Shengding Sun's website

Hello! I am currently a research associate in Department of Applied Mathematics and Theoretical Physics, University of Cambridge

I received my Bachelor of Science degree at UNC Chapel Hill

I received my Ph.D. degree in Algorithm, Combinatorics and Optimization at Georgia Tech. co-advised by  Dr. Greg Blekherman and Dr. Santanu S. Dey

Research Interest

Convex and real algebraic geometry; polynomial, semidefinite and descrete optimization; applications to quantum physics.

Personal Info


Phone: 919-370-1057 (US), 01223-337904 (UK)

Office location: F1.20, Centre of Mathematical Sciences (CMS), University of Cambridge 


F. Kılınç-Karzan, S. Sun. On the strength of Burer's lifted convex relaxation to quadratic programming with ball constraints. Submitted. 

G. Blekherman, S. Dey, S. Sun. Aggregations of quadratic inequalities and hyperplane hidden convexity. SIAM Journal of Optimization, 34.1 (2024), 98-126, doi: 10.1137/22M1528215

G. Blekherman, M, Kummer, R. Sanyal, K, Shu, S. Sun. Linear principal minor polynomials: hyperbolic determinantal inequalities and spectral containment. International Mathematics Research Notices, rnac291,

M. Farhadi, S. Gupta, S. Sun, P. Tetali, M. Wigal. Hardness and approximation of submodular minimum linear ordering problems. Mathematical Programming, (2023), doi: 10.1007/s10107-023-02038-z

G. Blekherman, S. Dey, K. Shu, S. Sun. Hyperbolic relaxation of k-locally positive semidefinite matrices. SIAM Journal of Optimization, 32:2 (2021), 470-490, doi: 10.1137/20M1387407

G. Blekherman, S. Dey, M. Molinaro, S. Sun. Sparse PSD approximation of the PSD cone. Mathematical Programming, 191 (2022), 981-1004, doi: 10.1007/s10107-020-01578-y

Conference Presentations

Poster: Aggregations of quadratic inequalities and hyperplane hidden convexity. Young Researchers Workshop 2022. Ithaca, NY.

Short talk: A new perspective of classical linear algebra using hyperbolic polynomials. International Conference on Continuous Optimization (ICCOPT) 2022. Bethelem, PA.

Poster: Generalizing determinantal inequalities using hyperbolic polynomials. Combinatorial, Computational, and Applied Algebraic Geometry (CCAAGS) 2022. Seattle, WA.

Poster: Hyperbolic relaxation of k-locally PSD matrices. Young Researchers Workshop 2021. Ithaca, NY.

Poster: Hyperbolic relaxation of locally PSD matrices. Integer Programming and Combinatorial Optimization 2021. Atlanta, GA.

Short talk: Negative eigenvalues of locally PSD matrices. SIAM Conference on Applied Algebraic Geometry (SIAM-AG) 2021, online.

Poster: Sparse PSD approximation of the PSD cone. Mixed Integer Programming Workshop (MIP) 2020, online. 


Summer 2022: Teaching Assistant for MSRI-BIRS Summer School in Sum of Squares, Kelowna, BC

Spring 2022: Instructor of MATH 3012 Applied Combinatorics

2018-2022: Teaching Assistant for Linear Algebra, Multivariable Calculus, Finite Mathematics