Joe Kileel's Home Page

I am a post-doc in the Program in Applied and Computational Mathematics, Princeton University, working with Amit Singer. In 2017, I completed my PhD in mathematics at UC Berkeley, under the supervision of Bernd Sturmfels. In 2012, I received a BA/MMath from the University of Cambridge.

I am broadly interested in interactions between applied math and computational algebraic geometry.

My current research is on developing algorithms for scientific and engineering problems with strong algebraic character. Specific focuses are:

To these ends, I employ such tools as invariant theory, representation theory, numerical homotopy continuation, automatic Gröbner basis generation, manifold optimization and structured tensor decomposition.

I acknowledge support from the Simons Collaboration on Algorithms and Geometry.

- Estimation under group actions: recovering orbits from invariants (with A. Bandeira, B. Blum-Smith, A. Perry, J. Weed and A. Wein)
Submitted to Journal of the American Mathematics Society

- 3D ab initio modeling in cryo-EM by autocorrelation analysis (with E. Levin, T. Bendory, N. Boumal and A. Singer)
IEEE International Symposium on Biomedical Imaging 2018, pp. 1569-1573   (code)

- Algebraic geometry for computer vision
University of California, Berkeley, PhD thesis, 139 pages, May 2017
Bernard Friedman Memorial Prize for Best Thesis in Applied Mathematics

- Numerical implicitization for Macaulay2 (with J. Chen)
Submitted to Journal of Software for Algebra and Geometry   (code)

- Distortion varieties (with Z. Kukelova, T. Pajdla and B. Sturmfels)
Foundations of Computational Mathematics, online first   (slides)

- The Chow form of the essential variety in computer vision (with G. Fl√łystad and G. Ottaviani)
Journal of Symbolic Computation 86 (2018) pp. 97-119   (slides)   (formulas)

- Minimal problems for the calibrated trifocal variety
SIAM Journal on Applied Algebra and Geometry 1 (2017) pp. 575-598   (slides)   (instances)

- A clever elimination strategy for efficient minimal solvers (with Z. Kukelova, B. Sturmfels and T. Pajdla)
IEEE Conference on Computer Vision and Pattern Recognition 2017, pp. 3605-3614

- Rigid multiview varieties (with M. Joswig, B. Sturmfels and A. Wagner)
International Journal of Algebra and Computation 26 (2016) pp. 775-788   (slides)   (poster)

- Hadamard products of linear spaces (with C. Bocci and E. Carlini)
Journal of Algebra 448 (2016) pp. 595-617   (poster)

Spring 2017:  Introduction to optimization, consultant
May 2016:  Outstanding Graduate Student Instructor Award
Spring 2016:  Tropical geometry, grader and guest lecturer
Spring 2016:  Analytic geometry and calculus, TA
Fall 2015:  Methods of mathematics: calculus, statistics and combinatorics, TA
Spring 2015:  Methods of mathematics: calculus, statistics and combinatorics, TA
Fall 2014:  Calculus, TA

October 2018:  AMS Special Session (Ann Arbor)
October 2018:  Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Schloss Dagstuhl)
October 2018:  Joint KMS-DMV Mathematics Conference (Seoul)
August 2018:  Numerical Computing in Algebraic Geometry (MPI Leipzig)
June 2018:  Optimization, Complexity and Invariant Theory Workshop (IAS)
March 2018:  SIAM Southeastern Atlantic Sectional Conference (UNC)
December 2017:  Mathematics, Information and Computation Seminar (Center for Data Science, Courant)
December 2017:  Lecture Series on Algebraic Vision (Seoul National University)
August 2017:  Summer School on Random Matrices (Columbia U)
August 2017:  SIAM Algebraic Geometry Conference (GeorgiaTech)
July 2017:  Minicourse on Algebraic Vision (Tübingen)
June - July 2017:  Center for Machine Perception, Czech Technical University in Prague
June 2017:  Computer Vision and Machine Learning Seminar (INRIA-Paris)
May 2017:  A View Toward Algebraic Geometry, Eisenbud Birthday Conference (Martha's Vineyard)
April 2017:  AMS Special Session (Washington State)
April 2017:  Experimental Mathematics Seminar (Rutgers)
March, April 2017:  Simons Collaboration Meetings on Algorithms and Geometry (New York)
February 2017:   Mathematics Department Colloquium (Saskatchewan)
October - December 2016:  Max Planck Institute for Mathematics in the Sciences (Leipzig)
November 2016:  Algebraic Geometry Seminar (Chemnitz)
November 2016:  Diskrete Mathematik, Geometrie und Optimierung Seminar (Frankfurt)
November 2016:   AMS Special Session (NCSU)
October 2016:  Computing & Mathematical Sciences Seminar (Caltech)
October 2016:  Czech Workshop on Applied Mathematics in Engineering (Prague)
September 2016:   Algebra Seminar (GeorgiaTech)
May - September 2016:   Laboratory for Analysis and Architecture of Systems (Toulouse)
May 2016:  Workshop on Software and Applications of Numerical Algebraic Geometry (Notre Dame)
May 2016:  AIM Workshop on Algebraic Vision (San Jose)
April 2016:  Applied Algebra Days 3 (Madison)
April 2016:  Algebraic Geometry Seminar (UChicago)
April 2016:  AMS Special Session (Utah)
January 2016:  Joint Mathematics Meetings (Seattle)
October 2015:  Western Algebraic Geometry Symposium (Seattle)
October 2015:  London Algebra Colloquium (Queen Mary)
October 2015:  Algebraic Vision (TU Berlin)
August 2015:  SIAM Algebraic Geometry Conference (Daejeon)
June 2015:  Effective Methods in Algebraic Geometry (Trento)
May 2015:  Workshop on Nonlinear Algebra (Berlin)
May 2015:  Tropical Doener Workshop (FU Berlin)
May 2015:  Department of Mathematics, University of Oslo
October 2014:  Western Algebraic Geometry Symposium (Idaho)
July - August 2014:  Modern Applications of Representation Theory (UChicago)
June 2014:  Macaulay2 Summer School and Conference (UIUC)
June 2014:  Computational Nonlinear Algebra (ICERM)

Program in Applied and Computational Mathematics

Princeton University, Princeton, NJ 08544

213 Fine Hall,