### Overview

Research area: dynamical systems, complex dynamics, Teichmüller theory

My research is in dynamics and geometry, especially the dynamics of rational maps on the Riemann sphere, the corresponding moduli space, and its interplays with Kleinian groups, hyperbolic geometry, Teichmüller theory and Berkovich dynamics.

### Publications

(with R. Lodge and S. Mukherjee) On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps, Geom. Funct. Anal., 32:1428–1485, 2022.

(with R. Lodge and S. Mukherjee) Circle packings, kissing reflection groups and critically fixed anti-rational maps, Forum Math. Sigma, 10: e3, 2022.

On geometrically finite degenerations I: boundaries of main hyperbolic components, J. Eur. Math. Soc. (JEMS), to appear, 2021.

Trees, length spectra for rational maps via barycentric extensions and Berkovich spaces, Duke Math. J., 171(14): 2943–3001, 2022.

Limits of rational maps, R-trees and barycentric extension, Adv. Math., 394:108075, 2021.

On the inhomogeneity of Mandelbrot set, Int. Math. Res. Not. IMRN, 2021(8):6051–6076, 2021.

## MATH Courses - Fall 2023

- MATH 4200 : Differential Equations and Dynamical Systems
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 5200 : Differential Equations and Dynamical Systems