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.
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).
A quiver-theoretic approach to integrated principal components analysis Cole Franks, Visu Makam
Optimal sample complexity for matrix and tensor normal models via geodesic convexity Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael WalterIn preparation
Barriers for recent methods in geodesic optimization (arXiv )Cole Franks, Philipp ReichenbachSubmitted
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
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 WigdersonFOCS, 2019
A simplified disproof of Beck's three permutations
conjecture and an application to root-mean-squared discrepancy (arXiv, journal)Cole FranksCombinatorics, 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 WigdersonFOCS, 2018
Operator scaling with specified marginals (arXiv, proceedings) Cole FranksSTOC, 2018
The Delta Squared Conjecture holds for graphs of small order (pdf, journal) Cole FranksInvolve, 2015
Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones (arXiv, journal) Philip Chodrow, Cole Franks, Brian LinsLinear Algebra and its Applications, 2013
On the structure group of a decomposable model space (arXiv, journal) Corey Dunn, Cole Franks, Joseph PalmerContributions to Algebra and Geometry, 2013
A simple algorithm for Horn’s problem and two results on discrepancy
, May 2019