## About Me

I am an Assistant Professor in the Departments of Computer Science and Mathematics at the University of Colorado at Boulder, where I am a member of the CS Theory Group and the Complex Systems Group. My research has two main thrusts (with deep underlying relations beneath):

- Interactions between theoretical computer science and mathematics (particularly algebraic geometry, representation theory, and group theory), and
- Developing the theory of complex systems and complex networks, and applying this theory with my collaborators in a variety of fields, such as ecology, evolutionary biology, economics, climate, and beyond. I'm always looking for new problems that need new theory!

I was previously an Omidyar Fellow at the interdisciplinary Santa Fe Institute for complex systems. Prior to SFI, I was a postdoc in the University of Toronto CS Theory Group, and prior to that I got my Ph.D. at the University of Chicago.

## What's new

(Jul 12, 2019) Gave a talk on

(Jul 1, 2019) New preprint posted! Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions, joint with Youming Qiao.

(May 20, 2019) My first ever ecology paper (or, at least, one to which I contributed in some small way): Ecogeographical rules and the macroecology of food webs. With a ton of great people: B. Baiser, D. Gravel, A. R. Cirtwell, J. A. Dunne, A. K. Fahimipour, L. J. Gilarranz, D. Li, N. D. Martinez, A. McGrew, T. N. Romanuk, D. B. Stouffer, L. B. Trotta, F. S. Valdovinos, R. J. Williams, S. A. Wood, and J. D. Yeakel.

(May 6, 2019) New preprint posted: Incorporating Weisfeiler-Leman into algorithms for group isomorphism, joint with Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson.

(Dec 27, 2018) Wildness for tensors accepted to

(Oct 22, 2018) New paper posted online: Wildness for tensors! Joint with Vyacheslav Futorny and Vladimir V. Sergeichuk.

(Oct 1, 2018) New expository paper published in the

(July 23-26, 2018) Invited speaker at the Clay Math Institute/Oxford Workshop on Complexity Theory! I spoke on "Complexity in Ideals of Polynomials." Student support available.

(July 23, 2018) Report from the January Dagstuhl Workshop on Proof Complexity now available, including lots of great open questions!

See all past updates

*Tensor Isomorphism: completeness, graph-theoretic methods, and consequences for Group Isomorphism*—watch the talk here—at the Banff International Research Station Workshop on Algebraic Techniques in Computational Complexity. Based on these three papers.(Jul 1, 2019) New preprint posted! Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions, joint with Youming Qiao.

(May 20, 2019) My first ever ecology paper (or, at least, one to which I contributed in some small way): Ecogeographical rules and the macroecology of food webs. With a ton of great people: B. Baiser, D. Gravel, A. R. Cirtwell, J. A. Dunne, A. K. Fahimipour, L. J. Gilarranz, D. Li, N. D. Martinez, A. McGrew, T. N. Romanuk, D. B. Stouffer, L. B. Trotta, F. S. Valdovinos, R. J. Williams, S. A. Wood, and J. D. Yeakel.

(May 6, 2019) New preprint posted: Incorporating Weisfeiler-Leman into algorithms for group isomorphism, joint with Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson.

(Dec 27, 2018) Wildness for tensors accepted to

*Linear Algebra and its Applications*! Joint with Vyacheslav Futorny and Vladimir V. Sergeichuk.(Oct 22, 2018) New paper posted online: Wildness for tensors! Joint with Vyacheslav Futorny and Vladimir V. Sergeichuk.

(Oct 1, 2018) New expository paper published in the

*Bulletin of the AMS*: New applications of the polynomial method: the cap set conjecture and beyond!(July 23-26, 2018) Invited speaker at the Clay Math Institute/Oxford Workshop on Complexity Theory! I spoke on "Complexity in Ideals of Polynomials." Student support available.

(July 23, 2018) Report from the January Dagstuhl Workshop on Proof Complexity now available, including lots of great open questions!

See all past updates