At GAeL, Leuven, Belgium, 2015. Photo credit: Dennis Presotto.
My research is about the connections between symmetry and differential equations. Symmetry can be used to solve differential equations and differtial equations can be used to construct local versions of the representations of symmetry groups. Within algebraic geometry and representation theory, I study holonomic D-modules related to Sato-Bernstein b-functions, period integrals, and the Knizhnik-Zamolodchikov equations. All of these topics relate to understanding singularities through monodromy. I also study applications of representation theory to machine learning. I am interested in solving differtial equations by incorporating symmetry into deep learning models using equivariant neural networks. I am also interested in discovering symmetry in data using neural networks. My current mentors are Jan-Willem van de Meent, Rose Yu, Valerio Toledano Laredo, and Tina Eliassi-Rad. Previously, I was a NSF Postdoctoral Fellow and Zelevinsky Research Instructor in the Math Department at Northeastern University. I was a Ph.D. student of Victor Ginzburg at the University of Chicago until I graduated in 2015. My CV can be found here. |
PublicationsML and biology articles list authors in order of contribution and end with the PI. Astericks denote equal contribution. Math publications list authors alphabetically. |
Walters, R.*, Li, J.*, Yu R. (2021). Trajectory Prediction using Equivariant Continuous Convolution. International Conference on Learning Representations (ICLR). |
Walters, R.*, Wang, R.*, Yu, R. (2021). Incorporating Symmetry into Deep Dynamics Models for Improved Generalization. International Conference on Learning Representations (ICLR). |
Wong, S., Walters, R., Jiang, L., Molnar, T., Yu, R. (2020). Traffic Forecasting using Vehicle-to-Vehicle Communication and Recurrent Neural Networks. Machine Learning for Autonomous Driving (ML4AD), NeurIPS Workshop. |
Flapan, L., Walters, R., Zhao, X. (2019). Period integrals and Hodge modules. arXiv preprint arXiv:1910.00035 . |
Bapat, A., Walters, R. (2017). The Strong Topological Monodromy Conjecture for Coxeter Hyperplane Arrangements. Mathematical Research Letters 24 (4): 947-954. |
Bapat, A., Walters, R. (2015). The Bernstein-Sato b-Function of the Vandermonde determinant. arXiv preprint arXiv:1503.01055 . |
Walters, R. (2015). The Bernstein-Sato b-Function of the space of cyclic pairs. Publications of the Research Institute for Mathematical Sciences 51, (2): 273-288. |
Colin, C., Jacob,A., Quinn, C., Walters, R. (2008) The isoperimetric problem on planes with density. Bulletin of the Australian Mathematical Society 78 (2): 177-197. |
Yin, H., Slusky, J, S., Berger, B. W., Walters, R. S., Vilair, G., Litinov, R. I., Lear, J. D., Caputo, G. A., Bennett, J. S., DeGrado, W. F. (2007). Computational design of peptides that target transmembrane helices. Science 315:181723. |
Walters, R. F. and DeGrado, W. F. (2006). Helixpacking motifs in membrane proteins. Proc Natl Acad Sci USA 103:1365813663. |
Senes, A., Chadi, D.C., Law, P.B., Walters, R.F., Nanda, V., Degrado, W.F. (2007). E(z), a depthdependent potential for assessing the energies of insertion of amino acid sidechains into membranes. J Mol Biol 366 (2): 43648. |
Seminars |
Geometry, Physics, and Representation Theory. At Northeastern. Co-organizer Fall 2017 - Spring 2019. |
Pick My Brain. At Northeastern. Fall 2017. Spring, Fall 2018. Spring, Fall 2019. |
Seminar on Hodge Modules. At Northeastern and MIT, Fall, 2016. |
Putnam Exam Prep, Fall 2018 - Spring 2021 |
Teaching Resources. |
Talks |
Equivariant Neurel Networks for Dynamics. Spiral Seminar, Northeastern, December 4, 2020. |
Two Constructions of Yangians . From the Workshop of Yangians and Quantum Loop Algebras, Austin, May 2014. |
The Derived Category of Constuctible Sheaves with Iordan Ganev. From the Summer School on Quiver Hecke Algebras, Corsica, June 2014. |
Expository talk on paper "Accelerating Eulerian fluid simulation with convolutional networks." Given in CS7180 in Spring 2019. |
Links |
Learning projects in machine learning. |
My information on the Khoury college of CS website. My information on the math department page and the announcement of my starting at Northeastern. |
Faculty train, recruit young scientists in emerging math fields. |
Wayne C. Booth Prize: Robin Walters, PhD student in mathematics. By Steve Koppes. |
Robin Walters find mathematics more fun than a hit movie. By Steve Koppes. Alternate link. |