`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.

MIT 18.434 Seminar in Theoretical Computer Science, Spring 2020

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

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** (arXiv )

Cole Franks, Philipp Reichenbach

Submitted

**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

- 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