Biography

I am a postdoc in the data science group of the Mathematical Institute at the University of Oxford. I work on computational topology, as well as representations of Lie algebras and Hecke algebras. I received my PhD at the University of Utah under the supervision of Prof. Peter Trapa.

In my spare time I enjoy baking bread, swimming, and reading.

Publications

• Discrete Microlocal Morse Theory
  Adam Brown and Ondrej Draganov.
  Submitted, 2022. [arXiv:2209.14993]
• Contravariant Pairings Between Standard Whittaker Modules and Verma Modules
  Adam Brown and Anna Romanov.
  Journal of Algebra, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017 [arXiv:2106.10029]
• Probabilistic Convergence and Stability of Random Mapper Graphs
  Adam Brown, Omer Bobrowski, Elizabeth Munch, and Bei Wang.
  Journal of Applied and Computational Topology, 2021. https://doi.org/10.1007/s41468-020-00063-x
  [arXiv:1909.03488]
• Contravariant forms on Whittaker modules
  Adam Brown and Anna Romanov.
  Proceedings of the American Mathematical Society, 2020. https://doi.org/10.1090/proc/15205
  [arXiv:1910.08286]
• Sheaf-theoretic stratification learning from geometric and topological perspectives
  Adam Brown and Bei Wang.
  Discrete & Computational Geometry, 2020. https://doi.org/10.1007/s00454-020-00206-y
  [arXiv:1712.07734]
  
• Arakawa-Suzuki Functors for Whittaker modules
  Adam Brown.
  Journal of Algebra, Volume 538, p. 261--289, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027
  [arXiv:1805.04676]
  
• Arakawa-Suzuki Functors for Whittaker modules, University of Utah Dissertation.
  Adam Brown.
  PhD Thesis
  
• Sheaf-theoretic stratification learning
  Adam Brown and Bei Wang.
  International Symposium on Computational Geometry (SOCG), 2018.https://doi.org/10.4230/LIPIcs.SoCG.2018.14
  [arXiv:1712.07734]
  

Seminar & Conference Talks

Oxford University Algebra Seminar

• The local Lanlands correspondence and unitary represetnations of GL(n). October 2022

  Representation Theory XVII

  • The local Lanlands correspondence and unitary represetnations of GL(n). October 2022

    IST Austria Geometry/Topology Seminar

    • Discrete Microlocal Morse Theory. September 2022

      Austrian TDA Meeting

      • Discrete Microlocal Morse Theory. August 2022

        University of Manchester Algebra Seminar

        • The local Lanlands correspondence and unitary represetnations of GL(n). March 2022

          Persistence, Sheaves, and Homotopy Theory Seminar

          • Computing Minimal Injective Resolutions. February 2022

            Computational Persistence Workshop, Purdue University

            • Computing Injective Resolutions of Cellular Sheaves. November 2021

              IST Austria Geometry/Topology Seminar

              • Topological Structure of Ocean Eddies. June 2021

                Heidelberg University, Topological Data Analysis Seminar

                • Probabilistic Convergence of Random Mapper Graphs. June 2021

                  University of Vienna, Representation Theory/Automorphic Forms Seminar

                  • The local Langlands correspondence and unitary representations of GL(n). November 2020

                    Midwest Representation Theory Conference

                    • Unitary representations of GL(n) and the geometry of Langlands parameters. October 2020
                    • Video

                      University of Utah, Number Theory/Representation Theory Seminar

                      • Contravariant forms on Whittaker modules. January 2020

                        IST Austria, Geometry/Topology Seminar

                        • Persistent Microlocal Geometry. December 2019

                          University of Oxford, Algebra/Representation Theory Seminar

                          • Contravariant forms on Whittaker modules. September 2019

                            Osterreichische Mathematische Gesellschaft

                            • Convergence and stability of random mapper. September 2019

                              Young Topologists Meeting, EPFL, Switzerland

                              • Probabilistic convergence and stability of random mapper. July 2019

                                IST Austria, Geometry/Topology Seminar

                                • Convergence and stability of random mapper. July 2019

                                  Representation Theory XVI, Dubrovnik, Croatia

                                  • Arakawa-Suzuki functors for Whittaker modules. June 2019

                                    Southeastern Lie Theory Workshop, LSU

                                    • The geometric foundation of Arakawa-Suzuki functors. May 2019

                                      University of Georgia, Algebra Seminar

                                      • Arakawa-Suzuki functors for Whittaker modules. November 2018

                                      University of Maryland, College Park, Lie Groups and Representations Seminar

                                      • Arakawa-Suzuki functors for Whittaker modules. September 2018

                                      University of Utah, Number Theory and Representation Theory Seminar

                                      • Arakawa-Suzuki functors for Whittaker modules. September 2018

                                      Symposium on Computational Geometry

                                      • Sheaf-theoretic stratification learning. Summer 2018 Slides
                                      
                                      

                                      University of Utah Graduate Student Colloquium

                                      • Applications of intersection homology in representation theory and data science. Spring 2018
                                      • Topological data analysis: A new frontier (for sheaves). Spring 2017
                                      • An invitation to harmonic analysis. Spring 2016 Slides
                                      • A survey of the theory and applications of representations. Fall 2014
                                      • Applications of representation theory in harmonic analysis. Spring 2013
                                      
                                      

                                      University of Utah Representation Theory Student Seminar

                                      • Duality between SL_n and the graded affine Hecke algebra. Fall 2016
                                      • Weyl character formula. Spring 2015
                                      • Dirac cohomology of Harish-Chandra modules. Spring 2015
                                      • Clifford algebras. Spring 2015
                                      • Introduction to sheaves. Fall 2014
                                      • Abelian categories. Fall 2014
                                      
                                      

                                      University of Utah Undergraduate Student Colloquium

                                      • Applications of representation theory to the heat equation. Spring 2015 Slides

                                      The Leonardo Museum

                                      • p-Adic numbers: A new way to count. Spring 2017

Teaching

Teaching Statement

Stipendiary Lecturer

• Metric Spaces and Complex Analysis, Somerville College. Michaelmas Term 2022

Instructor

• Cellular Sheaves and Persistent Homology, IST Austria. Spring 2021
• Sheaf Theory and Applications, IST Austria. Spring 2020. Sheaf Theory Notes
• MATH 1010: Intermediate Algebra , U of Utah. Fall 2013, Fall 2015
• MATH 10: Intermediate Algebra Review, U of Utah. Spring 2017
• MATH 1060: Trigonometry, U of Utah. Spring 2014
• MATH 1210: Calculus I, U of Utah. Fall 2014, Fall 2016
• MATH 2200: Discrete Mathematics, U of Utah. Summer 2014



Teaching Assistant

• MATH 3140: Engineering Vector Calculus and PDE's, U of Utah. Spring 2015