Cole Franks

franks at mit

I am an instructor of applied mathematics at MIT mentored by Ankur Moitra and Michel Goemans.

For the fall 2021 semester, I am honored to be visiting the Simons Institute for the Theory of Computing to participate in the Geometric Methods in Optimization and Sampling program.

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


UROP: Kronecker sum covariances for high-dimensional statistics. Jennifer Ai (2020), Brin Harper (2020), Lisa Kondrich (2021).

UROP: Average case hardness of combinatorial discrepancy. Naveen Venkat (2021).

UROP+: Learning mixtures of elliptical distributions. Kerri Lu (2021).


See GitHub for all code; fun ones are Crosswords and Tensor Scaling.


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

Near optimal sample complexity for matrix and tensor normal models via geodesic convexity (arXiv)
Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter

Barriers for recent methods in geodesic optimization (arXiv , proceedings)
Cole Franks, Philipp Reichenbach
CCC, 2021

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

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