Organizing Committee
Abstract

This workshop will focus on techniques and structures in real algebraic geometry and optimization, including computational tools for semi-algebraic sets, semidefinite programming techniques for polynomial optimization, and applications of these tools to problems in computer vision. Real algebraic geometry provides powerful tools to analyze the behavior of optimization problems, the geometry of feasible sets, and to develop new relaxations for hard non-convex problems. On the other hand, numerical solvers for semidefinite programs have led to new fast algorithms in real algebraic geometry. Algebraic methods over the real numbers are essential for many real-world applications. This workshop aims to explore the cutting edge of techniques in real algebraic geometry and convex optimization as well as applications of these tools to problems in computer vision and other information sciences.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee

Workshop Schedule

Monday, October 15, 2018
TimeEventLocationMaterials
8:30 - 8:55Registration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Real Geometry of Matrix Completion - Rainer Sinn, FU Berlin11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15On Convexity of Polynomials over a Box - Georgina Hall, INSEAD Business School11th Floor Lecture Hall
11:30 - 12:15Learning Paths from Signature Tensors - Anna Seigal, UC Berkeley11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:45 - 3:30Lowerbounds on semidefinite representations of hyperbolic programs - Nikhil Srivastava, UC Berkeley11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Strict Complementarity in Convex Algebraic Geometry (with a focus on Elliptopes) - Levent Tuncel, University of Waterloo11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, October 16, 2018
TimeEventLocationMaterials
9:00 - 9:45On the stability of semidefinite relaxations - Diego Cifuentes, MIT11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15The Geometry of SDP-Exactness in Quadratic Optimization - Bernd Sturmfels, MPI Leipzig11th Floor Lecture Hall
11:30 - 12:15Certificates of polynomial nonnegativity via hyperbolic optimization - James Saunderson, Monash University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Negative dependence and Hodge-Riemann relations - Petter Branden, KTH Royal Institute of Technology11th Floor Lecture Hall
3:30 - 5:00Coffee/Tea Break and Poster Session11th Floor Collaborative Space 
Wednesday, October 17, 2018
TimeEventLocationMaterials
9:00 - 9:45Fast algebraic solvers for computer vision problems - Zuzana Kúkelová, Czech Technical University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Camera Configurations and Viewing Graphs - Matthew Trager, NYU11th Floor Lecture Hall
11:30 - 12:15Towards algorithms for analyzing the topology of semi-algebraic sets - Mohab Safey El Din, Sorbonne University11th Floor Lecture Hall
12:30 - 12:40Group Photo11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Pythagoras numbers of projective varieties - Mauricio Velasco, Universidad de Los Andes11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Convex sets without representation as spectrahedral shadow - Claus Scheiderer, Universität Konstanz11th Floor Lecture Hall
Thursday, October 18, 2018
TimeEventLocationMaterials
9:00 - 9:45Large Graphs and Symmetric Sums of Squares - Annie Raymond, University of Washington11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15The Tale of One Variety (And Its Family) - Alexander Razborov, University of Chicago11th Floor Lecture Hall
11:30 - 12:15Lower Bounds on Sums-of-Squares Proof-Size - Albert Atserias, Universitat Politècnica de Catalunya11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Spectral Algorithms Capture Sum-of-Squares on Average - Tselil Schramm, Harvard University and MIT11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Efficient Algorithms for Distributional Problems via Sum-of-Squares Proofs - Pravesh Kothari, Institute for Advanced Study and Princeton University11th Floor Lecture Hall
Friday, October 19, 2018
TimeEventLocationMaterials
9:00 - 9:45Non-commutative Sums of Squares in Quantum Information - Sabine Burgdorf, University of Konstanz11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15The Paulsen Problem Made Simple - Ankur Moitra, MIT11th Floor Lecture Hall
11:30 - 12:15Slack variety of a polytope and its applications - João Gouveia, University of Coimbra11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Polyhedral approximations of the positive semidefinite cone - Hamza Fawzi, University of Cambridge11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45An Experimental Comparison of SONC and SOS Certificates for Unconstrained Optimization - Timo de Wolff, Technical University Berlin11th Floor Lecture Hall

Associated Semester Workshops

Nonlinear Algebra
Nonlinear Algebra Image
Nonlinear Algebra Bootcamp
Nonlinear Algebra Bootcamp Image
Core Computational Methods
Core Computational Methods Image
Nonlinear Algebra in Applications
Nonlinear Algebra in Applications Image

Lecture Videos

Efficient Algorithms for Distributional Problems via Sum-of-Squares Proofs

Pravesh Kothari
Institute for Advanced Study and Princeton University
October 18, 2018

Lower Bounds on Sums-of-Squares Proof-Size

Albert Atserias
Universitat Politècnica de Catalunya
October 18, 2018

The Tale of One Variety (And Its Family)

Alexander Razborov
University of Chicago
October 18, 2018

Large Graphs and Symmetric Sums of Squares

Annie Raymond
University of Massachusetts, Amherst
October 18, 2018

Pythagoras numbers of projective varieties

Mauricio Velasco
Universidad de Los Andes
October 17, 2018

Fast algebraic solvers for computer vision problems

Zuzana Kúkelová
Czech Technical University
October 17, 2018

Negative dependence and Hodge-Riemann relations

Petter Branden
KTH Royal Institute of Technology
October 16, 2018

On Convexity of Polynomials over a Box

Georgina Hall
INSEAD Business School
October 15, 2018