## Talks

### Operator Scaling with Specified Marginals

STOC (2018),

[slides]

**Abstract**

A characterization theorem and algorithm to test, given positive semidefinite matrices P and Q and a completely positive map T, whether it is possible to pre- and post- compose T with matrix similarities so that T is both trace-preserving and maps P to Q. This generalizes the (r,c)-scaling problem, which asks, given a nonnegative matrix and vectors r and c, if the matrix can be pre- and post- multiplied by diagonals so that its row sums become r and the column sums become c.

### Mechanism Design

Rutgers Graduate Student Pizza Seminar (2016)

**Abstract**

How to fairly distribute goods and services among people who may not be honest about how much they value said goods and services.

### Area Paradoxes

Rutgers Graduate Student Pizza Seminar (2015)

**Abstract**

Besikovitch's construction of sets in the unit cube with volume 0.1 and arbitrarily small surface area (first few steps at right).

## Contact

### W. Cole Franks

Hill Center, Room 606

Department of Mathematics

Rutgers, The State University Of New Jersey

110 Frelinghuysen Rd.

Piscataway, NJ 08854-8019

email: wcf17 at math dot rutgers dot edu