I study applied algebraic geometry and tensor networks in statistics, computer science, and quantum information. Information-processing systems described as networks (e.g. Bayesian networks, quantum circuits) in seemingly disparate fields in fact have common mathematical foundations.
They are connected by variations on the graphical modeling language of tensor networks, or more generally monoidal categories with various additional properties. Basic questions about each type of information-processing system (such as what probability distributions or quantum states can be represented, or what word problems can be solved efficiently) quickly become interesting problems in shared algebraic geometry, representation theory, polyhedral geometry, and category theory.
Upcoming and Recent events
- The Classification Program of Counting Complexity, Simons Institute 28 March - 1 April 2016.
- Wildness in Computer Science, Physics, and Mathematics, Santa Fe Institute 12-16 October 2015.
- Computational Category Theory, NIST 28-29 September 2015.
- Symbolic and Numerical Methods for Tensors and Representation Theory, Simons Institute 17-20 November 2014.
- Tensors in Computer Science and Geometry, Simons Institute, 10-14 November 2014.
- Celebrating 10 Years of Categorical Quantum Mechanics, Oxford, 15-19 October 2014.
- Modern Applications of Representation Theory IMA PI Summer School, University of Chicago, 20 July- 6 August 2014. Includes videos of all lectures in the three-week summer school.
- Algebraic Statistics 2014, May 19-22, 2014.