Department of Mathematics and Statistics
Seeley Mudd Building
31 Quadrangle Dr Amherst, MA 01002
Office: Science Center E206
Tel: (413) 542-5893.
E-mail: celliott AT amherst DOT edu
A pdf copy of my CV is available here.
I am a visiting assistant professor in mathematics at Amherst College. I'm interested in mathematical constructions in classical and quantum field theories using derived algebraic geometry. For example, I think about:
- The construction and classification of (not necessarily topological) twists of classical and quantum field theories, especially using techniques of derived algebraic geometry and homotopical algebra.
- The connection between structures appearing in various versions of the geometric Langlands correspondence and twists of four- and five-dimensional supersymmetric gauge theories.
- The theory of factorization algebras as a model for perturbative field theory.
- Spring 2022: Ordinary Differential Equations for Scientists and Engineers
- Fall 2021: Math 411: Introduction to Abstract Algebra
- Spring 2021: Math 797RM -- Moduli Spaces in Representation Theory.
- Spring 2021: Math 132 -- Calculus II.
- Fall 2020: Math 132H -- Calculus II Honors
- Spring 2020: Math 132 -- Calculus II.
- Fall 2019: Math 131H -- Calculus I Honors
Papers and Preprints
- Defects via factorization algebras (joint with Ivan Contreras and Owen Gwilliam), https://arxiv.org/abs/2208.01730
- The derived pure spinor formalism as an equivalence of categories (joint with Fabian Hahner and Ingmar Saberi), http://arxiv.org/abs/2205.14133
- Framed E_n-Algebras from Quantum Field Theory (joint with Owen Gwilliam), arxiv.org/abs/2204.03702
- Higher Deformation Quantization for Kapustin-Witten Theories (joint with Owen Gwilliam and Brian Williams), arxiv.org/abs/2108.13392
- Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory (joint with Philsang Yoo), arxiv.org/abs/2008.10988
- 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
- Holomorphic Poisson Field Theories (joint with Brian Williams), Higher Structures, Vol 5, Issue 1, 2021, arxiv.org/abs/2008.02302
- A Taxonomy of Twists of Supersymmetric Yang-Mills Theory (joint with Pavel Safronov and Brian Williams), accepted for publication in Selecta Mathematica, arxiv.org/abs/2002.10517
- Multiplicative Hitchin Systems and Supersymmetric Gauge Theory (joint with Vasily Pestun), Selecta Mathematica, Vol 25, Issue 64, 2019, arxiv.org/abs/1812.05516
- 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
- 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
- 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
- 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
- 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.
Conferences and Workshops
- In August 2022 I organised a summer school on Physical Mathematics of QFT, together with Owen Gwilliam and Matteo Lotito..
- In July 2021 I organised a program at ICTS in Bangalore on Quantum Fields, Geometry and Representation Theory See the link for details and registration.
- In August 2020, because of the postponement of our physical mathematics conference due to COVID, I recorded a series of masterclass videos on supersymmetry and the BV formalism.
- In January 2019 I organised a conference on Higher Structures in Holomorphic and Topological Field Theory, together with Vasily Pestun.
- In December 2014 I organised a workshop on Mathematical Aspects of Six-Dimensional Quantum Field Theory, together with David Nadler, Harrison Chen, Kevin Wray and Alex Zorn. Videos for the lectures are now available here.
- In January 2012 I organised a workshop with Sam Gunningham and David Nadler on Gauge Theory and Floer Theory. 2012 Northwestern Masterclass in Gauge Theory
Notes I've Written
- In November 2021 I gave a talk entitled Framing Anomalies for Topological AKSZ Theories at the University of Durham.
- In March 2021 I gave a talk entitled What is Supersymmetry? for "The What Is Graduate Seminar" (TWIGS) at UMass Amherst.
- In March 2021 I gave a talk on Gauge Symmetry Breaking via Derived Geometry at Nottingham University.
- In January 2021 I gave a talk on Geometric Langlands for Physicists as part of a joint Math/Physics department seminar at UMass (notes and video recordings for this lecture and later lectures in the series are available upon request).
- In July 2019 I gave a pair of expository talks at QFT for Mathematicians at the Perimeter Institute, on Supersymmetry Algebras, and on Yang-Mills Theory and Asymptotic Freedom.
- In May 2018 I gave a pair of lectures on Topological Twists of SUSY Factorization Algebras at IST, Austria.
- In May 2017 I gave a talk on Vacua and Singular Supports at the Perimeter Institute.
- In February 2016 I gave a talk on holomorphic Chern-Simons and (Super) Twistor Theory for a seminar on Reshetikhin-Turaev Invariants at Northwestern.
- In October 2014 I gave a talk on Perturbative and Non-Perturbative Twists of Classical Field Theories at the Simons Center (video).
- In October 2013 I gave a talk on the Feynman Path Integral in the Northwestern Math Graduate Student Seminar.
- In April 2013 I gave a talk on Abelian Duality for Generalised Maxwell Theories at the GRASP Seminar in Berkeley.
- In March 2013 I gave an expository talk on Topological Quantum Field Theory at the Northwestern Physics Brownbag Seminar.
- In October 2012 I gave a talk on Dirac Quantisation at the Northwestern Math Graduate Student Seminar.
- In August 2012 I gave a talk on TQFTs from Quasicoherent Sheaves on Stacks at the Categorical Representation Theory Workshop at the University of Oregon.
- In March 2012 I gave a talk on Supersymmetric Lagrangians at the Simons Center Workshop on Susy Gauge Theory (video).
- In May 2011 I gave a talk on The Non-abelian Hodge Correspondence for Non-compact Curves at the Talbot Workshop on Non-abelian Hodge Theory.
- Notes on Symmetries in Conformal Field Theory prepared for an informal seminar at Northwestern.
- Notes on Integrable Systems, the Classical Yang-Baxter Equation and the Toda Lattice prepared for a class on quantum groups at Northwestern.
- Notes on The Geometry of Affine Grassmannians prepared for an informal seminar at Northwestern.
- Notes on Motives and Motivic L-functions prepared for a seminar class at Northwestern.
- My Cambridge part III essay on D-modules.
- I have a set of notes on character sheaves which some people have found useful, but they're incomplete. E-mail me if you'd like a copy.
My notes from the 2012 Notre Dame Graduate Summer School on Topology and Field Theories.
Last modified Tuesday December 9th, 2020.