# Chris Elliott

**Address:**

Department of Mathematics and Statistics

University of Massachusetts, Amherst

Lederle Graduate Research Tower

MA 01002

**Office:** LGRT 1124

**E-mail:** celliott AT math DOT umass DOT edu

A pdf copy of my CV is available here.

I am a visiting assistant professor in mathematics at the University of Massachusetts, Amherst. 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 December 2020). I also have a non-technical description of my research.

### Teaching

- 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

**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), accepted for publication in Higher Structures, arxiv.org/abs/2008.02302**A Taxonomy of Twists of Supersymmetric Yang-Mills Theory**(joint with Pavel Safronov and Brian Williams), 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**(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**, 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 July 2021 I am organising a program at ICTS in Bangalore on
**Quantum Fields, Geometry and Representation Theory**See the link for details and registration. - In August 2020 I had been organising a summer school on
**Physical Mathematics of QFT**, together with Owen Gwilliam.**Postponed due to COVID-19**. In the meantime we've been making masterclass videos. - 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

- Since September 2019 I have been organising 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.

### Notes I've Written

- 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.