Cole Franks
Starting July 25, 2022 I will be a software engineer at Gridspace.
Before that (August 2019 to June 2022) I was an instructor of applied mathematics at MIT mentored by Ankur Moitra and Michel Goemans.
I received my Ph.D. in May, 2019 from Rutgers, where I was advised by Mike Saks.
Research
My mathematical research interests are in theoretical computer science and discrete mathematics. I am primarily interested in scaling algorithms. Scaling algorithms, which generalize Sinkhorn's algorithm for matrix scaling, solve non-convex optimization problems arising in computational invariant theory, quantum information, and statistics. I have also worked in combinatorial discrepancy, a framework for studying discrete approximation of continuous objects.
Papers
Shrunk subspaces via operator Sinkhorn iteration (arXiv) Cole Franks, Michel Goemans, Tasuku Soma
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 Submitted, 2021
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 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
PhD thesis
A simple algorithm for Horn’s problem and two results on discrepancy, May 2019Talks
- FOCS, November 2019: Geodesic first and second order methods for moment maps and polytopes
- MIT Combinatorics Seminar, October 2019: Three Permutations, Simplified
- SIAM Conference on Applied Algebraic Geometry, July 2019: Analytic algorithms for the moment polytope
- CMO BIRS workshop: Analytic techniques in Theoretical Computer Science, Aug 2018: On the Discrepancy of Random Matrices with Many Columns
- CWI Networks and Optimization interest group seminar, June 2018: Efficient algorithms for tensor scaling, quantum marginals, and moment polytopes
Teaching
MIT 18.434 Seminar in Theoretical Computer Science, Spring 2022 MIT 18.453 Combinatorial Optimization, Spring 2021 MIT 18.434 Seminar in Theoretical Computer Science, Spring 2020 Rutgers Math 454 Combinatorics, Summer 2017Mentoring
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).