I work in the fields of Convex Geometry, Information Theory, and Optimal Transport. My primary interests lie in exploring the interplay between convex geometry and information theory, which often lead me into foundational questions about transportation of measures. I also take a keen interest in the discrete sides of things, namely information-theoretic ideas in Combinatorics, Graph Theory, and Number Theory. 

Keywords : Convex bodies, entropy, log-concave measures, displacement interpolation, curvature-dimension conditions

Publications/preprints:

1. G. Aishwarya, D. Faifman: "Stability in the Banach isometric conjecture and nearly monochromatic Finsler surfaces'' 2024 (preprint). [paper]

2. G. Aishwarya, L. Rotem: "New Brunn--Minkowski and functional inequalities via convexity of entropy'' 2023 (preprint). [paper, related talk]

3. G. Aishwarya, I. Alam, D. Li, S. Myroshnychenko, and O. Zatarain-Vera: "Entropic exercises around the Kneser-Poulsen conjecture''. Mathematika, 69, no. 3, 2023. [paper, related talk]

4. G. Aishwarya and M. Madiman: "Conditional Rényi entropy and the relationships between Rényi capacities''. Entropy (Special issue on Information Measures with Applications edited by A. Lapidoth), vol. 22, no. 5, 2020. [paper]

5. G. Aishwarya and M.Madiman: "Remarks on Rényi versions of conditional entropy and mutual information''. Proceedings of the 2019 IEEE International Symposium on Information Theory, Paris, France, July 2019. [conference paper]

In preparation:

1. G. Aishwarya, D. Li, M. Madiman, and M. Meckes: "Diversity and dimension of probability measures in metric spaces" 2023 (preprint available on request)

2. G. Aishwarya and M. Madiman: "Magnitude, diversity, and primes: first steps" 2023 (preprint available on request)

Theses/notes:

1. "Some information-theoretic notions of size in the metric setting" 2021 (PhD thesis, available here)

2. "Topics in Geometric Measure Theory" 2016 (M.Sc. thesis, available here): Notes on basic Geometric Measure Theory; covers area and coarea formulas, Federer's Tube formula for sets of Postive reach, etc.