Forthcoming Seminars › Seminar Series

Number Theory Seminar

Thu, 13/10/2011
16:00 		Konstantin Ardakov (University of Nottingham) Number Theory Seminar Add to calendar L3
Iwasawa algebras and D-modules
Thu, 20/10/2011
16:00 		Igor Wigman (Cardiff University) Number Theory Seminar Add to calendar L3
Nodal length fluctuations for arithmetic random waves
Using the spectral multiplicities of the standard torus, weendow the Laplace eigenspaces with Gaussian probability measures.This induces a notion of random Gaussian eigenfunctionson the torus ("arithmetic random waves”.)  We study thedistribution of the nodal length of random Laplace eigenfunctions for higheigenvalues,and our primary result is that the asymptotics for the variance isnon-universal, and is intimately related to the arithmetic oflattice points lying on a circle with radius corresponding to the energy. This work is joint with Manjunath Krishnapur and Par Kurlberg
Thu, 27/10/2011
16:00 		Paul-James White (Oxford) Number Theory Seminar Add to calendar L3
Automorphic representations on the Unitary group
Thu, 03/11/2011
16:00 		Jacob Tsimerman (Harvard) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
Lower bounds for CM points and torsion in class groups
Let $ x $ be a CM point in the moduli space $ \mathcal{A}_g(\mathbb{C}) $ of principally polarized complex abelian varieties of genus $ g $, corresponding to an Abelian variety $ A $ with complex multiplication by a ring $ R $. Edixhoven conjectured that the size of the Galois orbit of x should grow at least like a power of the discriminant $ {\rm Disc}(R) $ of $ R $. For $ g=1 $, this reduces to the classical Brauer-Siegel theorem. A positive answer to this conjecture would be very useful in proving the André-Oort conjecture unconditionally. We will present a proof of the conjectured lower bounds in some special cases, including $ g\le 6 $. Along the way we derive transfer principles for torsion in class groups of different fields which may be interesting in their own right.
Thu, 10/11/2011
16:00 		Andrei Yafaev (UCL) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
A hyperbolic Ax-Lindemann theorem in the cocompact case
This is a joint work with Emmanuel Ullmo. This work is motivated by J.Pila's strategy to prove the Andre-Oort conjecture. One ingredient in the strategy is the following conjecture: Let S be a Shimura variety uniformised by a symmetric space X. Let V be an algebraic subvariety of S. Maximal algebraic subvarieties of the preimage of V in X are precisely the components of the preimages of weakly special subvarieties contained in V. We will explain the proof of this conjecture in the case where S is compact.
Thu, 01/12/2011
16:00 		Umberto Zannier (Pisa) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
Sharpening `Manin-Mumford' for certain algebraic groups of dimension 2
(Joint work with P. Corvaja and D. Masser.) The topic of the talk arises from the Manin-Mumford conjecture and its extensions, where we shall focus on the case of (complex connected) commutative algebraic groups $ G $ of dimension $ 2 $. The `Manin-Mumford' context in these cases predicts finiteness for the set of torsion points in an algebraic curve inside $ G $, unless the curve is of `special' type, i.e. a translate of an algebraic subgroup of $ G $. In the talk we shall consider not merely the set of torsion points, but its topological closure in $ G $ (which turns out to be also the maximal compact subgroup). In the case of abelian varieties this closure is the whole space, but this is not so for other $ G $; actually, we shall prove that in certain cases (where a natural dimensional condition is fulfilled) the intersection of this larger set with a non-special curve must still be a finite set. We shall conclude by stating in brief some extensions of this problem to higher dimensions.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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