Abhishek Gopal (Himalaya)

I'm a fourth-year graduate student and working as an Associate Instructor in the Department of Mathematics at Indiana University Bloomington.

I was born and raised in Fatehpur, a district in India located between Kanpur and Allahabad (now Prayagraj).

I completed my higher secondary education at Maharishi Vidya Mandir Sr. Sec. School in Fatehpur, graduating in 2015 after eight years of study there. I then pursued a Bachelor's degree in Mathematics and Physics at Ewing Christian College, affiliated with the University of Allahabad, graduating in May 2018. In September 2021, I earned my Master’s degree in Mathematics with Data Science from the Institute of Mathematics and Applications, affiliated with Utkal University.

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. This year, I co-organized the 22nd Graduate Student Topology and Geometry Conference 2025 at Indiana University Bloomington, which took place from April 11-13, 2025.

My CV, up to date as of August 2025, is available here.

Photo: Relaxing on the Passerelles Himalayennes Du Drac in Grenoble, France. Captured by Onur Korkmaz.

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 P. 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.

• Heegaard Floer Homology and Knots, Graduate Student Seminar, Indiana University Bloomington, USA, 2025
• Basic Knot Theory and 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 Strutures on the Knot Complements, 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)

Indiana University Bloomington

• Teach: D116 Introduction to Finite Math I, Fall 2025
• Recitation: M106 Math of Decision and Beauty, Su '23, F '23, S '24, S '25, Su '25
• Recitation: M212 Calculus II, Fall 2024
• Grade: M343 Differential Equations with Applications, Summer 2024
• Grade: M415 Complex Variables, Spring 2023
• Grade: M301 Linear Algebra and Applications, Fall 2022

Others

• Part-time Teaching Assistant, Uma Coaching Institute, India, 2016 - 2017

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Last updated: August 2025