## 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

(November 9-12, 2021) Gave two talks in the School and Conference on Geometric Complexity Theory:

- Representations in coordinate rings and partial stability in Geometric Complexity Theory
- Characterization by symmetries, natural proofs, and P vs NP in Geometric Complexity Theory

(Fall 2021) Teaching graduate-level Computational Complexity and undergraduate Algorithms. Trying out ungrading for the first time in the grad class. For the undergrad class I think we finally have mastery- and standards-based grading working really well in this course!

(July 20-22, 2021) Gave a talk at CCC '21 on On p-Group Isomorphism: search-to-decision, counting-to-decision, and nilpotency class reductions via tensors. Joint with Youming Qiao, based on part of this preprint.

(Summer 2021) Working with a great group of students and postdocs! Two undergraduates (Nicole Dong, Ezzeddine El Sai), 6 graduate students (Gabriel Andrade, Robby Green, Michael Levet, Joel Ornstein, Elise Tate, Tzu-Chi Yen), and 2 postdocs Nathan Lindzey, Abhiram Natarajan).

(Mar 8 - Jun 11, 2021) IPAM Fellow at the IPAM Long Program on "Tensor Methods and Emerging Applications to the Physical and Data Sciences".

(May 25, 2021) Gave a talk in the IPAM Long Program on "Tensor Methods and Emerging Applications to the Physical and Data Sciences", "Tensor Isomorphism in its various incarnations", based on this paper joint with Vyacheslav Futorny and Vladimir V. Sergeichuk and this preprint (appeared at ITCS '21), with Youming Qiao.

(May 10, 2021) "On p-Group Isomorphism: search-to-decision, counting-to-decision, and nilpotency class reductions via tensors" accepted to CCC '21! Joint with Youming Qiao, based on part of this preprint.

(Apr 30, 2021) Honorable mention for the CU Boulder CS Graduate Student Advising Award.

(Apr 28, 2021) Gave a talk in the TU Berlin Kolloquium on on Algorithmic Mathematics & Complexity, based on a part of this preprint (appeared at ITCS '21), with Youming Qiao.

(Feb 23, 2021) Gave a talk in the Codes and Expansions (CodEx) Seminar, Codes and Expansions in Algorithms for Matrix Multiplication.

(Jan 6-8, 2021) Gave a talk (watch the video, shorter live version with Q&A) at ITCS '21 on "On the complexity of isomorphism problems for tensors, groups, and polynomials I: Tensor Isomorphism-completeness". This is part of this preprint, with Youming Qiao.

(Dec 20, 2020) Paper accepted to STACS '21! Average-case algorithms for testing isomorphism of polynomials, algebras, and multilinear forms with Youming Qiao and Gang Tang.

(Dec 2, 2020) New preprint posted, Average-case algorithms for testing isomorphism of polynomials, algebras, and multilinear forms with Youming Qiao and Gang Tang.

(Nov 24, 2020) Gave a talk in the LA Combinatorics & Complexity Seminar, "Designing Strassen's algorithm for matrix multiplication", based on this paper joint with Cris Moore. Watch the video here!

(Nov 17, 2020) Paper accepted to ITCS '21! "On the complexity of isomorphism problems for tensors, groups, and polynomials I: Tensor Isomorphism-completeness." This is part of this preprint, with Youming Qiao.

See all past updates