Joe Kileel's Home Page

I am an assistant professor at UT Austin in the Department of Mathematics, Oden Institute for Computational Engineering and Sciences and Machine Learning Laboratory.

I work in applied mathematics and computational algebra. Specifically I am interested in: higher-order tensor methods; 3D reconstruction in imaging; and nonconvex optimization landscapes. My research is supported by the NSF.

Previously I was a postdoc at Princeton with
Amit Singer, and a graduate student at Berkeley with Bernd Sturmfels. Here is my CV.

- Fast expansion into harmonics on the ball
with N. Marshall, O. Mickelin, A. Singer
available on arXiv

- Covering number of real algebraic varieties and beyond: Improved bounds and applications
with Y. Zhang
available on arXiv

- Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC
with H. Fan, B. Kimia
available on arXiv

- Snapshot of algebraic vision
with K. Kohn
available on arXiv

- Tensor moments of Gaussian mixture models: theory and applications
with J. Pereira, T. Kolda
available on arXiv   (code)

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

- Scalable symmetric Tucker tensor decomposition
with R. Jin, T. Kolda, R. Ward
SIAM Journal on Matrix Analysis and Applications, to appear

- Algebraic constraints and algorithms for common lines in cryo-EM
with T. Muller, A. Duncan, E. Verbeke
Biological Imaging, 2024

- The G-invariant graph Laplacian Part I: Convergence rate and eigendecomposition
with E. Rosen, P. Hoyos, X. Cheng, Y. Shkolnisky
Applied and Computational Harmonic Analysis, 2024

- The effect of smooth parametrizations on nonconvex optimization landscapes
with E. Levin, N. Boumal
Mathematical Programming, 2024

- Moment-based metrics for molecules computable from cryo-EM images
with A. Zhang, O. Mickelin, E. Verbeke, N. Marshall, M. Gilles, A. Singer
Biological Imaging, 2024

- Moment estimation for nonparametric mixture models through implicit tensor decomposition
with Y. Zhang
SIAM Journal on Mathematics of Data Science, 2023

- Moment varieties for mixtures of products
with Y. Alexandr, B. Sturmfels
ACM International Symposium on Symbolic and Algebraic Computation, 2023

- Autocorrelation analysis for cryo-EM with sparsity constraints: improved sample complexity and projection-based algorithms
with T. Bendory, Y. Khoo, O. Mickelin, A. Singer
Proceedings of the National Academy of Sciences, 2023

- Estimation under group actions: recovering orbits from invariants
with A. Bandeira, B. Blum-Smith, A. Perry, J. Weed, A. Wein
Applied and Computational Harmonic Analysis, 2023  
Charles Chui Young Researcher Best Paper Award

- On the instability of relative pose estimation and RANSAC's role
with H. Fan, B. Kimia
IEEE Conference on Computer Vision and Pattern Recognition, 2022

- Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy
with E. Levin, N. Boumal
Mathematical Programming, 2022

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

- Manifold learning with arbitrary norms
with A. Moscovich, N. Zelesko, A. Singer
Journal of Fourier Analysis and Applications, 2021  

- Earthmover-based manifold learning for analyzing molecular conformation spaces
with N. Zelesko, A. Moscovich, A. Singer
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, A. Singer
Inverse Problems, 2020   (code)

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

- Numerical implicitization
with J. Chen
Journal of Software for Algebra and Geometry, 2019  (code)

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

- Distortion varieties
with Z. Kukelova, T. Pajdla, B. Sturmfels
Foundations of Computational Mathematics, 2018  

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

- Algebraic geometry for computer vision
University of California, Berkeley, Ph.D. thesis, May 2017
Bernard Friedman Memorial Prize for Best Thesis in Applied Mathematics

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

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

- Rigid multiview varieties
with M. Joswig, B. Sturmfels, A. Wagner
International Journal of Algebra and Computation, 2016  

- Hadamard products of linear spaces
with C. Bocci, E. Carlini
Journal of Algebra, 2016  

Fall 2024:  Calculus I
Spring 2024:  Foundational techniques of machine learning and data sciences
Fall 2023:  Scientific computation in numerical analysis
Spring 2023:  Foundational techniques of machine learning and data sciences
Spring 2022:  Scientific computation in numerical analysis
Fall 2021:  Geometric methods in data science
Spring 2021:  Real analysis I

Julia Lindberg: Bing instructor, Math Dept, January 2023-present

Gabriel Brown: CSEM Ph.D. student, July 2023-present

Addie Duncan: Math Ph.D. student, November 2023-present

Paulina Hoyos: Math Ph.D. student, September 2022-present

Elzbieta Polak: Math Ph.D. student, July 2021-present

Yifan Zhang: CSEM Ph.D. student, January 2021-present

George D. Torres: Math Ph.D. student, June 2022-August 2023, co-advised with Ngoc Tran (subsequently: research scientist at Striveworks)

João M. Pereira: Postdoc, Oden Institute, January 2021-May 2022, co-mentored with Rachel Ward (subsequently: assistant professor at IMPA, Brazil)

Bronson Zhou: Math undergraduate researcher, 2021-2022 (subsequently: Ph.D. student at Yale)

January 2025:  JMM Special Sessions (Seattle)
December 2024:  IMS International Conference on Statistics and Data Science (Nice)
October 2024:  SIAM Conference on Mathematics of Data Science (Atlanta)
October 2024:  SIAM TX-LA Meeting (Baylor)
September 2024:  Workshop on Computational Harmonic Analysis in Data Science and Machine Learning (Oaxaca)
September 2024:  AMS Section Meeting (San Antonio)
July 2024:  International Symposium on Mathematical Programming (Montreal)
July 2024:  NSF CompMath PI Meeting (U Washington)
March 2024:  Joint Mathematics of Data & Decisions and Algebraic Geometry Seminar (UC Davis)
March 2024, virtual:  Codes and Expansions (CodEx) Seminar
January 2024:  Winter Program in Machine Learning (UT Austin)
January 2024:  Topical Workshop on Higher-Order Statistics and Symmetric Tensors (ICERM)
January 2024:  JMM Special Session (San Francisco)
December 2023:  Bayesian Statistics and Statistical Learning Workshop (IMSI)
November 2023, virtual:  PSU-Purdue-UMD Joint Seminar on Mathematical Data Science
November 2023:  SIAM TX-LA Meeting (Lafayette)
October 2023:  FFT Conference (Maryland)
September 2023:  Tutorial Lecture (IMSI)
September 2023, virtual:  BIRS Workshop (Banff)
August 2023:  ICIAM 2023 Minisymposium (Tokyo)
July 2023:  SIAM Conference on Applied Algebraic Geometry (Eindhoven)
June 2023:  SIAM Conference on Optimization (Seattle)
May 2023:  Casa Matemática Oaxaca Workshop (Mexico)
May 2023:  Oden Institute Seminar (UT Austin)
February 2023:  SIAM Conference on Computational Science and Engineering (Amsterdam)
February 2023, virtual:  Topics in Algebra, Topology, Etc., Research Seminar (Boise)
January 2023:  Alan Turing / Oden Institutes Workshop (London)
January 2023:  Visit D. Edidin and Colloquium (Missouri)
January 2023:  JMM Special Session (Boston)
December 2022:  Mathematics Department Colloquium (UT Austin)
November 2022:  Applied and Computational Mathematics Colloquium (Princeton)
November 2022:  Instituto Nacional de Matemática Pura e Aplicada (Brazil)
October 2022, virtual:  Mathematical Machine Learning Seminar (MPI MIS + UCLA)
September 2022, virtual:  SIAM Conference on Mathematics of Data Science (San Diego)
September 2022:  ML + X Seminar (IFML, UT Austin)
September 2022:  PACM, Princeton University
Fall 2022, program fellow:  Program on Computational Microscopy (IPAM)
Summer 2022:  Combinatorial, Computational, and Applied Algebraic Geometry (Seattle)
May 2022:  Mathematical and Computational Challenges in Cryogenic Electron Microscopy (UBC)
March 2022, virtual:  AMS Special Session (Tufts)
February 2022:  IMA Data Science Seminar (U Minnesota)
January 2021, virtual:  Algebraic Geometry Seminar (UC Davis)
December 2021, virtual:  NeurIPS 2021
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)

Department of Mathematics, PMA 12.154

Oden Institute for Computational Engineering and Sciences, POB 3.434

University of Texas at Austin