Joe Kileel's Home Page

I am a Simons postdoc 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, where my thesis won best in applied mathematics.

My area is the mathematics of data science. Depending on the context, this involves numerical analysis, statistics, optimization and/or computational algebraic geometry. When thinking about an inverse problem or dataset, I seek to identify underlying algebraic or geometric structure to improve algorithms. My main results regard 3-D reconstruction in cryo-electron microscopy, low-rank tensor decomposition, and structure-from-motion in computer vision.

Fall 2020 I will be joining UT Austin’s Mathematics Department and Oden Institute as Assistant Professor. Here is my curriculum vitae.

- Fast moment inversion for cryo-EM and XFEL with uniform distribution of viewing angles (with C. Liu)

- Subspace power method for symmetric tensor decomposition and generalized PCA (with J. Pereira)
Submitted to Mathematical Programming

- Earthmover-based manifold learning for analyzing molecular conformation spaces (with N. Zelesko, A. Moscovich and A. Singer)
Accepted to IEEE International Symposium on Biomedical Imaging 2020   (code)

- Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles (with N. Sharon, Y. Khoo, B. Landa and A. Singer)
Inverse Problems 36 044003 (2020), pp. 1-40   (code)

- On the expressive power of deep polynomial neural networks (with M. Trager and J. Bruna)
Advances in Neural Information Processing Systems 2019, pp. 10310-10319   (code)

- Estimation under group actions: recovering orbits from invariants (with A. Bandeira, B. Blum-Smith, A. Perry, J. Weed and A. Wein)
Under revision, 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 (with J. Chen)
Journal of Software for Algebra and Geometry 9 (2019), pp. 55-63   (code)

- Distortion varieties (with Z. Kukelova, T. Pajdla and B. Sturmfels)
Foundations of Computational Mathematics 18 (2018), pp. 1043–1071  

- The Chow form of the essential variety in computer vision (with G. Fløystad and G. Ottaviani)
Journal of Symbolic Computation 86 (2018), pp. 97-119   (supplementary)

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

- 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  

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

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

Spring 2021:  Program on Tensor Methods and Emerging Applications to the Physical and Data Sciences (IPAM)
May 2020, postponed:  International Conference on Approximation Theory and Beyond (Vanderbilt)
May 2020, postponed:  SIAM Conference on Mathematics of Data Science (Cincinnati)
March 2020:  School of Mathematics Colloquium (Georgia Tech)
February 2020:  Applied Mathematics Division Colloquium (Brown)
February 2020:  Mathematics Department Colloquium (NYU Courant)
February 2020:  Mathematics Department Colloquium (Madison)
January 2020:  Mathematics Department Colloquium (Duke)
January 2020:  Mathematics Department Colloquium (Rutgers)
January 2020:  Mathematics Department Colloquium (Oden Institute, UT Austin)
January 2020:  Mathematics Department Colloquium (Toronto)
December 2019:  NeurIPS 2019 (Vancouver)
December 2019:  Joint Applied Mathematics/Statistics & Data Science Seminar (Yale)
November 2019:  Novel Medical Imaging Workshop (Texas A&M)
November 2019:  Linear Algebra Seminar (Auburn)
October 2019:  Computational Harmonic Analysis and Data Science Workshop (Oaxaca)
October 2019:  Algebra Seminar (U Washington)
October 2019:  SIAM Pacific Northwest Section Special Session (Seattle)
September 2019:  AMS Special Session (Madison)
August 2019:  Big Data Conference (Harvard)
August 2019:  Computational Cryo-EM Workshop (Center for Computational Mathematics, Flatiron)
July 2019:  SIAM Algebraic Geometry Conference (Bern)
May 2019:  Computational and Applied Mathematics Colloquium (UChicago)
May 2019:  Applied Algebra Seminar (Madison)
April 2019:  Algebra Seminar (Georgia Tech)
March 2019:  AMS Special Session (Auburn)
January 2019:  Algebraic Vision Research Cluster (ICERM)
December 2018:  Symbolic-Numeric Computing Seminar (CUNY)
November 2018:  Mathematics, Information and Computation Seminar (Center for Data Science, Courant)
November 2018:  Nonlinear Algebra Seminar (ICERM)
October 2018:  Math and Data Working Group (Center for Data Science, Courant)
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 (Georgia Tech)
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

209 Fine Hall,