I am currently pursuing an MS (Res.) in the Department of Mathematics at the Indian Institute of Science (IISc), Bangalore.
My primary research interests are metric geometry and analysis. I enjoy tackling problems that carry a convex flavor, and I am fascinated by the wide range of techniques in analysis that are used to approach such problems. I am also interested in the intersection of these areas with theoretical computer science, especially computational geometry.
My updated CV can be found here.
Email: anantn at iisc dot ac dot in
Academic Background
MS (Res.) in Mathematics
Aug 2022 - Present
Indian Institute of Science
Supervisor: Purvi Gupta
B.Sc. (Honours) in Mathematics
Aug 2019 - June 2022
Sri Venkateswara College
University of Delhi
Publications & Preprints
- Membership queries for convex floating bodies via Hilbert geometry (with P. Gupta). arXiv
Master's Project & Thesis
Master's Thesis (Aug 2024 - Present), IISc, Bangalore
Membership Queries via Hilbert Geometry
Supervisor: Purvi Gupta
My thesis focuses on exploring Hilbert geometry through the lens of computational geometry. In a joint work with P. Gupta, we propose an approximate membership query for the convex floating bodies of a given bounded convex domain \( K \subset \mathbb{R}^d \), where the error is measured by the affine-invariant Hilbert metric on \( K \). We produce an efficient data structure to answer this query, which relies on a comparison between convex floating bodies and Hilbert metric balls. Alternately, the data structure computes the approximate depth in a convex body of a query point.
Master's Project (Jan 2024 - June 2024), IISc, Bangalore
Volume Entropy of Hilbert Metrics via Flag Approximability of Convex Bodies
Report
Slides
Supervisor: Purvi Gupta
For my project, I studied a proof of the entropy upper bound conjecture for Hilbert geometry, by Vernicos and Walsh (2018). It involves establishing a concrete relationship between volume entropy and flag approximability, where the latter is a combinatorial measure of complexity of polytopes that approximate a given convex body in the Hausdorff metric. The paper cleverly uses techniques from convex geometry, Finsler geometry and combinatorics. For instance, I studied a paper by Arya, da Fonseca, and Mount (2016) which provides a way to control the combinatorial complexity of approximating polytopes using the Busemann volume of Hilbert metric balls, simply reducing it to a comparison between these balls and Macbeath regions.