Kevin Shu's Personal Website

About

I'm a postdoctoral researcher in the CMS department at Caltech, under the supervision of Venkat Chandrasekaran. My main interests are on the intersection between convex geometry and algebraic geometry. I like any question that relates to optimization of things with algebraic structure.

I received a PhD in Algorithms, Combinatorics and Optimization at Georgia Tech, where I was grateful to be advised by Greg Blekherman.

In addition to mathematics, I also make computers do things (like rendering this website here), crocheting and rock climbing.

I do have a github, but it is not very well curated. That is also where this website is hosted.

Preprints

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Accelerated Gradient Descent via Long Steps
Ben Grimmer, Kevin Shu, Alex Wang
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Symmetric Hyperbolic Polynomials
Greg Blekherman, Julia Lindberg, Kevin Shu
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Quadratic Programming with Sparsity Constraints via Polynomial Roots
Kevin Shu
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On Computational Equivalence of Some Definitions of P-matrices
Kevin Shu, Spencer Gordon
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Approximate PSD-Completion for Generalized Chordal Graphs
Kevin Shu
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Extreme Nonnegative Quadratics over Stanley Reisner Varieties
Kevin Shu

Publications

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Hidden convexity, optimization, and algorithms on rotation matrices
Akshay Ramachandran, Kevin Shu, Alex Wang
Published in Mathematics of Operations Research, 2024
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Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment
Grigoriy Blekherman, Mario Kummer, Raman Sanyal, Kevin Shu, Shengding Sun
Published in International Mathematics Research Notices, 2022
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Hyperbolic Relaxation of k-Locally Positive Semidefinite Matrices
Grigoriy Blekherman, Santanu S. Dey, Kevin Shu, Shengding Sun
Published by the SIAM Journal for Optimization, 2022
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Sums of Squares and Sparse Semidefinite Programming
Grigoriy Blekherman, Kevin Shu
Published by the SIAM Journal for Applied Algebra and Geometry, 2021
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Syntactic Structures and Code Parameters
Matilde Marcolli, Kevin Shu
Published in Mathematics in Computer Science, March 2017

Presentations

📺
Symmetric Hyperbolic Polynomials
Presented at the SIAM Conference on Applied Algebraic Geometry, 2023.
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Sparse Regression and PCA via Polynomial Roots
Presented at the SIAM Conference on Optimization, 2023.
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Hyperbolicity Cones and Sparse Optimization
Presented at the MIT LIDS seminar , 2023.
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Symmetrically Hyperbolic Polynomials
Presented at the Öberwolfach Workshop on New Directions in Algebraic Geometry, 2023.
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Sparse Quadratic Programs via Polynomial Roots
Presented at the Carnegie Mellon University ACO seminar, 2023.
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Nonnegative Quadratics on Stanley Reisner Varieties
Presented at the the University of Wisconsin Madison Applied Algebra Seminar.
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Approximating Sparse Semidefinite Programs
Presented at INFORMS 2021.
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Poster on Sparse Semidefinite Programs
Presented at the MIP and IPCO conferences in 2021.
Won honorable mentions in both poster competitions
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Causal Inference and Optimization
Presented at the ACO Student Seminar in 2021.
📺
Lightning Talk on Hyperbolic Relaxations of Locally Matrices.
Presented at the ICERM - Symmetry, Randomness, and Computations in Real Algebraic Geometry in 2020.

Blog

The main content of the blog can be found here

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There is now an animated version of one of my blogposts on Brickman's theorem available here

The first post on this blog is about this online fractal generator, an example of which is the following:

Resumé

A PDF copy of my resumé can be found here.

Contact

✉ kshu AT caltech.edu

𜳒 Annenberg Building 315, Pasadena, California