Departement Mathematik

Number theory seminar

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Frühjahrssemester 2018

Datum / Zeit Referent:in Titel Ort
23. Februar 2018
14:15-15:15 		Peter Humphries
University College London
Details

Number Theory Seminar

Titel Quantum unique ergodicity in almost every shrinking ball
Referent:in, Affiliation Peter Humphries, University College London
Datum, Zeit 23. Februar 2018, 14:15-15:15
Ort HG G 43
Abstract I will discuss the problem of small scale equidistribution of Hecke-Maass eigenforms, namely the problem of the rate at which hyperbolic balls can shrink as the Laplacian eigenvalue tends to infinity for which the Laplacian eigenfunctions still equidistribute on these balls. There is a natural barrier - the Planck scale - for which equidistribution fails, but conditionally equidistribution occurs in almost every shrinking ball at every larger scale. I will also discuss related small scale equidistribution problems for geometric invariants associated to quadratic fields.
Quantum unique ergodicity in almost every shrinking ballread_more
HG G 43
2. März 2018
14:15-15:15 		Dr. Ian Nicholas Petrow
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel The Weyl law for algebraic tori
Referent:in, Affiliation Dr. Ian Nicholas Petrow, ETH Zurich, Switzerland
Datum, Zeit 2. März 2018, 14:15-15:15
Ort HG G 43
The Weyl law for algebraic tori
HG G 43
23. März 2018
14:15-15:15 		Prof. Dr. Gebhard Böckle
Universität Heidelberg
Details

Number Theory Seminar

Titel Compatible systems of Galois representations of global function fields
Referent:in, Affiliation Prof. Dr. Gebhard Böckle, Universität Heidelberg
Datum, Zeit 23. März 2018, 14:15-15:15
Ort HG G 43
Abstract Let (r_l) be a semisimple compatible system of l-adic Galois representations r_l of the absolute Galois group of a global function field K of characteristic p. The main sources of such systems are (a) the ‘etale l-adic cohomologies of smooth projective varieties over K for varying l and (b) the compatible systems attached to cuspidal automorphic representations. For each place l denote by G_l the algebraic monodromy group at l and by G_l^geo its closed subgroup arising from the absolute Galois group of K F_p^alg. In the talk I shall report on joint work with Gajda and Petersen where we prove that for almost all l the image of r_l in G_l^geo is maximal in the sense of Larsen. For Q-rational compatible systems as in (a) this has been proved recently by Cadoret-Hui-Tamagawa. Our proof, which works for general E-rational systems, relies on (b). In the talk I shall explain the context and the result, indicate consequences and sketch how automorphic methods come to bear on the problem.
Compatible systems of Galois representations of global function fieldsread_more
HG G 43
30. März 2018
Details

Number Theory Seminar

Titel No seminar, Easter Friday
Referent:in, Affiliation
Datum, Zeit 30. März 2018,
Ort
No seminar, Easter Friday
6. April 2018
Details

Number Theory Seminar

Titel No seminar, Easter Vacations
Referent:in, Affiliation
Datum, Zeit 6. April 2018,
Ort
No seminar, Easter Vacations
13. April 2018
14:15-15:15 		Prof. Dr. Damaris Schindler
University of Utrecht
Details

Number Theory Seminar

Titel Diophantine inequalities for ternary diagonal forms
Referent:in, Affiliation Prof. Dr. Damaris Schindler, University of Utrecht
Datum, Zeit 13. April 2018, 14:15-15:15
Ort HG G 43
Abstract We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables are assumed to be of size P. We study this problem on average over a one-parameter family of forms and discuss a generalization of work of Bourgain on generic ternary diagonal quadratic forms to higher degree.
Diophantine inequalities for ternary diagonal formsread_more
HG G 43
20. April 2018
14:15-15:15 		Nicolas Müller
ETH Zürich
Details

Number Theory Seminar

Titel Hyperelliptic Curves with Many Automorphisms
Referent:in, Affiliation Nicolas Müller, ETH Zürich
Datum, Zeit 20. April 2018, 14:15-15:15
Ort HG G 43
Abstract A smooth projective connected complex algebraic curve is said to have "many automorphisms" if it cannot be deformed non-trivially together with its automorphism group. It is known that they correspond to isolated points in the moduli space of curves. Given his life-long interest in special points on moduli spaces, Frans Oort asked whether these points are special, i.e., whether the jacobian has complex multiplication. We answer this question in the special case of hyperelliptic curves.
Hyperelliptic Curves with Many Automorphismsread_more
HG G 43
27. April 2018
14:15-15:15 		Prof. Dr. Gergely Harcos
Rényi Institute
Details

Number Theory Seminar

Titel On the global sup-norm of GL(n) cusp forms
Referent:in, Affiliation Prof. Dr. Gergely Harcos, Rényi Institute
Datum, Zeit 27. April 2018, 14:15-15:15
Ort HG G 43
Abstract The sup-norm problem, a close relative of the subconvexity problem, has been studied widely for the group GL(2). There are fewer results for GL(n), and it was only recently that an explicit upper bound was derived for the global sup-norm of unramified Maass cusp forms there. I will discuss this result, which is joint work with Valentin Blomer and Peter Maga.
On the global sup-norm of GL(n) cusp formsread_more
HG G 43
4. Mai 2018
14:15-15:15 		Prof. Dr. Emmanuel Peyre
Université Grenoble-Alpes
Details

Number Theory Seminar

Titel Heights and beyond
Referent:in, Affiliation Prof. Dr. Emmanuel Peyre, Université Grenoble-Alpes
Datum, Zeit 4. Mai 2018, 14:15-15:15
Ort HG G 43
Abstract The program initiated by Manin and his collaborators on the asymptotic behaviour of points of bounded height lead to the notion of accumulating subsets, that is subsets which contain more rational points of bounded height than the complement, but which are not dense for adelic topology. The aim of this talk is to present a survey of these phenomena as well as various invariants related to slopes which might be used to characterize the corresponding rational points.
Heights and beyondread_more
HG G 43
* 9. Mai 2018
15:45-16:45 		Prof. Dr. Matthew Morrow
IMJ PRG
Details

Number Theory Seminar

Titel (Topological) cyclic homology in arithmetic geometry
Referent:in, Affiliation Prof. Dr. Matthew Morrow, IMJ PRG
Datum, Zeit 9. Mai 2018, 15:45-16:45
Ort HG G 43
Abstract Cyclic homology was introduced by Connes and Feigin—Tsygan in the 1980s as a extension of de Rham cohomology to singular varieties or even to non-commutative spaces in characteristic zero. I will overview the classical theory (in particular, familiarity with cyclic homology is not expected) and then explain a new analogous framework in finite and mixed characteristic, as well as some resulting applications in p-adic arithmetic geometry. Joint work with Bhargav Bhatt and Peter Scholze.
(Topological) cyclic homology in arithmetic geometryread_more
HG G 43
11. Mai 2018
14:15-15:15 		Dr. William Sawin
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel The circle method and slopes of the tangent bundle of hypersurfaces
Referent:in, Affiliation Dr. William Sawin, ETH Zurich, Switzerland
Datum, Zeit 11. Mai 2018, 14:15-15:15
Ort HG G 43
Abstract This lecture builds on the seminar of E. Peyre in the previous week, elaborating on a special case of the conjecture that he described, and discussing a possible approach to its proof.
The circle method and slopes of the tangent bundle of hypersurfacesread_more
HG G 43
* 16. Mai 2018
14:15-15:15 		Prof. Dr. Daniel Loughran
University of Manchester
Details

Number Theory Seminar

Titel Probabilistic arithmetic geometry
Referent:in, Affiliation Prof. Dr. Daniel Loughran, University of Manchester
Datum, Zeit 16. Mai 2018, 14:15-15:15
Ort HG G 43
Abstract A famous theorem due to Erdős and Kac states that the number of prime divisors of an integer N behaves like a normal distribution. In this talk we consider analogues of this result in the setting of arithmetic geometry, and obtain probability distributions for questions related to local solubility of algebraic varieties. This is joint work with Efthymios Sofos.
Probabilistic arithmetic geometryread_more
HG G 43
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Details

Number Theory Seminar

Titel Number Theory Days 2018
Referent:in, Affiliation
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Ort Universität Basel; Alte Universität, Rheinsprung 9, Basel
Number Theory Days 2018
Universität Basel; Alte Universität, Rheinsprung 9, Basel

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