Abhishek Gopal

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

In my spare time, I also do photography. You can catch my shots here. Most of the shots were taken with my phone and some with rented cameras. In the context of my mathematical journey, I idolize two people: Leonhard Euler and Bertrand Russell.

I was born and brought up in Fatehpur, a district nestled between Kanpur and Allahabad (now Prayagraj), India. For eight years, I attended my higher secondary schooling at Maharishi Vidya Mandir Sr. Sec. School, Fatehpur, India, and then graduated in 2015. I then attended Ewing Christian College, which is affiliated with the University of Allahabad, India, for three years for a Bachelor’s program with a major in Mathematics and Physics, graduating in May 2018. I received my Master’s degree in Mathematics with Data Science in September 2021 from the Institute of Mathematics and Applications, which is affiliated with Utkal University.

Next semester, I am co-organizing the 22nd Graduate Student Topology and Geometry Conference 2025 at Indiana University Bloomington, which will take place from April 11-13, 2025. Additionally, I am a member of TACOs (Topologically Allied Conference Organizers) of IU.

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

I am working in the domain of low-dimensional topology and hyperbolic geometry, focusing on 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.

• Summer School in Mathematics: Low-dimensional Topology, Institut Fourier, France, 2024
• Georgia Topology Summer School and Conference, University of Georgia, USA, 2024
• Graduate Student Topology and Geometry Conference 2024, Michigan State University, USA, 2024
• 66th Texas Geometry and Topology Conference, Rice University, USA, 2023
• Midwest Topology Seminar, University of Illinois Urbana-Champaign, USA, 2023
• Graduate Student Topology and Geometry Conference 2023, Harvard University, USA, 2023
• The Unity of Mathematics: A Conference in Honour of Sir Michael Atiyah, University of Cambridge, UK, 2021
• International Conference on Discrete Groups, Geometry and Arithmetic, NCM and TIFR, India, 2021
• 48th Annual Conference of Odisha Mathematical Society, IMA, India, 2021
• 36th Annual Ramanujan Mathematical Society Conference, Amrita Vishwa Vidyapeetham, India, 2021
• Orthogonal Polynomials, Special Functions and Operator Theory and Applications, ICMS and LMS, UK, 2021
• International Workshop on Mathematics Meets the World: Recent Trends and Developments, VIT, India, 2020
• Groups In Galway 2020 International Conference, NUI and IMS, Ireland, 2020
• 35th Annual Conference of Ramanujan Mathematical Society, Central University of Rajasthan, India, 2020

• 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
• Simple Geodesics and McShane’s Identity: Part II, Teichmüller Theory Seminar, Indiana University Bloomington, USA, 2024
• Simple Geodesics and McShane’s Identity: Part I, Teichmüller Theory Seminar, Indiana University Bloomington, USA, 2024

Indiana University Bloomington

• Recitation: M212 Calculus II, Fall 2024
• Grade: M343 Differential Equations with Applications, Summer 2024
• Recitation: M106 Math of Decision and Beauty, Su '23, F '23, S '24
• 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

Join me at: Discord, Instagram, X/Twitter, Mastodon, Flickr

Disambiguation/Disclaimer: I am not Abhishek Gopal, a molecular biology researcher at NCF, India. Nor am I Abhishek Gopal, a product manager at Amazon. I can be distinguished from the many other Abhishek Gopals in the world (who the reader can go out and discover for themselves) by adding math after my name - so far as I know I am the only Abhishek Gopal in mathematics.

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Last updated: October 2024