I am a Junior Fellow at the Society of Fellows, Harvard University.
Before this, I was a Hooke Research Fellowship in the Mathematical Institute at the University of Oxford and a Junior Research Fellowship at The Queen's College. I received my PhD from UC Berkeley, where my advisor was Bernd Sturmfels. My thesis was awarded the SIAM Richard C. DiPrima Prize and the Friedman Memorial Prize.
My research interests lie in tensors and multilinear algebra, applied algebraic geometry, and algebraic statistics.
Office hours: by appointment. If you a graduate or undergraduate student interested in working on a research project with me, feel free to get in touch.
19. Lower bounds on the rank and symmetric rank of real tensors (with Kexin Wang), arXiv:2202.11740.
18. Symmetries in Directed Gaussian Graphical Models (with Visu Makam and Philipp Reichenbach), arXiv:2108.10058.
16. A blood atlas of COVID-19 defines hallmarks of disease severity and specificity (as part of 100+ author Covid-19 Multi-omics Blood Atlas (COMBAT) Consortium), Cell 185 (2022) 916–938. [medRxiv]
15. Toric Invariant Theory for Maximum Likelihood Estimation in Log-linear Models (with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach), Algebraic Statistics 12 (2021) no. 2, 187-211. [arXiv]
14. The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices (with Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, and Orlando Marigliano), Le Matematiche 76 (2021) no. 2, 535-557. [arXiv]
13. Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation (with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach), SIAM Journal on Applied Algebra and Geometry 5 (2021) no. 2, 304-337. [arXiv] [Case study]
9. Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer (with Mariano Beguerisse-Díaz, Birgit Schoeberl, Mario Niepel and Heather Harrington), Journal of the Royal Society Interface 16 (2019) no. 151, 20180661. [arXiv] [News story]
3. Singular Vectors of Orthogonally Decomposable Tensors (with Elina Robeva), Linear and Multilinear Algebra 65 (2017) no. 12, 2457-2471. [arXiv]
2. Eigenconfigurations of Tensors (with Hirotachi Abo and Bernd Sturmfels), Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics 685, Amer. Math. Soc., Providence, RI (2017) 1-25.
1. Local dynamics of intersections: V. I. Arnold's theorem revisited (with Sergei Yakovenko) Israel Journal of Mathematics 201 (2014) no. 2 813-833. [arXiv]
Ideas for a complex world, a public lecture I gave as part of the Oxford Mathematical Institute public lecture series, Oxford, November 2020. Featured in the Oxford Mathematics Annual Newsletter 2021.
The Algebraic Statistics of an Oberwolfach Workshop, Snapshots of modern mathematics from Oberwolfach (2018) no. 1.
Applied Algebra and Geometry: A SIAGA of Seven Pictures, also featured as a series of three articles in SIAM news: I, II, III, Spring 2016.
Iwasawa Theory of Elliptic Curves with Complex Multiplication, Part III essay (master's thesis) supervised by John Coates, Cambridge, Spring 2014.
Imagining things: What do you think about, when you think about maths?, a mini documentary about mathematical thinking, directed by Richard Braham and me, Cambridge, 2013.
Spring 2022: I organized, with Xiao-Li Meng, a mini-workshop on Algebraic Statistics at Harvard University.
Summer 2021: I organized, with Michael Walter, a mini-symposium at the SIAM Conference on Applied Algebraic Geometry called "Applied Invariant Theory: Statistics and Algorithms".
2020-2021: I organized, with Vidit Nanda, the Data Science seminar at the Mathematical Institute in Oxford.
Spring 2021: I gave two introductory lectures at the IPAM long program on "Tensor Methods and Emerging Applications to the Physical and Data Sciences". They were (i) From linear algebra to multi-linear algebra (ii) Tensors in statistics and data analysis.
Summer 2019: I organized, with Carlos Améndola, Joscha Diehl, and Francesco Galuppi, a mini-symposium at the SIAM Conference on Applied Algebraic Geometry, called "Signature tensors of paths".
Spring 2019: I organized a learning seminar on Applied Invariant Theory.
Summer 2018: I organized, with Elina Robeva, a mini-symposium at the SIAM Annual meeting "Theoretical Challenges of Tensor Decomposition".
Summer 2018: I organized, with Andre Uschmajew and Bart Vandereycken, a mini-symposium in the SIAM Conference on Applied Linear Algebra, called "Tensors and Multilinear Algebra".
Summer 2017: I organized, with Elina Robeva, a mini-symposium in the SIAM Conference on Applied Algebraic Geometry, called "Tensors: From Algebra to Applications".
Spring 2017: I organized the workshop Interactions between Algebra and the Sciences with Jacinta Torres.
Fall 2016: I co-organized a tensors reading group Foundational Tensor Theory with Rockford Sison.
Fall 2015: I organized a Commutative Algebra reading group.
Summer 2013: I did a research project at Imperial College, London under the supervision of Mike Levin. We analysed biological pathways associated with susceptibility to inflammatory diseases.
Summer 2012: I attended the Kupcinet-Getz Program at the Weizmann Institute in Israel, working with Sergei Yakovenko on algebraic properties of local dynamics of intersections, see here.
Trinity 2020: Tutorials for Statistics and Data Analysis, The Queen's College, Oxford.
Spring 2018: GSI for Math 10B with Prof. Kelli Talaska, UC Berkeley.
Spring 2017: Head GSI for Math 10B with Prof. Craig Evans. A fun worksheet I made for the last class of the semester, UC Berkeley.
Spring 2016: I organized a Mathematical Biology reading group for a group of Berkeley undergraduate students.
Fall 2015: GSI for Math 10A with Prof. Richard Bamler, UC Berkeley.