Chris Elliott
A valuable collaboration

Chris Elliott

E-mail:
Google Scholar:https://scholar.google.com/citations?user=LyMto6kAAAAJ
Linkedin:https://www.linkedin.com/in/chris-elliott-21a500230/
Resume: Here
Academic CV: Here.


I am a mathematician, formerly working as an academic and -- starting in 2025 -- working in industry on neural network alignment. My mathematical background in academia involved the interactions between geometry, topology and mathematical physics, especially:



A more detailed description of some of my academic work can be found in my research statement. I also have a (somewhat older) non-technical description of my research.


Papers and Preprints

  1. Twists of Superconformal Algebras (joint with Owen Gwilliam and Matteo Lotito): https://arxiv.org/abs/2403.19753
  2. Defects via factorization algebras (joint with Ivan Contreras and Owen Gwilliam), Letters in Mathematical Physics, Vol 113, 2023, https://arxiv.org/abs/2208.01730
  3. The derived pure spinor formalism as an equivalence of categories (joint with Fabian Hahner and Ingmar Saberi), Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol 19, No 22, 2023, http://arxiv.org/abs/2205.14133
  4. Framed E_n-Algebras from Quantum Field Theory (joint with Owen Gwilliam), Reviews in Mathematical Physics, Vol 35, No 07, 2023 arxiv.org/abs/2204.03702
  5. Higher Deformation Quantization for Kapustin-Witten Theories (joint with Owen Gwilliam and Brian Williams), Annales Henri Poincaré, Vol 25, pages 5045–5112, 2024 arxiv.org/abs/2108.13392
  6. Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory (joint with Philsang Yoo), accepted for publication in Communications in Number Theory and Physics, arxiv.org/abs/2008.10988
  7. Spontaneous Symmetry Breaking: a view from derived geometry (joint with Owen Gwilliam), Journal of Geometry and Physics, Vol 162, 2021, arxiv.org/abs/2008.03599
  8. Holomorphic Poisson Field Theories (joint with Brian Williams), Higher Structures, Vol 5, Issue 1, 2021, arxiv.org/abs/2008.02302
  9. A Taxonomy of Twists of Supersymmetric Yang-Mills Theory (joint with Pavel Safronov and Brian Williams), Selecta Mathematica, Vol 28, 2022, arxiv.org/abs/2002.10517
  10. Multiplicative Hitchin Systems and Supersymmetric Gauge Theory (joint with Vasily Pestun), Selecta Mathematica, Vol 25, Issue 64, 2019, arxiv.org/abs/1812.05516
  11. Topological Twists of Supersymmetric Algebras of Observables (joint with Pavel Safronov), Communications in Mathematical Physics, Vol 371, pages 727-786, 2019, arxiv.org/abs/1805.10806
  12. A Physical Origin for Singular Support Conditions in Geometric Langlands (joint with Philsang Yoo), Communications in Mathematical Physics, Vol 368, Issue 3, Pages 985-1050, 2019, arxiv.org/abs/1707.01292
  13. Asymptotic Freedom in the BV Formalism (joint with Brian Williams and Philsang Yoo), Journal of Geometry and Physics, Vol 123, January 2018, Pages 246-283, arxiv.org/abs/1702.05973
  14. Geometric Langlands Twists of N=4 Gauge Theory from Derived Algebraic Geometry (joint with Philsang Yoo), Advances in Theoretical and Mathematical Physics, Vol 22, Number 3, Pages 615-708, 2018, arxiv.org/abs/1507.03048
  15. Abelian Duality for Generalised Maxwell Theories, Mathematical Physics, Analysis and Geometry, Vol 22, Issue 22, 2019, arxiv.org/abs/1402.0890 (poster).


You can also read my thesis, which is a combination of the last two papers above, with an expository introduction and some remarks on future work.


Teaching Materials


Conferences and Workshops


Seminars

  • From 2019 to 2022 I organised the UMass Representation Theory Seminar together with Tina Kanstrup.
  • In March-July 2020 I organised an online working seminar on Quantum field theory, representation theory and geometry together with Brian Williams. If you would like to join the mailing list for announcements of any future lectures, click here to sign up.
  • In January-March 2015 I co-organised a learning seminar on Instantons and the Nekrasov Partition Function with Philsang Yoo and Brian Williams.
  • In January-March 2014 I co-organised a reading seminar on papers in geometric representation theory with Aron Heleodoro. We read and discussed important papers from geometric representation theory in the last forty years.
  • In October-November 2013 I co-organised a learning seminar on String Topology with Brian Williams, focusing on string topology as part of a partially extended 2d topological field theory.
  • In April-June 2013 I co-organised a learning seminar on S-duality with Kevin Costello.
  • In February 2012 I organised a preseminar for the Simons Center Workshop on SUSY Gauge Theory. Hiro Tanaka compiled a partial list of notes from the participant talks here.


    Lecture Series

  • In 2020 I recorded a lecture series on super Yang--Mills in the BV formalism, together with Brian Williams. You can find the lecture notes, videos and some exercises here.
  • In 2017 I gave a series of lectures on An Algebraic Introduction to Kapustin-Witten Theory at the Hausdorff Institute for Mathematics in Bonn.


    Notes I've Written