Gravitational Lensing Workshop


Department of Mathematics and Statistics

University of South Florida

4202 E. Fowler Avenue, Tampa, FL 33620



Location: NES 104 (link to the Tampa campus map)

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

How can Mathematics Reveal Dark Matter?

9:55 - 10:15

Break - coffee


10:15 - 11:05

Marcus Werner

Universal magnification invariants and Lefschetz fixed point theory

11:05 - 11:20



11:20 - 12:10

Alexandre Eremenko

On the number of solutions of a transcendental equation arising in the theory of gravitational lensing

12:10 - 12:15



12:15 - 12:35

Amir Aazami

Orbifolds, the A,D,E Classification and Gravitational Lensing

12:35 - 12:55

Alberto Teguia

Foundations of  Stochastic Microlensing



For the workshop poster, click here.


For registration, attendance and other questions, contact the organizers at and



Link to Talk 1:


Title: How Can Mathematics Reveal Dark Matter?




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.




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.




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 pre-images), the total signed magnification of the lensed images will always sum to zero.





Talk 5:


Title: Foundations of  Stochastic Microlensing.




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.