Departement Mathematik

Number theory seminar

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Herbstsemester 2011

Datum / Zeit Referent:in Titel Ort
23. September 2011
14:15-15:15 		Prof. Dr. Jens Funke
University of Durham
Details

Number Theory Seminar

Titel Spectacle cycles and half-integral weight modular forms
Referent:in, Affiliation Prof. Dr. Jens Funke, University of Durham
Datum, Zeit 23. September 2011, 14:15-15:15
Ort HG G 43
Abstract The classical Shintani lift is the adjoint of the Shimura correspondence. It realizes periods of even weight cusp forms as Fourier coefficients of a half-integral modular form. In this talk we revisit the Shintani lift from a (co)homological perspective. In particular, we extend the lift to Eisenstein series and give a geometric interpretation of this extension. This is joint work with John Millson.
Spectacle cycles and half-integral weight modular formsread_more
HG G 43
30. September 2011
14:15-15:15 		Dr. Paul-Olivier Dehaye
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel The lower order terms conjecture for moments of the Riemann zeta function
Referent:in, Affiliation Dr. Paul-Olivier Dehaye, ETH Zurich, Switzerland
Datum, Zeit 30. September 2011, 14:15-15:15
Ort HG G 43
Abstract In 2006, Conrey Farmer Keating Rubinstein and Snaith published a conjecture concerning moments of the Riemann zeta function on the critical line. Theirs supersedes the so-called random matrix conjecture (due to Keating and Snaith), which only gives the first order term. The conjecture follows from a "recipe" involving a small set of allowed manipulations of Dirichlet polynomials, but computations tend to be very complicated (even to show agreement with less precise conjectures). In my talk, I will present new tools to implement this recipe, based on symmetric function theory. This will allow me to present a more explicit version of the final conjecture, with potential applications.
The lower order terms conjecture for moments of the Riemann zeta functionread_more
HG G 43
7. Oktober 2011
14:15-15:15 		Prof. Dr. Alexander Gamburd
CUNY Graduate Center
Details

Number Theory Seminar

Titel Generalization of Selberg's 3/16 Theorem and Affine Sieve
Referent:in, Affiliation Prof. Dr. Alexander Gamburd, CUNY Graduate Center
Datum, Zeit 7. Oktober 2011, 14:15-15:15
Ort HG G 43
Abstract A celebrated theorem of Selberg states that for congruence subgroups of the modular group there are no exceptional eigenvalues below 3/16. We will present joint work with Bourgain and Sarnak, in which we establish a generalization of Selberg's theorem for "thin" (infinite index) "congruence" subgroups of SL(2, Z). Time permitting, applications to affine sieve will also be discussed.
Generalization of Selberg's 3/16 Theorem and Affine Sieveread_more
HG G 43
14. Oktober 2011
14:15-15:15 		Dr. Francesco Veneziano
University of Basel
Details

Number Theory Seminar

Titel Bounds on the number of points "with small denominator" on algebraic curves
Referent:in, Affiliation Dr. Francesco Veneziano, University of Basel
Datum, Zeit 14. Oktober 2011, 14:15-15:15
Ort HG G 43
Bounds on the number of points "with small denominator" on algebraic curves
HG G 43
21. Oktober 2011
14:15-15:15 		Dr. Lenny Taelman
University of Leiden
Details

Number Theory Seminar

Titel Herbrand-Ribet in positive characteristic
Referent:in, Affiliation Dr. Lenny Taelman, University of Leiden
Datum, Zeit 21. Oktober 2011, 14:15-15:15
Ort HG G 43
Herbrand-Ribet in positive characteristic
HG G 43
28. Oktober 2011
14:15-15:15
Details

Number Theory Seminar

Titel No seminar. Heinz Hopf Lectures 2011 (25-oct and 27-oct-2011 at 17:15 in HG G 60; symposium on 26-oct-2011)
Referent:in, Affiliation
Datum, Zeit 28. Oktober 2011, 14:15-15:15
Ort HG G 43
No seminar. Heinz Hopf Lectures 2011 (25-oct and 27-oct-2011 at 17:15 in HG G 60; symposium on 26-oct-2011)
HG G 43
4. November 2011
14:15-15:15 		Dr. Djordje Milicevic
MPI Bonn
Details

Number Theory Seminar

Titel Large values of eigenfunctions and arithmetic hyperbolic 3-manifolds of Maclachlan-Reid type
Referent:in, Affiliation Dr. Djordje Milicevic, MPI Bonn
Datum, Zeit 4. November 2011, 14:15-15:15
Ort HG G 43
Abstract One aspect of quantum chaos are extreme values of high-energy eigenfunctions, which, on Riemannian manifolds of negative curvature, are not well understood and can depend heavily on the global geometry of the manifold. The principal result to be presented shows that there is a distinguished class of arithmetic hyperbolic 3-manifolds on which a sequence of L^2-normalized high-energy Hecke-Maass eigenforms achieve values as large as a power of the Laplacian eigenvalue. Power growth, first observed in this context by Rudnick and Sarnak, is (by far) not expected generically and stands in stark contrast with the statistical models suggested by the so-called random wave conjecture on eigenfunctions of classically ergodic systems. The arithmetic hyperbolic 3-manifolds on which the exceptional behavior is exhibited can be characterized in terms of their invariant quaternion algebras and are, up to commensurability, precisely those containing immersed totally geodesic surfaces, as described by Maclachlan and Reid. We will explain how number theory allows us to see some of the global geometry of the manifold and discuss the question of identifying the Hecke-Maass eigenforms achieving power growth through representation theory.
Large values of eigenfunctions and arithmetic hyperbolic 3-manifolds of Maclachlan-Reid typeread_more
HG G 43
11. November 2011
14:15-15:15 		Dr. Noah Giansiracusa
University of Zurich
Details

Number Theory Seminar

Titel GIT compactifications of M_(0,n) and flips
Referent:in, Affiliation Dr. Noah Giansiracusa, University of Zurich
Datum, Zeit 11. November 2011, 14:15-15:15
Ort HG G 43
Abstract Since the early days of geometric invariant theory (GIT) it has been recognized that natural compactifications of the moduli space M_(0,n) of n distinct points on the line are obtained as GIT quotients P1^n//Aut(P1). These were famously used by Deligne and Mostow to investigate hypergeometric functions and prove arithmetic results. In this talk, I will discuss a generalization of these quotients where one considers n-pointed rational normal curves and their degenerations as parameterized by a Chow variety. One new feature of these GIT quotients is the existence of flips occurring through variation of GIT as in the work of Thaddeus and Dolgachev-Hu.
GIT compactifications of M_(0,n) and flipsread_more
HG G 43
18. November 2011
14:15-15:15 		Dr. Hung Manh Bui
University of Zurich
Details

Number Theory Seminar

Titel Zeros of the Riemann zeta-function
Referent:in, Affiliation Dr. Hung Manh Bui, University of Zurich
Datum, Zeit 18. November 2011, 14:15-15:15
Ort HG G 43
Abstract We discuss the method of Levinson and joint work with Conrey and Young, in which we show that more than 41% of the zeros of the Riemann zeta-function are on the critical line.
Zeros of the Riemann zeta-functionread_more
HG G 43
25. November 2011
14:15-15:15 		Prof. Dr. David Masser
University of Basel
Details

Number Theory Seminar

Titel Pell's Equation over Polynomial Rings
Referent:in, Affiliation Prof. Dr. David Masser, University of Basel
Datum, Zeit 25. November 2011, 14:15-15:15
Ort HG G 43
Abstract It is classical that for any positive integer d not a perfect square there are positive integers x and y (y not 0) with x^2-dy^2=1. The analogous assertion for D,X,Y not 0 in C[t] with X^2-DY^2=1 clearly requires that the degree of D be even, and it is easy to see that it holds for all quadratic D. However for quartic D the problem changes character; this can be seen from that fact that the set of complex l such that X,Y exist for D=t^4+t+l is infinite but "scarce"; for example it contains at most finitely many rationals. For sextic D things change again, and we will sketch a proof that there are at most finitely many complex l such that X,Y exist for D=t^6+t+l. This follows from recent work with Umberto Zannier about unlikely intersections for semiabelian schemes.
Pell's Equation over Polynomial Ringsread_more
HG G 43
2. Dezember 2011
14:15-15:15 		Prof. Dr. Philipp Habegger
University of Frankfurt
Details

Number Theory Seminar

Titel Small Heights and Non-Abelian Extensions
Referent:in, Affiliation Prof. Dr. Philipp Habegger, University of Frankfurt
Datum, Zeit 2. Dezember 2011, 14:15-15:15
Ort HG G 43
Abstract The absolute logarithmic Weil height can attain arbitrarily small, positive values on the field of algebraic numbers. In a finite field extension of the rational numbers there is a gap principle: the height is either zero or at least some positive constant depending only on the field. Regarding infinite algebraic extensions of Q, Amoroso and Dvornicich proved that the field F, the largest extension of Q with abelian Galois group, satisfies the same height-gap principle. Let E be an elliptic curve defined over the rationals without potential complex multiplication. The group of all torsion points of K generates an infinite and non-abelian Galois extension of Q. In the talk I will first introduce height functions, discuss some historical aspects, and then sketch a proof that K cannot contain points of small positive height. The Néron-Tate height on E(K) satisfies a similar gap principle. Both proofs use the theory of Lubin-Tate modules as well as archimedean and non-archimedean equidistribution results by Bilu, Chambert-Loir and others.
Small Heights and Non-Abelian Extensionsread_more
HG G 43
16. Dezember 2011
14:15-15:15 		Prof. Dr. James Cogdell
Ohio State University
Details

Number Theory Seminar

Titel The local Langlands correspondence for GL(n) and the exterior
Referent:in, Affiliation Prof. Dr. James Cogdell, Ohio State University
Datum, Zeit 16. Dezember 2011, 14:15-15:15
Ort HG G 43
Abstract The local Langlands correspondence is a correspondence between n-dimensional representations of the Weil-Deligne group of a local field F and the irreducible admissible representations of GL(n,F); it is a step towards a non-abelian local class field theory. As established by Harris-Taylor and Henniart, this correspondence preserves L- and epsilon-factors of pairs. But as envisioned by Langlands, this should preserve all L-functions and their epsilon factors. Henniart has shown that the correspondence preserves the exterior and symmetric square L-functions. We (with Shahidi and Tsai) can now show it preserves the epsilon factors as well. The proof is an application of local/global techniques and the stability of these local factors under highly ramified twists.
The local Langlands correspondence for GL(n) and the exteriorread_more
HG G 43

Organisatoren:innen: Clemens Fuchs, Özlem Imamoglu, Emmanuel Kowalski, Richard Pink, 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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