Cole Franks

franks at mit

I am an instructor of applied mathematics at MIT, where my mentors are Ankur Moitra and Michel Goemans.

I received my Ph.D. in May, 2019 from Rutgers, where I was advised by Mike Saks.


I work in theoretical computer science and discrete mathematics. My research has two branches: scaling algorithms and combinatorial discrepancy. Scaling algorithms, which generalize Sinkhorn's algorithm for matrix scaling, are algorithms for a class of optimization problems which arise in computational invariant theory, quantum information, and statistics. My work in combinatorial discrepancy is focused on upper and lower bounds for discrepancy in various worst case and random settings.

Cole Franks


MIT 18.453 Combinatorial Optimization, Spring 2021
MIT 18.434 Seminar in Theoretical Computer Science, Spring 2020


A quiver-theoretic approach to integrated principal components analysis
Cole Franks, Visu Makam
In preparation

Optimal sample complexity for matrix and tensor normal models via geodesic convexity
Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter
In preparation

Barriers for recent methods in geodesic optimization
Cole Franks, Philipp Reichenbach
In preparation

Minimal length in an orbit closure as a semiclassical limit (arXiv)
Cole Franks, Michael Walter
Submitted, QIP 2020

Rigorous Guarantees for Tyler's M-estimator via quantum expansion (arXiv, proceedings )
Cole Franks, Ankur Moitra
COLT, 2020

Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes  (arXiv, proceedings )
Peter Bürgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
FOCS, 2019

A simplified disproof of Beck's three permutations conjecture and an application to root-mean-squared discrepancy (arXiv, journal)
Cole Franks
Combinatorics, Probability and Computing, 2020

On the Discrepancy of Random Matrices with Many Columns (arXiv, journal)
Cole Franks, Michael Saks
Random Structures and Algorithms

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes (arXiv, proceedings)
Peter Bürgisser, Cole Franks, Ankit Garg, Michael Walter, Rafael Oliveira, Avi Wigderson
FOCS, 2018

Operator scaling with specified marginals (arXiv, proceedings)
Cole Franks
STOC, 2018

The Delta Squared Conjecture holds for graphs of small order (pdf, journal)
Cole Franks
Involve, 2015

Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones (arXiv, journal)
Philip Chodrow, Cole Franks, Brian Lins
Linear Algebra and its Applications, 2013

On the structure group of a decomposable model space (arXiv, journal)
Corey Dunn, Cole Franks, Joseph Palmer
Contributions to Algebra and Geometry, 2013

PhD thesis

A simple algorithm for Horn’s problem and two results on discrepancy, May 2019