I am a reader in the School of Mathematics at TIFR, Mumbai. Previously I held postdoctoral positions at Temple University, University of Bristol and Technion-IIT. I received PhD from the University of Utah and completed undergraduate studies from IIT Bombay in Engineering Physics. My research is in geometric group theory. I am interested in outer automorphisms of free groups, mapping class groups and CAT(0) groups and cube complexes.
12. Conformal dimension bounds for certain Coxeter group Bowditch boundaries joint with Elizabeth Field, Robert Alonzo Lyman, Emily Stark (arXiv) 2025
11. Combinatorial isoperimetric inequality for the free factor complex. (pdf) (arXiv) To appear in Proceedings of the American Mathematical Society 2025
10. Limit sets of unfolding paths in Outer space. With Mladen Bestvina and Jing Tao. [(article), (arXiv)] Journal of the Institute of Mathematics Jussieu 2024
9. Orientable maps and polynomial invariants of free-by-cyclic groups. With Spencer Dowdall and Samuel Taylor. [(article),(arXiv)] Advances in Mathematics 2023
8. Appendix to Heirarchically hyperbolic groups and uniform exponential growth by Carolyn Abbott, Thomas Ng, Davide Spriano. With Harry Petyt. [(article)] Math. Z. 2023
7. Planar lattice subsets with minimal vertex boundary. With Ivan Levcovitz, Alex Margolis and Emily Stark. [(article),(arXiv)] Electronic Journal of Combinatorics 2021
6. Groups acting on CAT(0) cube complexes with uniform exponential growth. With Kasia Jankiewicz and Thomas Ng. [(article),(arXiv)]. Algebraic & Geometric Topology 2023
5. Cannon-Thurston maps for CAT(0) groups with isolated flats. With Benjamin Beeker, Mathew Cordes, Giles Gardam and Emily Stark. [(article),(arXiv)] Mathematische Annalen 2021
4. Homotopy type of the complex of free factors of a free group. With Benjamin Bruck. [(article), (arXiv)] Proceedings of London Mathematical Society 2020
3. Loxodromic for the cyclic splitting complex and their centralizers. With Derrick Wigglesworth. [(article), (arXiv)] Pacific Journal of Math 2019
2. Loxodromic Elements in the relative free factor complex. [(article), (arXiv)] Geometriae Dedicata 2018
1. Relative Currents [(article), (arXiv)] Conformal Geometry and Dynamics 2018
0. PhD thesis - Relative currents and loxodromic elements in the relative free factor complex.
TIFR
Topology II - Topics, February-March 2025, Homework Assignment
Topology I - Algebraic Topology, Monsoon 2023, Course Webpage
Temple University
MATH 9064 Topics course in Geometry/Topology, Spring 2022, Course Webpage
MATH 1041 Calculus I, Fall 2021
MATH 8062 Algebraic Topology, Spring 2021
MATH 1041.016 Calculus I, Spring 2021
University of Utah
I taught the following courses at the University of Utah.
MATH 2270, Linear Algebra, Summer 2016
MATH 2210, Calculus III, Fall 2015, Fall 2014, Spring 2014
MATH 1210, Calculus I, Fall 2013
MATH 1100, Business Calculus, Spring 2013
MATH 1060, Trigonometry, Fall 2012
MATH 1030, Introduction to Quantitative Analysis, Spring 2012
MATH 1090, Business Algebra, Fall 2011, Summer 2013
My art blog Rock, Paper, Scissors.
Some posters I drew for math conferences :
Ventotene 2017, Ventotene 2019, Ventotene 2021, Nahsholim 2018, Technion Grad School 2018, Into the Forest 2019, BestFest 2019
As an undergraduate, I worked with Professor Laurent Bartholdi, at Georg-August University of Gottingen for a summer. Under his guidance I developed some animations explaining what is a torus using POV-ray. Torus movies
In collaboration with Klaus-Peter Brenner and Laurent Bartholdi, I developed computed animated visualization of rotational symmetric structure of the Shona music of Zimbabwe. Webpage
Thierry Coulbois's train track software on Sage. Github
Videos