In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.
|Job title:||Senior Lecturer in Pure Mathematics|
|Division:||Department of Mathematics|
|Organisation:||Imperial College London|
|Tags:||Fellowship: Early Career Fellowship, Imperial College London|
|Related theme:||Mathematical sciences|
I obtained a PhD in mathematics from Stony Brook University in 2009, following BSc and MSc degrees from Sharif University in Iran. I held research positions at University of Warwick (Leverhulme Trust fellowship), Universite Paul Sabatier in Toulouse, and Imperial College London (Chapman fellow).
The interface of analysis, geometry and combinatorics is manifested in rich mathematical structures as in Kleinian groups and hyperbolic manifolds; stochastic Loewner evolutions and conformal invariants; or as in low-dimensional analytic dynamics, to name a few. Ideas have been translated from one area to the other, resulting in major progresses in a seemingly different area.
Low-dimensional analytic dynamics has gone through an extremely creative phase of developments over the last three decades. This has led to deep connections to many areas of mathematics, including, complex analysis, complex geometry, Teichmuller theory, non-linear partial differential equations, geometric group theory, and number theory. Despite all this activity, a number of questions have proved to be extremely difficult.
The main theme of the proposed research is to develop a theory based on a (near-parabolic) renormalization operator to investigate two types of problems in low dimensional analytic dynamics. One is the local (and global) dynamics of a class of holomorphic germs tangent to an irrational rotation that have remained mysterious to date. The second type of questions concerns families of analytic transformations. These are often concerned with "the geometric, analytic and measurable features of the set of transformations with a certain dynamical property in a given family.
Often, such features at fine scales are independent of the particular family of maps (universality). The non-linear nature of the operator acting on an infinite dimensional function-space (dynamical systems) makes the method challenging and interesting to study.
Career benefits of Fellowship
The EPSRC fellowship provides the resources to fully devote myself to a long-term and ambitious research program, a task that would not happen otherwise.