Departement Mathematik

Number theory seminar

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Frühjahrssemester 2015

Datum / Zeit Referent:in Titel Ort
27. Februar 2015
14:15-15:15 		Florian Ivorra
Université de Rennes
Details

Number Theory Seminar

Titel Perverse Nori motives
Referent:in, Affiliation Florian Ivorra, Université de Rennes
Datum, Zeit 27. Februar 2015, 14:15-15:15
Ort HG G 43
Abstract Let k be a field of characteristic zero with a fixed embedding of fields k -->C. Using a Tannakian approach, Madhav Nori has defined an Abelian category of mixed motives NMM(k) over k . This construction is universal and being a motive in NMM(k) may be seen as the best structure that one can put on the relative homology of a pair of algebraic k -varieties. In this lecture I will explain an extension of the theory of Nori to a relative context. It is indeed possible, for every quasi-projective k-variety X, to define an Abelian category N(X) which is modeled after perverse sheaves and coincides with the category defined by Nori when X = k. I will sketch also the construction of a realisation functor from the triangulated category of étale constructible motives over X introduced by Ayoub, Morel and Voevodsky to the bounded derived category of N(X) and discuss some ongoing works in this direction.
Perverse Nori motivesread_more
HG G 43
13. März 2015
14:15-15:15 		Martin Sombra
ICREA and University of Barcelona
Details

Number Theory Seminar

Titel Unlikely intersections and multiple roots of sparse polynomials
Referent:in, Affiliation Martin Sombra, ICREA and University of Barcelona
Datum, Zeit 13. März 2015, 14:15-15:15
Ort HG G 43
Abstract I will report on joint work with Francesco Amoroso (Caen) and Umberto Zannier (Pisa). I will present a structure theorem for the multiple non-cyclotomic irreducible factors appearing in the family of all univariate polynomials with a given set of coefficients and varying exponents. This result shows that the multiple non-cyclotomic irreducible factor of a sparse polynomial, are also sparse. To obtain this, we give a version of a theorem of Bombieri and Zannier on the intersection of a subvariety of codimension 2 of the multiplicative group with torsion curves, with an explicit dependence on the height of the subvariety.
Unlikely intersections and multiple roots of sparse polynomialsread_more
HG G 43
* 27. März 2015
14:15-15:15 		Tanguy Rivoal
Institut Fourier
Details

Number Theory Seminar

Titel Arithmetic theory of E and G-operators.
Referent:in, Affiliation Tanguy Rivoal, Institut Fourier
Datum, Zeit 27. März 2015, 14:15-15:15
Ort HG G 19.2
Arithmetic theory of E and G-operators.
HG G 19.2
3. April 2015
Details

Number Theory Seminar

Titel Easter Friday, no seminar
Referent:in, Affiliation
Datum, Zeit 3. April 2015,
Ort
Easter Friday, no seminar
10. April 2015
Details

Number Theory Seminar

Titel Vacations, no seminar
Referent:in, Affiliation
Datum, Zeit 10. April 2015,
Ort
Vacations, no seminar
17. April 2015
14:15-15:15 		Philippe Michel
EPF Lausanne
Details

Number Theory Seminar

Titel On moments of L-functions
Referent:in, Affiliation Philippe Michel, EPF Lausanne
Datum, Zeit 17. April 2015, 14:15-15:15
Ort HG G 43
Abstract We present (in the classical language) a new proof of Matt Young's theorem providing an asymptotic formula for the fourth moment of Dirichlet L-functions (averaged over Dirichlet characters of large prime levels) with a somewhat improved error term. We will also discuss extensions f this result to moments of characters twists of Hecke L-functions of modular forms. The proof combines the theory of automorphic forms (versions of the shifted convolution problem) with bounds for sums of algebraic exponentials sums (Kloosterman sums) when the summations variables are beyond the Polya-Vinogradov range. If time permits we will discuss and motivate still conjectural but potentially interesting variations of these results. This is joint work with V. Blomer, E. Fouvry, E. Kowalski and D. Milicevic.
On moments of L-functionsread_more
HG G 43
* 8. Mai 2015
13:00-14:00 		Yingkun Li
Universität Darmstadt
Details

Number Theory Seminar

Titel The span of restrictions of coherent Eisenstein series
Referent:in, Affiliation Yingkun Li, Universität Darmstadt
Datum, Zeit 8. Mai 2015, 13:00-14:00
Ort HG G 43
Abstract In the theory of modular forms, Eisenstein series plays an important role because of its explicit Fourier coefficients. It is well-known that the algebra of modular forms on $SL_2(\mathbb{Z})$ is generated by the classical Eisenstein series $E_4$ and $E_6$. For a fixed weight $k$, Kohnen and Zagier showed that it suffices to consider the span of the products of two Eisenstein series $E_\ell$ and $E_{k - \ell}$. In this talk, we will look at a related question, first raised by Tonghai Yang, about the span of the restrictions of coherent Eisenstein series. We will discuss the construction of these Eisenstein series, its relationship to special values of L-function, and other related open problems.
The span of restrictions of coherent Eisenstein seriesread_more
HG G 43
15. Mai 2015
Details

Number Theory Seminar

Titel Number Theory Days 2015 (Lausanne)
Referent:in, Affiliation
Datum, Zeit 15. Mai 2015,
Ort EPF Lausanne
Number Theory Days 2015 (Lausanne)
EPF Lausanne
22. Mai 2015
14:15-15:15 		José Ignacio Burgos Gil
Instituto de Ciencias Matemáticas
Details

Number Theory Seminar

Titel Equidistribution of small points on toric varieties
Referent:in, Affiliation José Ignacio Burgos Gil, Instituto de Ciencias Matemáticas
Datum, Zeit 22. Mai 2015, 14:15-15:15
Ort HG G 43
Abstract As the culmination of work of many mathematicians, Yuan has obtained a very general equidistribution result for small points in arithmetic varieties. Roughly speaking Yuan's theorem states that given a « very » small generic sequence of points, with respect to a positive hermitian line bundle, the associated sequence of measures converges weakly to the measure associated to the hermitian line bundle. Here very small means that the height of the points converges to the lower bound of the essential minimum given by Zhang inequalities. The existence of a very small generic sequence is a strong condition on the arithmetic variety because it implies that the essential minimum attains its lower bound. We will say that a sequence is small if the height of the points converges to the essential minimum. By definition every arithmetic variety contains small generic sequences. We show that for toric line bundles on toric varieties arithmetic Yuan's theorem can be splitted in two parts. A) Given a small generic sequence of points, with respect to a positive hermitian line bundle, the associated sequence of measures converges weakly to a measure. B) If the sequence is very small, the limit measure agrees with the measure associated to the hermitian line bundle.
Equidistribution of small points on toric varietiesread_more
HG G 43
29. Mai 2015
14:15-15:15 		Dimitar Jetchev
EPF Lausanne
Details

Number Theory Seminar

Titel The p-part of the Birch and Swinnerton-Dyer Conjecture for Elliptic Curves of Analytic Rank One
Referent:in, Affiliation Dimitar Jetchev, EPF Lausanne
Datum, Zeit 29. Mai 2015, 14:15-15:15
Ort HG G 43
Abstract I will explain the recent proof of the p-part of the Birch and Swinnerton-Dyer Conjectural formula for elliptic curves over Q of analytic rank one. The proof is based on choosing a suitable parametrization of the elliptic curve with a Shimura curve, using Kolyvagin's Euler system method to get the upper bounds and an anticyclotomic Iwasawa main conjecture as well as a control theorem to get the lower bounds. This is joint work with Chris Skinner and Xin Wan.
The p-part of the Birch and Swinnerton-Dyer Conjecture for Elliptic Curves of Analytic Rank Oneread_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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