B.Sc. : Ramakrishna Mission Vidyamandira, Belur Math.

M.Sc. : Ramakrishna Mission Vidyamandira, Belur Math.

Ph.D. : Rutgers University  (Newark).  Supervisor - Dr. Lee Mosher. 

After I finished my bachelor's and master's degrees in Mathematics from Ramakrishna Mission Vidyamandira in 2008, I joined the graduate program in Rutgers University Newark to pursue my Ph.D. in Mathematics with Dr. Lee Mosher. In 2015 I joined  IISER Mohali as a  National Post Doctoral Fellow with Dr Krishnendu Gongopadhyay as my mentor. In 2019 I joined Ashoka University as an assistant professor. 

My research interests are primarily in the area of Geometric group theory. Geometric group theory primarily focuses on finitely generated, infinite groups. In a way, it is the modern study of symmetry, a concept central to geometry since ancient times. In modern mathematics, the symmetries of a geometric object are abstracted in the algebraic concept of a group. Geometric group theory combines methods of abstract group theory with methods of geometry, enriching both of those topics, and deepening our understanding of groups and of geometries. Over the last half-century the methods of geometric group theory have been applied with great success to groups which arose in topological settings during the course of the late 19th and early 20th century. One of the key ideas is to treat groups as metric spaces via the word metric. 

Within the area of geometric group theory I mainly focus on the study of non-abelian free groups and their automorphisms. You can read about them in the first chapter of these excellent notes by Lee Mosher  here. 

I also find probabilistic methods to study groups a very interesting topic and have been learning more about it recently with my colleague Dr. Kumarjit Saha. 

My google scholar page contains a list of all my publications. You can also refer to the this file for a slightly more detailed version. 

1. (with Funda Gultepe) : Geometry of extensions of free groups via automorphisms with fixed points on the complex of free factors; (to appear in Algebraic & Geometric Topology)

2. (with Funda Gultepe) : Relative hyperbolicity of free extensions of free groups; (to appear in Transactions of the American Math. Soc.) 

3. (with Mahan Mj.)        : Regluing graphs of free groups; (Algebraic & Geometric Topology 22 (2022) 1969-2006)

4. Relative hyperbolicity of free-by-cyclic extensions; (Compositio Math. 2023, 159 (1), 153-183)

5. Limits of Conjugacy classes under iterates of hyperbolic elements of Out(F); (Groups, geometry and dynamics, 2020, 14(1), 177-211) 

6. Applications of Weak attraction theory in Out($F_n$); (Geometriae Dedicata, 2016 (vol 181), pages 1-22)

If you are curious about the central ideas in geometric group theory here are a few excellent basic references to get you started. 

1) Introduction to group theory by Oleg Bogopolski (this is an excellent textbook which revisits undergrad group theory from a more geometric perspective, recommended reading even if you are not particularly interested in geometric group theory). 

2) Groups, graphs and trees by John Meier. 

3) Geometric group theory by Clara Loh. 

4) Notes by Alessandro Sisto (starts with the basics of Cayley graph and  word metric). 

For studying group theory from a probabilistic perspective, the following are two excellent freely available resources: 

1) Notes by Steven Lalley. 

2) Notes by Gabor Pete.

If you are curious about what I presently study in my research, please take a look at the expository notes by Lee Mosher here.

I generally teach two courses every semester.  Courses that I have taught so far at Ashoka University include: 

Calculus, Multivariate Calculus, Linear Algebra, Algebra 1, Algebra 2, Complex Analysis, Elementary differential geometry of curves and surfaces, ODE and mathematical modelling, Introduction to Topology. 

In Monsoon 2025 I am on leave.