Bradley J. Nelson
Contact
Email: bradnelson@uchicago.eduLocation: Department of Statistics The University of Chicago
GitHub: bnels
I am a William H. Kruskal Instructor in the Department of Statistics at the University of Chicago. I completed my PhD at the Institute for Computational and Mathematical Engineering (ICME) at Stanford Univesity in June 2020, advised by Gunnar Carlsson and coadvised by Jonathan Taylor.
My primary research interests are in applied and computational algebraic topology, particularly topological data analysis. I am interested in the interface between applied/computational topology and other areas of mathematics, data science, and computing.
News
Announcements

August 2020 I'm happy to be starting at the University of Chicago as a William H. Kruskal Instructor in the Department of Statistics! 
January 2020 Code Release: Basic Applied Topology Subprograms (BATS)  a set of C++ headers for applied algebraic topology. Python bindings here. 
November 2019 New preprint: Persistent and Zigzag Homology: A Matrix Factorization Viewpoint
Teaching
University of Chicago

Winter 2021 STAT 37411=CAAM 37411  Topological Data Analysis.
[Course Description] [GitHub] [Website]
A new course I am teaching on Topological Data Analysis. 
Fall 2020 STAT 37830=CAAM 37830  Scientific Computing with Python.
[Course Description] [GitHub] [Website] [Reader]
This is a new course I am designing and teaching for students getting started with scientific computing. Covers the Python language and its numerical libraries, as well as use of computing resources.
Stanford University

Fall 2018 CME 193  Introduction to Scientific Python.
[Explore Courses] [GitHub] [Website]
Introduction to Python and its popular scientific computing libraries. 
Spring 2018 CME 258  Libraries for Numerical Linear Algebra and Optimization.
[Explore Courses] [GitHub]
Designed and cotaught with Ron Estrin. Introduction to different libraries for numerical linear algebra and optimization. 
Winter 2018 CME 257  Advanced Topics in Scientific Computing with Julia.
[Explore Courses] [GitHub]
Updated for Julia v0.6.2, and added a new lecture on metaprogramming. 
Fall 2015 CME 257  Advanced Topics in Scientific Computing with Julia.
[Explore Courses] [GitHub]
This is a new course that I created to introduce the Julia language to students interested in using it for development/research.
Research
Overview
My primary research focus is on topological data analysis. This is a relatively young branch of applied mathematics, rooted in the more classical subject of algebraic topology. The general goal is to learn something about data using various topological invariants, and a popular tool is persistent homology.
More broadly, I am interested in applied mathematics, machine learning, and data science.
Recent/Current Projects

Persistent and Zigzag Homology: A Matrix Factorization Viewpoint.
G. Carlsson, A. Dwaraknath, B. J. Nelson.
[arXiv:1911.10693] [Code on GitHub] 
A Topology Layer for Machine Learning.
R. BruelGabrielsson, B. J. Nelson, A. Dwaraknath, P. Skraba, L. J. Guibas, G. Carlsson.
[arXiv:1905.12200] [Code on GitHub] 
Clustering of Electromagnetic Showers and Particle Interactions with Graph Neural Networks in Liquid Argon Time Projection Chambers Data.
F. Drielsma, et al.
[arXiv:2007.01335] Part of a larger pipeline developed by the Neutrino Group at the Stanford Linear Accelerator. [Link to Repository] 
Texture Based Classification of Seismic Image Patches Using Topological Data Analysis.
R. Sarkar, B. J. Nelson.
81st EAGE Conference and Exhibition 2019.
DOI: 10.3997/22144609.201901608
[link] [slides] [poster]
PhD Dissertation

Parameterized Topological Data Analysis. Bradley J. Nelson.
Ph.D. dissertation. Stanford University. June 2020.
[link][defense slides]
Older Publications

Boundary integral equation solution of high frequency scattering from obstacles in an unbounded linearly gradedindex medium.
A. H. Barnett, B. J. Nelson, and J. M. Mahoney.
Journal of Computational Physics 297C:407426, 2015. 
Chiral Polymerization in Open Systems From ChiralSelective Reaction Rates.
M. Gleiser, B. J. Nelson, and S. I. Walker.
Origins of Life and Evolution of Biospheres 42:333346, 2012.
Older, Unpublished Projects

Sparse canonical correlation analysis.
X. Suo, V. Minden, B. Nelson, R. Tibshirani, M. Saunders.
arXiv:1705.10865
Talks and Presentations

03.01.2021 SIAM CSE, Minisymposium on Emerging Directions in Computational Topolgy
Parallel Computation of Zigzag Homology using Matrix Factorizations. [abstract] [slides] 
01.08.2021 Joint Mathematics Meetings, AMS Special Session on Applied Topology
A fibration model for ddimensional image patches. [abstract] [slides] 
11.05.2020 CAAM Colloquium, University of Chicago
Topological Data Analysis, Linear Algebra, and Optimization. [announcement] [slides] 
05.03.2019 Stanford Exploration Project Seminar
Stanford, CA [slides] 
10.01.2018 AI at SLAC seminar
Stanford Linear Accelerator (Menlo Park, CA) 
08.11.2017 Applied Algebraic Topology 2017
Hokkaido University (Sapporo, Japan) [slides] 
08.01.2017 SIAM Algebraic Geometry 2017
Atlanta, GA [slides]
Miscellaneous

Questions about mathematical modeling or algorithms?
Come by Computational Consulting.
A service offered by ICME graduate students.