Joe Kileel's Home Page



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

My research focuses on mathematical methods for data analysis and scientific computing, drawing on ideas from geometry and computational algebra. Current topics are tensor methods, inverse problems in imaging, and nonconvex optimization landscapes. I receive research support from NSF, DOE, and the Sloan Foundation.

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

Papers
- Group invariant spectral embedding
with Y. Vigder, P. Hoyos, D. Thong, J. Andén, A. Moscovich
available on arXiv

- Testing the mixture model hypothesis via spectral gap
with M. Boedihardjo, V. Tombs
available on arXiv

- Multi-context principal component analysis
with K. Wang, S. Bhate, J. Pereira, M. Figlerowicz, A. Seigal
available on arXiv

- Multi-subspace power method for decomposing all tensors
with K. Wang, J. Pereira, A. Seigal
available on arXiv

- Norming sets for tensor and polynomial sketching
with Y. Zhang
available on arXiv

- The fascinating world of 2 x 2 x 2 tensors: its geometry and optimization challenges
with G. Brown, T. Kolda
available on arXiv

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

- Efficient tensor decomposition via moment matrix extension
with B. Shi, J. Lindberg
Journal of Symbolic Computation, to appear

- First proof
with M. Abouzaid et al.
Bulletin of the AMS, to appear

- Two datasets are better than one: Method of double moments for 3-D reconstruction in cryo-EM
with O. Mickelin, A. Singer, S. Xu
Inverse Problems, 2026

- QuadSync: quadrifocal tensor synchronization via Tucker decomposition
with D. Miao, G. Lerman
IEEE Conference on Computer Vision and Pattern Recognition, 2026 (oral)

- SO(3)-invariant PCA with application to molecular data
with M. Fraiman, P. Hoyos, T. Bendory, O. Mickelin, N. Sharon, A. Singer
IEEE International Symposium on Biomedical Imaging, 2026 (oral)

- Higher-order group synchronization
with A. Duncan
Research in the Mathematical Sciences, 2026

- Geometry and optimization of shallow polynomial networks
with Y. Arjevani, J. Bruna, E. Polak, M. Trager
SIAM Journal on Applied Algebra and Geometry, 2026

- Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC
with H. Fan, B. Kimia
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2026

- Covering number of real algebraic varieties and beyond: improved bounds and applications
with Y. Zhang
Foundations of Computational Mathematics, 2025

- Snapshot of algebraic vision
with K. Kohn
AMS Proceedings of Symposia in Pure Mathematics, 2025

- Subspace power method for symmetric tensor decomposition
with J. Pereira
Numerical Algorithms, 2025   (code)

- Fast expansion into harmonics on the ball
with N. Marshall, O. Mickelin, A. Singer
SIAM Journal on Scientific Computing, 2025

- Tensor-based synchronization and the low-rankness of the block trifocal tensor
with D. Miao, G. Lerman
Advances in Neural Information Processing Systems, 2024

- Scalable symmetric Tucker tensor decomposition
with R. Jin, T. Kolda, R. Ward
SIAM Journal on Matrix Analysis and Applications, 2024

- 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 (oral)   (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  


Teaching
Fall 2026:  Scientific computation in numerical analysis
Spring 2026:  Foundational techniques of machine learning and data sciences
Fall 2025:  Tensor methods
Spring 2025:  Calculus I
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



People
Present

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

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

Paul Beckman: Peter O'Donnell Jr. postdoc, Oden Institute, 2025 - present, co-mentored with Gunnar Martinsson

Michael Liu: CSEM Ph.D. student, 2025 - present

Mina Parast: Math Ph.D. student, 2026 - present


Past

Addie Duncan: Math Ph.D. student, 2023 - 2026 (next: industry)

Yifan Zhang: CSEM Ph.D. student, 2021 - 2026 (next: quant at Citadel Securities)

Elzbieta Polak: Math Ph.D. student, 2021 - 2025 (next: data scientist at Travelers)

Julia Lindberg: Bing instructor, Math Dept, January 2023 - 2025 (next: assistant professor at Georgia Tech)

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

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

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



Travel
Spring 2027:  Semester Program on Metric Algebraic Geometric (ICERM)
Spring 2027:  Workshop on Numerical Algebraic Geometry and Electronic Structure (IPAM)
Spring 2027:  Workshop on ML and AG (IPAM)
January 2027:  Joint Math Meetings (Chicago)
December 2026:  Workshop on Matrix Optimization (National University of Singapore)
November 2026:  SIAM Mathematics of Data Science Conference (Salt Lake City)
November 2026, virtual:  Applied Math Seminar (Texas Tech)
October 2026:  SIAM TX-LA Meeting (Dallas)
Fall 2026:  Seminar on AI / Mathematics / Statistics (Harvard)
October 2026:  Wallenberg Advanced Scientific Forum (Stockholm)
September 2026:  Conference of Italian Network for Applied and Birational Algebraic Geometry (Siena, Italy)
July 2026:  DOE ASCR Applied Mathematics PI Meeting (Washington, DC)
July 2026:  Workshop on Mathematics of 3D Reconstruction (ICERM)
July 2026:  Workshop on Rigidity Theory and Geometric Data Science (ICERM)
June 2026:  Workshop on Metric Algebraic Geometry (Mittag-Leffler, Sweden)
June 2026:  Kolloquium (Osnabrück University)
May 2026:  Conference of International Linear Algebra Society (Virginia Tech)
April 2026:  Texas Algebraic Geometry Symposium (Texas A&M)
March 2026:   Joint Applied and Computational Math Seminar and Applied Algebra Seminar (UW Madison)
March 2026:   SQuaRE on Randomized Tensor Methods (AIM)
February 2026:  Young Mathematician Lecture Series (National University of Singapore)
January 2026:  Joint Math Meetings (DC)
December 2025:  Simons Institute (Berkeley)
November 2025:  Applied Math Seminar (UC Berkeley / LBL)
November 2025:  Workshop on Randomness, Invariants and Complexity (Simons Institute, Berkeley)
September 2025:  SIAM TX-LA Meeting (UT Austin)
July 2025:  International Conference on Continuous Optimization (USC)
July 2025:  SIAM Conference on Applied Algebraic Geometry (Madison)
June 2025:  ILAS 2025, Minisymposium on Numerical Multilinear Algebra (Taiwan)
April 2025:  Mathematics Department Colloquium (UT San Antonio)
March 2025:  Sophex Seminar (Math Department, UT Austin)
March 2025:  Babuška Forum (Oden Institute, UT Austin)
March 2025:  DOE Advanced Scientific Computing Research CS PI Meeting (Frisco, TX)
March 2025:  SIAM Conference on Computational Science and Engineering (Fort Worth)
February 2025:  Mathematics of Deep Learning Workshop (UT Austin)
February 2025, virtual:  Math Machine Learning Seminar (MPI + UCLA)
January 2025, virtual:  One World Mathematics of INformation, Data, and Signals (1W-MINDS) Seminar
January 2025:  JMM Special Sessions (Seattle)
December 2024:  IMS International Conference on Statistics and Data Science (Nice)
November 2024:  Mathematics Department Colloquium (Michigan State)
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 Mathematics Department 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)


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