Rafael Oliveira

Rafael Oliveira

Assistant Professor of Computer Science

University of Waterloo

I am an Assistant Professor in the Cheriton School of Computer Science with a cross appointment in the Pure Math department at the University of Waterloo.

Interests

  • Algebraic Complexity
  • Complexity Theory
  • Optimization
  • Invariant Theory
  • Algebraic Geometry
  • Commutative Algebra
  • Extremal Combinatorics

Education

  • PhD in Computer Science, 2012-2017

    Princeton University

  • MEng in Computer Science, 2011-2012

    Massachusetts Institute of Technology

  • BSc in Mathematics, 2007-2011

    Massachusetts Institute of Technology

  • BSc in Electrical Engineering and Computer Science, 2007-2011

    Massachusetts Institute of Technology

Group

Postdocs

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Akash K Sengupta

Postdoctoral Fellow

Algebraic Geometry, Number Theory, Algebraic Complexity

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Robert Andrews

Postdoctoral Fellow

Algebraic Complexity, Complexity Theory

PhD Students

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Abhibhav Garg

PhD Student

Algebraic Complexity, Algebraic Geometry

Masters Students

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Daniel Santana

Masters Student

Post-Quantum Cryptography, Cybersecurity

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John Smith

Masters Student

Algebraic Complexity, Analytic Combinatorics

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Omkar Baraskar

Masters Student

Algebraic Complexity, Quantum Computation

Undergraduate Students

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Tam An Le Quang

Student

Algebraic Complexity, Algebraic Geometry





Alumni >

Publications

Quickly discover relevant content by filtering publications.
Strong Algebras and Radical Sylvester-Gallai Configurations
Rafael Oliveira, Akash K Sengupta
56th ACM Symposium on Theory of Computing, STOC 2024
PDF
Radical Sylvester-Gallai Theorem for Tuples of Quadratics
Abhibhav Garg, Rafael Oliveira, Shir Peleg, Akash K Sengupta
38th Computational Complexity Conference, CCC 2023
PDF
Radical Sylvester-Gallai Theorem for Cubics
Rafael Oliveira, Akash K Sengupta
63rd IEEE Symposium on Foundations of Computer Science, FOCS 2022
PDF
Robust Radical Sylvester-Gallai Theorem for Quadratics
Abhibhav Garg, Rafael Oliveira, Akash K Sengupta
38th International Symposium on Computational Geometry, SoCG 2022
PDF
Scaling problems, algorithms and applications to computer science and statistics
Rafael Oliveira, Akshay Ramachandran
Survey, 33o Coloquio Brasileiro de Matematica
PDF
Near-Optimal Sample Complexity for Matrix and Tensor Normal Models via Geodesic Convexity
Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter
Submitted, 2021
PDF
Conditional Lower Bounds on the Spectrahedral Representation of Explicit Hyperbolicity Cones
Rafael Oliveira
45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020
PDF
Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings
Ankit Garg, Christian Ikenmeyer, Visu Makam, Rafael Oliveira, Michael Walter, Avi Wigderson
Computational Complexity Conference, CCC 2020
PDF
Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and moment polytopes
Peter Buergisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
60th Annual Symposium on Foundations of Computer Science, FOCS 2019
PDF
More barriers for rank methods, via a "numeric to symbolic"" transfer
Ankit Garg, Visu Makam, Rafael Oliveira, Avi Wigderson
60th Annual Symposium on Foundations of Computer Science, FOCS 2019
PDF
See all publications

Talks

Radical Sylvester-Gallai theorem for cubics - and beyond

Mar 2, 2023 IIT Kanpur
Slides

Computational Variants of the General Lax Conjecture

Hyperbolicity cones are convex semialgebraic sets generalizing both polyhedral and spectrahedral cones, the latter forming the basic …

Mar 1, 2023 IIT Kanpur
Slides

Radical Sylvester-Gallai theorem for cubics - and beyond

In 1893, Sylvester asked a basic question in combinatorial geometry: given a finite set of distinct points v1,…,vm∈ℝN such that the …

Feb 24, 2023 IIT Bombay
Slides

Computational Variants of the General Lax Conjecture

Hyperbolicity cones are convex semialgebraic sets generalizing both polyhedral and spectrahedral cones, the latter forming the basic …

Feb 20, 2023 TIFR
Slides Video

Radical Sylvester-Gallai theorem for cubics - and beyond

In 1893, Sylvester asked a basic question in combinatorial geometry: given a finite set of distinct points v1,…,vm∈ℝN such that the …

May 13, 2022 University of Waterloo
Slides
See all talks

Prospective Students

I am currently accepting new students who have a strong mathematical background and are interested in the following areas and their connections to other scientific areas:

  • Complexity Theory
  • Algebraic Complexity Theory
  • Computational Algebra
  • Computational Invariant Theory
  • Optimization
  • Computational Algebraic Geometry
  • Convex Algebraic Geometry
  • Coding Theory
  • Symbolic Computation

If you would like to apply please send your application directly to the School of Computer Science and mention that you are interested in working with me in your application.

To Undergraduates Looking for Research Opportunities

I am happy to learn that you are interested in one of my research projects!

Before you contact me, please carefully read the detailed description of the project you are interested in, including the background material that I am asking from applicants. Also please continue reading!

The best way to work with me is for us to first start working on a problem via an URA or for you to do a final project for one of my classes, and that could develop into a research project in a future term.

I will only consider students directly to URFs if they have an outstanding background, which includes solid command of more advanced material than the prerequisites and/or great performance in mathematics/informatics/physics olympiads.

Current Open Projects

Research Programs by U Waterloo

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