I’m a postdoctoral research associate at Pacific Northwest National Lab, working in the Math of Data Science group with Henry Kvinge and Tegan Emerson.
Previously I completed a PhD in mathematics (algebraic geometry) at the University of Washington, where my advisor was Sándor Kovács.
Research
I am interested in holistic evaluation of deep learning models, including
 feature (dis)similarity,
 explainability and interpretability,
 bias and
 robustness.
My pure math research focused on birational geometry and singularities, mostly in positive and mixed characteristic.
Publications
 Charles Godfrey, Henry Kvinge, Elise Bishoff, Myles Mckay, Davis Brown, Tim Doster and Eleanor Byler. How many dimensions are required to find an adversarial example? In The 3rd Workshop of Adversarial Machine Learning on Computer Vision at CVPR 2023.
 Charles Godfrey, Michael Rawson, Henry Kvinge and Davis Brown. Fast computation of permutation equivariant layers with the partition algebra. In ICLR 2023 Workshop on Physics for Machine Learning.
 Davis Brown, Charles Godfrey (equal contribution), Cody Nizinski, Jonathan Tu, Henry Kvinge. Robustness of edited neural networks. In ICLR 2023 Workshop on Mathematical and Empirical Understanding of Foundation Models.
 Henry Kvinge, Davis Brown and Charles Godfrey. Exploring the Representation Manifolds of Stable Diffusion Through the Lens of Intrinsic Dimension. In ICLR 2023 Workshop on Mathematical and Empirical Understanding of Foundation Models.
 Charles Godfrey, Davis Brown (equal contribution), Tegan Emerson and Henry Kvinge. On the Symmetries of Deep Learning Models and their Internal Representations. To appear in NeurIPS 2022. Code available at https://github.com/pnnl/modelsym
 Elizabeth Coda, Nico Courts, Colby Wight, Loc Truong, WoongJo Choi, Charles Godfrey, Tegan Emerson, Keerti Kappagantula and Henry Kvinge. Fiber bundle morphisms as a framework for modeling manytomany maps. In ICLR 2022 workshop on geometrical and topological representation learning.
 Higher Direct Images of Ideal Sheaves, Correspondences in Log Hodge Cohomology and Globally FFull Varieties. PhD thesis, University of Washington 2021.
Preprints
 Correspondences in log Hodge cohomology (2023).
 Henry Kvinge, Grayson Jorgenson, Davis Brown, Charles Godfrey and Tegan Emerson. Neural frames: A Tool for Studying the Tangent Bundles Underlying Image Datasets and How Deep Learning Models Process Them (2022).
 Charles Godfrey, Elise Bishoff, Myles Mckay, Davis Brown, Grayson Jorgenson, Henry Kvinge and Eleanor Byler. Convolutional networks inherit frequency sensitivity from image statistics (2022).
 Takumi Murayama and Charles Godfrey. Pure subrings of du bois singularities are du bois singularities (2022).
 Higher direct images of ideal sheaves (2022).
Upcoming talks
 June 59, 2023: ICERM Mathematical and Scientific Machine Learning Workshop.
 May 4th, 2023: SPIE Defense + Commercial Sensing 2023.
 May 5th, 2023: ICLR 2023 Workshop on Physics for Machine Learning.
Axioms
I believe in Federico Ardila’s axioms:

Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.
Acknowledgments
During the spring of 2019 I was in residence at the Mathematical Sciences Research Institute in Berkeley, California, supported by the National Science Foundation under Grant No. 1440140. During the academic year of 20182019 I was supported by the University of Washington Department of Mathematics Graduate Research Fellowship.