Joe Kileel's Home Page



I am an Assistant Professor in the Department of Mathematics and Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin.

My research is in applied mathematics, computational algebra and data science. Specific areas of interest include: numerical tensor computations; inverse problems arising in scientific imaging and computer vision (particularly cryo-electron microscopy); and theory for non-convex optimization.

I am fortunate to have been a postdoc of Amit Singer and a PhD student of Bernd Sturmfels. Here is my curriculum vitae.

Papers
- Geometry and optimization of shallow polynomial networks (with Y. Arjevani, J. Bruna and M. Trager)
In-preparation

- Large-scale tensor decomposition: implicit subspace power method (with J. Pereira and T. Kolda)
In-preparation

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

- Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy (with E. Levin and N. Boumal)
Available on arXiv

- Landscape analysis of an improved power method for tensor decomposition (with T. Klock and J. Pereira)
Accepted to Advances in Neural Information Processing Systems 2021

- Symmetry breaking in symmetric tensor decomposition (with Y. Arjevani, J. Bruna, M. Field, M. Trager and F. Williams)
Available on arXiv

- Manifold learning with arbitrary norms (with A. Moscovich, N. Zelesko and A. Singer)
Journal of Fourier Analysis and Applications 27 82 (2021), pp. 1-56  

- Subspace power method for symmetric tensor decomposition and generalized PCA (with J. Pereira)
Available on arXiv

- Earthmover-based manifold learning for analyzing molecular conformation spaces (with N. Zelesko, A. Moscovich and A. Singer)
IEEE International Symposium on Biomedical Imaging 2020, pp. 1715-1719   (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)
Available on arXiv

- 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  


Teaching
Fall 2021:  Geometric methods in data science, instructor
Spring 2021:  Real analysis I, instructor
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


Travel
Fall 2022:  Program on Computational Microscopy (IPAM)
Summer 2022:  Combinatorial, Computational, and Applied Algebraic Geometry (Seattle)
March 2022:  AMS Special Session (Tufts)
February 2022:  IMA Data Science Seminar (U Minnesota)
November 2021, virtual:  Applied Mathematics Seminar (Yale)
November 2021:  SIAM TX-LA Minisymposium (Rio Grande Valley)
October 2021, virtual:  BIRS-CMO Workshop on Geometry & Learning from Data (Oaxaca)
October 2021:  Applied Mathematics Colloquium (U Chicago)
August 2021:  PACM, Princeton University
August 2021, virtual:  SIAM Conference on Applied Algebraic Geometry (Texas A&M)
June 2021, virtual:  Data Science Seminar (Oxford)
May 2021, virtual:  Tensors Seminar Series (IPAM)
Spring 2021, program fellow, virtual:  Program on Tensor Methods and Emerging Applications to the Physical and Data Sciences (IPAM)
March 2021, virtual:  Applied and Computational Mathematics Seminar (National University of Singapore)
March 2021, virtual:  SIAM Conference on Computational Science and Engineering (Fort Worth)
January 2021, virtual:  Tsinghua Sanya International Mathematics Forum
November 2020, virtual:  Geometry Seminar (Texas A&M)
November 2020, virtual:  Babuška Forum (Oden Institute, UT Austin)
November 2020, virtual:  DeepMath 2020
October 2020, virtual:  SIAM Annual Meeting, TX-LA Section (Texas A&M)
September 2020, virtual:  Algebraic Statistics Online Seminar
May 2020, postponed:  International Conference on Approximation Theory and Beyond (Vanderbilt)
May - June 2020, virtual:  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)


Address
Department of Mathematics, PMA 12.154

Oden Institute for Computational Engineering and Sciences, POB 3.434

University of Texas at Austin

jkileel@math.utexas.edu