Akshay Ramachandran Office: M237 Email: akshay@cwi.nl Links to: CV (as of June 2023); DBLP;

About Me

I am a Postdoctoral Researcher at Centrum Wiskunde & Informatica (CWI). I am fortunate to be hosted by Professor Daniel Dadush in the Networks and Optimization (N&O) group as well as Professor Michael Walter who has moved to Ruhr Universitat Bochum. I'm interested in generalizations of convex analysis and convex optimization algorithms to non-Euclidean spaces with a special focus on applications to numerical linear algebra, quantum information theory, geometric invariant theory, and high dimensional statistics.

I completed my Ph.D. at the University of Waterloo's Cheriton School of Computer Science. I was very fortunate to be advised by Lap Chi Lau. Before UWaterloo, I spent four wonderful years at UC Berkeley, graduating in May 2016 with a degree in Electrical Engineering and Computer Science. At UC Berkeley, I was incredibly lucky to have the opportunity to work with Luca Trevisan and Nikhil Srivastava.

Research

Publications and Preprints (Show all)

The Paulsen Problem Revisited: Optimal Bounds via Smoothed Analysis and Scaling.
Lap Chi Lau, Akshay Ramachandran.
In Preparation.


Strongly Polynomial Frame Scaling to High Precision.
Daniel Dadush, Akshay Ramachandran.
Manuscript.
• Presented at SODA 2024


Near optimal sample complexity for dense matrix and tensor normal models.
Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter.
Manuscript.
• Submitted to Annals of Statistics.


Hidden convexity, optimization, and algorithms on rotation matrices .
Kevin Shu, Akshay Ramachandran, Alex Wang.
Manuscript.
• Submitted to Mathematics of Operations Research.


Scaling problems, algorithms and applications to computer science, functional analysis and statistics.
Rafael Oliveira, Akshay Ramachandran.
Survey
• In 33o Coloquio Brasileiro de Matematica


Spectral Analysis of Operator Scaling.
Tsz Chiu Kwok, Lap Chi Lau, Akshay Ramachandran.
Manuscript.
• Presented at FOCS 2019.
• In SICOMP Volume 50 (2021).


The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis.
Tsz Chiu Kwok, Lap Chi Lau, Yin Tat Lee, Akshay Ramachandran.
Manuscript.
• STOC 2018.


Sandpile Prediction on Trees in near linear time.
Akshay Ramachandran, Aaron Schild.
Manuscript.
• SODA 2017.



Thesis

• Geodesic Convex Analysis of Group Scaling for the Paulsen Problem and the Tensor Normal Model .
  Akshay Ramachandran.
  Ph.D. Thesis, 2021.
  • Won Mathematics Doctoral Prize (second place) in Faculty of Mathematics
  • Won Cheriton Distinguished Dissertation Award in Department of Computer Science

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Talks

• Eigenvalue Inequalities and the Subspaces that Induce them. Presented in AAC Seminar, June 2023 (Bochum, Germany).
• Operator scaling meets non-commutative optimal transport. In AIM SQuaREs Workshop, Mar 2023 (San Jose, CA, USA).
• Jordan’s Lemma and the CS Decomposition in Quantum Algorithms. Presented in QuSoft Junior Meeting, March 2023 (Amsterdam, Netherlands).
• The Brascamp-Lieb Polytope: Rank of Matrix Spaces and Combinatorial Optimization. Presented in UWaterloo A&C Seminar, Oct 2022 (Waterloo, Canada).
• Near optimal sample complexity for matrix and tensor normal models. Presented in Simons Workshop on Symmetry in Optimization, Nov 2021 (UC Berkeley, CA, USA).
• Advanced Course in Scaling problems, algorithms, and applications. Presented with Rafael Oliveira in Coloquio Brasileiro de Matematica, June 2021 (Online)
• Spectral analysis of matrix and operator scaling. Presented in FOCS 2019 (Baltimore, MD, USA).
• The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis. Presented in FOCS 2018 Workshop on Scaling Algorithms and Applications (Paris, France).
• Ramanujan graphs from the matching polynomial. Presented in UC Berkeley Topics Course on Geometry of Polynomials, Fall 2015 (Berkeley, CA).

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Teaching

• Instructional Assistant for Continuous Optimization at Mastermath Netherlands Fall 2022.
• Instructional Assistant for CS341 (Algorithms) at UWaterloo Spring 2019, Fall 2019, Winter 2020.
• Teaching Assistant for CS70 (Discrete Math and Probability) at UC Berkeley Summer 2015, Fall 2015, Spring 2016.