For my preprints and papers, click here.

Some talk slides

Mapping class group orbits in the PSL(2,C) character variety. Online talk at the IISER Bhopal Math symposium, March 2021.

Colouring maps on surfaces. Online talk for undergraduates (for a Pravega Webinar Series), September 2020.

Harmonic maps and wild Teichmüller spaces. TIFR Mumbai, March 2018.

Talk at the Grothendieck-Teichmüller workshop, Nankai University, Tianjin, July 2016.

Thurston-Teichmüller Theory and the dynamics of grafting. IISc Bangalore, July 2014.

XXII Rolf Nevanlinna Colloquium talk, Helsinki, August 2013.

This poster won a prize at the European Math Society/Danish Math Society Joint Mathematical Weekend in September 2013.

Resources for students

I've listed a few books and topics for interested students (advanced undergraduate/beginning postgraduate) below.

IISc students who wish to do a project with me should email indicating which of the topics he/she is interested in.

Hyperbolic Geometry

Books

"Fuchsian Groups" by S. Katok.

"The Geometry of Discrete Groups" by A. Beardon.

"Automorphisms of surfaces after Nielsen and Thurston" by Casson and Bleiler.

Videos

Mini-course on "Hyperbolic surfaces and their Teichmüller spaces". ICTS Bangalore, November 2017.

Possible project topics

Hyperbolic tilings or Triangle groups (these might involve computer programming), Crowned hyperbolic surfaces (something I was thinking about recently).

Topology of surfaces

Books

"A Primer on Mapping Class Groups" by Farb and Margalit.

"Office hours with a geometric group theorist", edited by Matt Clay and Dan Margalit.

Possible project topics

Branched coverings and Hurwitz's existence problem (should be familiar with the Riemann-Hurwitz formula!)

Complex Analysis (and its relation with geometry)

Books

"Teichmüller theory I and II" by Hubbard.

"Graphs on surfaces" by Lando and Zvonkine.

Possible project topics

Quadratic differentials, Trajectories of differentials (this would involve computer programming), Quasiconformal maps.