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.
Keywords : Convex bodies, entropy, log-concave measures, displacement interpolation, curvature-dimension conditions
Publications/preprints:
G. Aishwarya, D. Li, M. Madiman, and M. Meckes: "Metric complexity is a Bryant--Tupper diversity" 2025 (preprint). [paper, related blog post]
G. Aishwarya, D. Li: "Entropy and functional forms of the dimensional Brunn--Minkowski inequality in Gauss space'' 2025 (preprint). [paper, related talk]
G. Aishwarya, D. Li: "The Kneser--Poulsen phenomena for entropy'' International Mathematics Research Notices, Volume 2025, Issue 12, June 2025, rnaf140. [paper, related talk]
G. Aishwarya, D. Faifman: "Stability in the Banach isometric conjecture and nearly monochromatic Finsler surfaces'' 2024 (preprint). [paper, related talk]
G. Aishwarya, L. Rotem: "New Brunn--Minkowski and functional inequalities via convexity of entropy'' 2023 (preprint). [paper, related talk]
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]
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]
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:
G. Aishwarya, L. Rotem, and Y. Shenfeld: "Matrix displacement convexity and sectional curvature" 2025
G. Aishwarya and M. Madiman: "Magnitude, diversity, and primes: first steps" 2023 (preprint available on request)
Theses/notes:
"Some information-theoretic notions of size in the metric setting" 2021 (PhD thesis, available here)
"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.