Gravitational Lensing Workshop
Department of
Mathematics and Statistics
Location:
NES 104 (link to the
Time:
Friday, April 2, 2010, from 9:00 a.m. to 1:00 p.m.
8:30
 9:00 
Coffee and pastries 

9:00
 9:05 
Dima
Khavinson 
Opening
remarks 
9:05
 9:55 
Charles
Keeton 

9:55
 10:15 
Break  coffee 

10:15
 11:05 
Marcus
Werner 
Universal magnification invariants and Lefschetz fixed point
theory 
11:05
 11:20 
Break 

11:20
 12:10 
Alexandre
Eremenko 

12:10
 12:15 
Break 

12:15
 12:35 
Amir
Aazami 
Orbifolds, the A,D,E Classification and Gravitational Lensing 
12:35
 12:55 
Alberto
Teguia 
For
the workshop poster, click here.
For
registration, attendance and other questions, contact the organizers at dkhavins@cas.usf.edu and razvan@cas.usf.edu.
Link to Talk 1:
Title: How Can Mathematics
Reveal Dark Matter?
Abstract:
Astronomers have discovered
hundreds of instances in which gravity from a distant galaxy bends the light
from an
even more distant galaxy or
quasar. Such gravitational lens systems offer a unique opportunity to
study the elusive dark matter that dominates the material of the universe  but
only if we understand both the physics and mathematics of light bending.
I will discuss how mathematics and astrophysics unite to make gravitational lensing
a powerful tool for cosmology, and how the mathematical aspects of
gravitational lensing manifest themselves on a cosmic scale.
Link to Talk 2:
Title: Universal magnification invariants and Lefschetz fixed point theory.
Abstract:
Recent work by Aazami and
Petters has shown that the universal magnification invariants for fold and cusp
singularities can also be extended to higher singularities, which has important
implications in gravitational lensing. After a brief review of singularities
and some aspects of fixed theory, I will discuss how the holomorphic Lefschetz
fixed point formula offers a different perspective of universal magnification
invariants up to codimension three.
Link
to Talk 3:
Title: On the number of solutions
of a transcendental equation arising in the theory of gravitational lensing.
The equation in the title
describes the number of bright images of a point source under lensing by an
elliptic object with isothermal density. We prove that this equation has at
most 6 solutions. Any number of solutions from
1 to 6 can actually occur. Based on a joint work with Walter
Bergweiler.
Link
to Talk 4:
Title: Orbifolds, the A, D, E
Classification and Gravitational Lensing.
Abstract:
We prove that for families of
general mappings between planes exhibiting any caustic singularity of the A (n
larger than 1), D (n larger than 3), E (n = 6, 7, 8) families, and for a point
in the target space lying anywhere in the region giving rise to the maximum
number of lensed images (real preimages), the total signed magnification of
the lensed images will always sum to zero.
Talk
5:
Title: Foundations of
Stochastic Microlensing.
Abstract:
The talk
present an analytical treatment of stochastic microlensing.
Specifically, we study the exact and asymptotic
stochastic behavior of fundamental quantities
in stochastic microlensing. Also, we give an asymptotic formula on the expected
number of lensed images, which is a first
step toward addressing the stochastic version of the image counting
problem.