# Chris Elliott

**Address:**

Institut des Hautes Études Scientifiques

35 Route de Chartres

Bures-sur-Yvette 91440

France

**Office:** 0N6

**Tel:** +33 1 60 92 66 17

**E-mail:** celliott AT ihes DOT fr

A pdf copy of my CV is available here.

I am a 3-year postdoctoral fellow at the IHÉS, part of the ERC grant QUASIFT under Vasily Pestun. 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.

A more detailed description of some of my interests can be found in my research statement (current as of 2018). I also have a non-technical description of my research.

### Papers and Preprints

**Multiplicative Hitchin Systems and Supersymmetric Gauge Theory**(joint with Vasily Pestun), submitted, arxiv.org/abs/1812.05516**Topological Twists of Supersymmetric Algebras of Observables**(joint with Pavel Safronov), accepted for publication in Communications in Mathematical Physics, arxiv.org/abs/1805.10806**A Physical Origin for Singular Support Conditions in Geometric Langlands**(joint with Philsang Yoo), 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**(joint with Philsang Yoo), Advances in Theoretical and Mathematical Physics, Vol 22, Number 3, Pages 615-708, 2018, arxiv.org/abs/1507.03048*N*=4 Gauge Theory from Derived Algebraic Geometry**Abelian Duality for Generalised Maxwell Theories**, submitted, 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.

### Workshops

- 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

### Seminars

- 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.

### Notes I've Written

- 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 Thursday January 24th, 2019.