## 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

(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.

(Oct 28, 2020) Gave a talk in the Johns Hopkins CS Theory Seminar, "Isomorphism of tensors, algebras, and polynomials, oh my!", based on these three papers.

(Sep 24, 2020) Gave a (virtual) talk at the Clarkson University Center for Complex Systems Science (C

(Sep 10, 2020) Gave a (virtual) talk in our CS Colloquium: "Can we understand big systems from their small parts?", based in part on these three papers.

(Summer 2020) I worked with a great group of students and postdocs this summer! Two high school students (Michael Klyachman, Yerim Song), four undergraduates (Nicole Dong, Ezzeddine El Sai, Sam Serra, Tarek Tohme), 5 graduate students (Gabriel Andrade, Robby Green, Michael Levet, Joel Ornstein, Tzu-Chi Yen), and 3 postdocs Nathan Lindzey, Abhiram Natarajan, Eric Reckwerdt). Crazy but fun - keep an eye out of the results from some of these collaborations!

(Apr 18, 2020) New survey published, in

(Spring 2020) Implemented standards-based grading at scale (~300 students) in CSCI 3104 Intro Algorithms, along with Lijun Chen, and a talented team of graduate TAs and undergraduate course assistants.

See all past updates

(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.

(Oct 28, 2020) Gave a talk in the Johns Hopkins CS Theory Seminar, "Isomorphism of tensors, algebras, and polynomials, oh my!", based on these three papers.

(Sep 24, 2020) Gave a (virtual) talk at the Clarkson University Center for Complex Systems Science (C

^{3}S^{2}), "Understanding large systems from their small parts: Algorithms & theory".(Sep 10, 2020) Gave a (virtual) talk in our CS Colloquium: "Can we understand big systems from their small parts?", based in part on these three papers.

(Summer 2020) I worked with a great group of students and postdocs this summer! Two high school students (Michael Klyachman, Yerim Song), four undergraduates (Nicole Dong, Ezzeddine El Sai, Sam Serra, Tarek Tohme), 5 graduate students (Gabriel Andrade, Robby Green, Michael Levet, Joel Ornstein, Tzu-Chi Yen), and 3 postdocs Nathan Lindzey, Abhiram Natarajan, Eric Reckwerdt). Crazy but fun - keep an eye out of the results from some of these collaborations!

(Apr 18, 2020) New survey published, in

*Bull. EATCS*, with lots of open questions! Complexity in ideals of polynomials: questions on algebraic complexity of circuits and proofs.(Spring 2020) Implemented standards-based grading at scale (~300 students) in CSCI 3104 Intro Algorithms, along with Lijun Chen, and a talented team of graduate TAs and undergraduate course assistants.

See all past updates