Tue, 29 Jun 2021
14:00
Virtual

Asymptotics for the wave equation on black hole spacetimes

Stefanos Aretakis
(Toronto)
Abstract

We will present the precise late-time asymptotics for scalar fields on both extremal and sub-extremal black holes including the full Reissner-Nordstrom family and the subextremal Kerr family. Asymptotics for higher angular modes will be presented for all cases. Applications in observational signatures will also be discussed. This work is joint with Y. Angelopoulos (Caltech) and D. Gajic (Cambridge)

Mon, 28 May 2018

14:15 - 15:15
L4

The generalized Kahler potential

Marco Gualtieri
(Toronto)
Abstract

I will explain our recent description of the fundamental degrees of freedom underlying a generalized Kahler structure. For a usual Kahler
structure, it is well-known that the geometry is determined by a complex structure, a Kahler class, and the choice of a positive(1,1)-form in this class, which depends locally on only a single real-valued function: the Kahler potential. Such a description for generalized Kahler geometry has been sought since it was discovered in1984. We show that a generalized Kahler structure of symplectic type is determined by a pair of holomorphic Poisson manifolds, a
holomorphic symplectic Morita equivalence between them, and the choice of a positive Lagrangian brane bisection, which depends locally on
only a single real-valued function, which we call the generalized Kahler potential. To solve the problem we make use of, and generalize,
two main tools: the first is the notion of symplectic Morita equivalence, developed by Weinstein and Xu to study Poisson manifolds;
the second is Donaldson's interpretation of a Kahler metric as a real Lagrangian submanifold in a deformation of the holomorphic cotangent bundle.

 

Thu, 03 Nov 2016
16:00
L6

Joint Logic/Number Theory Seminar: Arithmetic applications of $\omega$-integral curves in varieties

Natalia Garcia-Fritz
(Toronto)
Abstract

In 2000, Vojta solved the n-squares problem under the Bombieri-Lang conjecture, by explicitly finding all the curves of genus 0 or 1 on the surfaces related to this problem. The fundamental notion used by him is $\omega$-integrality of curves. 
In this talk, I will show a generalization of Vojta's method to find all curves of low genus in some surfaces, with arithmetic applications.
I will also explain how to use $\omega$-integrality to obtain a bound of the height of a non-constant morphism from a curve to $\mathbb{P}^2$ in terms of the number of intersections (without multiplicities) of its image with a divisor of a particular kind. This proves some new special cases of Vojta's conjecture for function fields.
 

Mon, 15 Feb 2016
14:15
L4

Generalized Kähler structures from a holomorphic Poisson viewpoint

Marco Gualtieri
(Toronto)
Abstract

After reviewing the main results relating holomorphic Poisson geometry to generalized Kahler structures, I will explain some recent progress in deforming generalized Kahler structures. I will also describe a new way to view generalized kahler geometry purely in terms of Poisson structures.

Mon, 10 Nov 2014
14:15
L5

Tropical moment maps for toric log symplectic manifolds

Marco Gualtieri
(Toronto)
Abstract

I will describe a generalization of toric symplectic geometry to a new class of Poisson manifolds which are
symplectic away from a collection of hypersurfaces forming a normal crossing configuration.  Using a "tropical
moment map",  I will describe the classification of such manifolds in terms of decorated log affine polytopes,
in analogy with the Delzant classification of toric symplectic manifolds. 

Thu, 26 Apr 2012

16:00 - 17:00

Weyl sums for quadratic roots

John Friedlander
(Toronto)
Abstract

We study exponential sums of Weyl type taken over roots of quadratic congruences. We are particularly interested in the situation where the range of summation is small compared to the discriminant of the polynomial. We are then able to give a number of arithmetic applications.

This is work which is joint with W. Duke and H. Iwaniec.

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