14:15-15:15
Ort 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. Mai 2016
14:15-15:15 		Ezra Waxman
Tel Aviv University
Details

Number Theory Seminar

Titel The Distribution of Slopes of Gaussian Primes for the Rational Function Field
Referent:in, Affiliation Ezra Waxman, Tel Aviv University
Datum, Zeit 13. Mai 2016, 14:15-15:15
Ort 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. Mai 2016
14:15-15:15 		Steve Kudla
University of Toronto
Details

Number Theory Seminar

Titel Borcherds forms near the boundary
Referent:in, Affiliation Steve Kudla, University of Toronto
Datum, Zeit 20. Mai 2016, 14:15-15:15
Ort 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. Mai 2016
14:15-15:15 		Djordje Milićević
Bryn Mawr College
Details

Number Theory Seminar

Titel p-adic analytic twists, modularity, and strong subconvexity
Referent:in, Affiliation Djordje Milićević, Bryn Mawr College
Datum, Zeit 27. Mai 2016, 14:15-15:15
Ort 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. Juli 2016
14:15-15:15 		Prof. Dr. Andre Reznikov
Bar-Ilan University
Details

Number Theory Seminar

Titel Hyperbolic lattice points counting and bounds on various Fourier coefficients of Maass forms
Referent:in, Affiliation Prof. Dr. Andre Reznikov, Bar-Ilan University
Datum, Zeit 14. Juli 2016, 14:15-15:15
Ort 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

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

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

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09

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