## Portfolio item number 1

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Published in *International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC)*, 2012

We prove Humpert-Martin’s conjecture on the degree chromatic polynomial of a tree.

Recommended citation: Diego Cifuentes (2012). "On the degree-chromatic polynomial of a tree." *DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC)*, Nagoya, Japan. __https://dmtcs.episciences.org/3020__

Published in *ACM SIGCOMM*, 2013

Recommended citation: Swarun Kumar, Diego Cifuentes, Shyamnath Gollakota, and Dina Katabi (2013). "Bringing cross-layer MIMO to today’s wireless LANs." *Proceedings of the ACM SIGCOMM*, Hong Kong, China. __https://doi.org/10.1145/2534169.2486034__

Published in *Linear Algebra and its Applications*, 2016

A novel algorithm to compute permanents, mixed discriminants and hyperdeterminants of structured matrices and multidimensional arrays.

Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "An efficient tree decomposition method for permanents and mixed discriminants." *Linear Algebra and its Applications*. 493:45-81. __http://dx.doi.org/10.1016/j.laa.2015.12.004__

Published in *SIAM J. Discrete Math.*, 2016

We begin the study of how to exploit chordal structure in computational algebraic geometry, and in particular, for solving polynomial systems.

Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "Exploiting chordal structure in polynomials ideals: A Gröbner bases approach." *SIAM J. Discrete Math.*. 30(3):1534-1570. __http://dx.doi.org/10.1137/151002666__

Published in *SIAM J. Appl. Algebra Geometry*, 2017

We introduce a novel representation of structured polynomial ideals: chordal networks.

Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "Chordal networks of polynomial ideals." *SIAM J. Appl. Algebra Geometry*. 1(1):73-170. __http://dx.doi.org/10.1137/16M106995X__

Published in *SIAM J. Optimization*, 2017

A new SOS-based method for optimizing polynomials over algebraic varieties.

Recommended citation: Diego Cifuentes, Pablo Parrilo (2017). "Sampling algebraic varieties for sum of squares programs." *SIAM J. Optimization*. 27(4):2381-2404. __https://doi.org/10.1137/15M1052548__

Published in *preprint*, 2017

SDP relaxations provide a tractable alternative for polynomial optimization problems. We study sufficient conditions for stability of these relaxations.

Recommended citation: Diego Cifuentes, Sameer Agarwal, Pablo Parrilo, Rekha Thomas (2017). "On the local stability of semidefinite relaxations." *arXiv:1710.04287*. __https://arxiv.org/abs/1710.04287__

Published in *J. Software Algebra Geom.*, 2018

Introducing a Macaulay2 package for sums of squares problems.

Recommended citation: Diego Cifuentes, Thomas Kahle, Pablo Parrilo (2020). "Sums of squares in Macaulay2." *J. Software Algebra Geom*. 10(1):17--24 __https://doi.org/10.2140/jsag.2020.10.17__

Published in *preprint*, 2019

We investigate the complexity of problems such as normal forms, Gröbner basis and Graver basis

Recommended citation: Diego Cifuentes, Shmuel Onn (2019). "On the Complexity of Toric Ideals." *arXiv:1902.01484*. __https://arxiv.org/abs/1902.01484__

Published in *preprint*, 2019

We prove global guarantees for the Burer-Monteiro method in general SDPs

Recommended citation: Diego Cifuentes (2021). "On the Burer-Monteiro method for general semidefinite programs." *Optimization Letters*, https://doi.org/10.1007/s11590-021-01705-4 __https://doi.org/10.1007/s11590-021-01705-4__

Published in *preprint*, 2019

We propose a novel SDP relaxation for computing rank deficient matrices in an affine subspace

Recommended citation: Diego Cifuentes (2019). "A convex relaxation to compute the nearest structured rank deficient matrix." *arXiv:1904.09661*. __https://arxiv.org/abs/1904.09661__

Published in *preprint*, 2019

We prove that the Burer-Monteiro method can solve SDPs in polynomial time

Recommended citation: Diego Cifuentes, Ankur Moitra (2019). "Polynomial time guarantees for the Burer-Monteiro method." *arXiv:1904.07147*. __https://arxiv.org/abs/1912.01745__

Published in *Mathematical Programming*, 2020

We study the set of objective functions for which SDP relaxations are exact.

Recommended citation: Diego Cifuentes, Corey Harris, Bernd Sturmfels (2020). "The geometry of SDP exactness in quadratic optimization." *Mathematical Programming*. 182:399-428. __https://doi.org/10.1007/s10107-019-01399-8__

Published in * J. Symbolic Computation*, 2020

We study the Voronoi decomposition determined by a real algebraic variety.

Recommended citation: Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels, Madeleine Weinstein (2020). "Voronoi Cells of Varieties." *J. Symbolic Computation, Special Issue on MEGA 2019*. __https://doi.org/10.1016/j.jsc.2020.07.009__

Published in *preprint*, 2020

We prove that a classical computer can efficiently sample from a quantum GBS system given by a shallow, local circuit.

Recommended citation: Haoyu Qi, Diego Cifuentes, Kamil Brádler, Robert Israel, Timjan Kalajdzievski, Nicolás Quesada (2020). "Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions." *arXiv:2009.11824*. __https://arxiv.org/abs/2009.11824__

*Matlab*, 2016

Download: “zip”, “tar.gz”. Github: sparse-permanents

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Math olympiads, *Universidad Antonio Nariño*, 2010

Instructor of Algebra, Combinatorics and Geometry at the Colombian Math Olympiads during 2010–2012.

Undergraduate course, *Universidad de los Andes*, 2010

Mathematical concepts for electrical engineering, such as calculus of complex variable, partial differential equations and numerical methods.

Undergraduate course, *Universidad de los Andes*, 2011

A first course in linear algebra.

Undergraduate course, *MIT EECS*, 2014

Elementary discrete mathematics for computer science and engineering. Emphasis on mathematical definitions and proofs as well as on applicable methods.

Graduate course, *MIT EECS*, 2014

Introduction to linear optimization and its extensions, emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems.

Graduate course, *MIT EECS*, 2016

Research-oriented course, focused on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities, with particular emphasis on the connections with semidefinite optimization.

Graduate course, *MIT EECS*, 2017

Graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations.

Undergraduate course, *MIT Math*, 2018

Calculus of several variables. The honors section puts more focus on mathematical concepts.

Undergraduate course, *MIT Math*, 2019

Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming. This is a communication intensive subject.

Undergraduate course, *MIT Math*, 2019

Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming.

Undergraduate course, *MIT Math*, 2020

Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.

Undergraduate course, *MIT Math*, 2020

Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming.