In my spare time, I enjoy photography. You can view my shots here. Most of them were taken using my phone and my camera.
I serve on the organizing committee of the Peer Mentoring Initiative (PMI) a program where experienced graduate students help new students feel at home in the department. We support incoming graduate students in ways the department or administration may not always be able to—whether through tier exam preparation, housing guides, or practical tips for navigating graduate school life. I'm also a member of the advisory committee of the Mathematics Graduate Student Association at Indiana University Bloomington.
I am studying low-dimensional topology and hyperbolic geometry, focusing on Floer homology invariants of links, 3- and 4-manifolds, and hyperbolic knot theory. I am being advised by Dylan Thurston.
In my master thesis, I worked with Manas R. Mohapatra on the characterizations of hyperbolic Lambert and Saccheri quadrilaterals in the Poincaré disk. We derived a new hyperbolic area formula using Heron's and Bretschneider's formulas and established sharp bounds for their area. We also extended these results to include adjacent side lengths, diagonals, and geometric properties of the hyperbolic Lambert kite, exploring its connections to hyperbolic tiling inspired by M.C. Escher's “Circle Limit” diagrams.
On Abouzaid’s and Auroux’s Fukaya Categories Paper, Fukaya Categories and Immersed Curve Reading Seminar, Indiana University Bloomington, USA, 2026 (2 talks)
Knots, Links, and Hyperbolic Geometry, HyperboliciTea, Boston College, USA, 2026
On the Surface Algebra $\mathcal{A}(\mathcal{Z})$, Knot Floer Homology, and $CFK^{-}$ to $\widehat{CFD}$ (2 talks), Working Seminar on Bordered Heegaard Floer Theory, USA, 2025
Knot Invariants via Heegaard Floer Homology, Graduate Student Seminar, Indiana University Bloomington, USA, 2025
From Knots to Polynomials: An Introduction to the Jones Polynomial, TQFT Learning Seminar, Indiana University Bloomington, USA, 2025
On the Non-Genericity of Hyperbolic Knots, Knot Theory Learning Seminar, Indiana University Bloomington, USA, 2025 (2 talks)
Introduction to Heegaard Floer Homology, Topology and Friends Graduate Student Seminar (TopFrogs), Indiana University Bloomington, USA, 2025 (2 talks)
Introduction to Hyperbolic Knot Theory, Graduate Student Seminar, Indiana University Bloomington, USA, 2024
Hyperbolic Structures on Knot Complements: Geometry Meets Topology, Topology and Friends Graduate Student Seminar (TopFrogs), Indiana University Bloomington, USA, 2024
Mirzakhani's Generalization of the McShane's Identity for Bordered Surfaces, Teichmüller Theory Seminar, Indiana University Bloomington, USA, 2024 (3 talks)
Seminars
This semester (Spring 2026), I am co-organizing the Fukaya Categories and Immersed Curves Reading Seminar at Indiana University Bloomington. The seminar schedule is provided below.
Date
Speaker
Topic
January 22, 2026
Sergei Kopylov
Introduction to $\mathcal{A}_{\infty}-$Categories
January 29, 2026
Himalaya
Abouzaid’s Construction of Fukaya Categories for Surfaces
February 5, 2026
Arijit Paul
Fukaya Categories of Surfaces: Properties and Examples
February 12, 2026
Paul Kirk
Lagrangian Floer Theory I
February 19, 2026
Paul Kirk
Lagrangian Floer Theory II
February 26, 2026
Arijit Paul
Fukaya Categories of Surfaces: Proofs
March 5, 2026
Himalaya
Auroux's Guide for Fukaya Categories
March 12, 2026
Sergei Kopylov
Maslov Index
March 26, 2026
Onur Korkmaz
Exact Triangles in the Fukaya Category
Previous (Click ▶ to see the schedule):
Working Seminar on Bordered Heegaard Floer Theory (Fall 2025)
Date
Speaker
Topic
September 2, 2025
Jonathan Hanselman
Overview of Bordered Heegaard Floer Homology and Immersed Curves Invariants
September 9, 2025
Arijit Paul
Heegaard Diagram, Pointed Matched Circles, and Bordered Heegaard Diagram
September 16, 2025
Himalaya
$\mathcal{A}(\mathcal{Z})$ Algebra of the Pointed Matched Circles
September 23, 2025
Jaehoon Yoo
Cylindrical Reformulation of Heegaard Floer Theory
September 30, 2025
Arijit Paul
Type D Structures and $\widehat{CFD}$
October 7, 2025
Onur Korkmaz
$\widehat{CFD}$: Examples
October 14, 2025
Jonathan Hanselman
Computing $\widehat{CFD}$ of a Knot Complement I
October 21, 2025
Jonathan Hanselman
Computing $\widehat{CFD}$ of a Knot Complement II
October 28, 2026
Arijit Paul
$\mathcal{A}_{\infty}-$modules, Type A Structures, and the Pairing Theorem
November 4, 2025
Himalaya
Knot Floer Homology and $\textrm{CFK}^{-}\to \widehat{CFD}$
November 11, 2025
Onur Korkmaz
Extended Type D Structures and Immersed Curve Invariants I
November 18, 2025
Onur Korkmaz
Extended Type D Structures and Immersed Curve Invariants II
December 2, 2025
Patrick Chan
Cosmetic Surgery Conjecture and Recent Progress
Meetings were held every Tuesday, with group discussions on Thursdays.
Hyperbolic Knot Theory Seminar (Spring 2025)
Date
Speaker
Topic
January 21, 2025
Dalton Sconce
Existence and Uniqueness of Prime Decomposition of Knots I
January 28, 2025
Dalton Sconce
Existence and Uniqueness of Prime Decomposition of Knots II
February 5, 2025
Arijit Paul
Satellite Knots and Incompressible Surfaces
February 11, 2025
Himalaya
On the Non-genericity of Hyperbolic Knots I
February 18, 2025
Himalaya
On the Non-genericity of Hyperbolic Knots II
February 25, 2025
Sergei Kopylov
On the Non-genericity of Hyperbolic Knots III: Proofs
March 4, 2025
Sergei Kopylov
On the Non-genericity of Hyperbolic Knots IV: Proofs
March 11, 2026
Dalton Sconce
Combinatorial Lemma and Tangles from the Non-genericity Paper
March 25, 2026
Patrick Chan
The Last Leg of “On the Question of Genericity of Hyperbolic Knots” Roadmapped
The seminar centered on the paper “On the Question of Genericity of Hyperbolic Knots” by Andrei Malyutin. Meetings were held every Tuesday.
This semester, I am assisting with the Calculus I course at Boston College, which is a first course in the calculus of one variable intended for Biology, Economics, Management, Psychology/Neuroscience and Premedical students.
I'm a fourth-year graduate student in the Department of Mathematics at Indiana University Bloomington. Currently, I am a visiting graduate student in the Department of Mathematics at Boston College.