Department of Mathematics, Northwestern University

**e-mail:** theojf at math dot northwestern dot edu

**Office:** 312 Lunt Hall, Northwestern University, Evanston, IL, 60202

My primary research interests are in mathematical physics, focusing on quantum field theory, and specifically perturbative quantization and path integrals and so on. I am also very interested in questions in category theory and representation theory. A more detailed description of my current research interests and projects my be found by reading my recent grant applications.

My PhD adviser at Berkeley is Nicolai Reshetikhin. My sponsoring scientist at Northwestern in Kevin Costello. Other collaborators include Alex Chirvasitu, Owen Gwilliam, Dan Berwick-Evans, and Claudia Scheimbauer.

My papers and preprints include:

The (op)lax square of an (∞,

*n*)-category. With Claudia Scheimbauer. 2015. (abstract, PDF, arXiv: 1502.06526).Tree- versus graph-level quasilocal Poincaré duality on

*S*^{1}. 2014. To appear in*Journal of homotopy and related structures*. (abstract, PDF, arXiv: 1412.4664).Reflexivity and dualizability in categorified linear algebra. With Martin Brandenburg and Alexandru Chirvasitu. 2014. (abstract, PDF, arXiv: 1409.5934).

Chains(

**R**) does not admit a geometrically meaningful properadic homotopy Frobenius algebra structure. 2013. (abstract, PDF, arXiv: 1308.3423).Poisson AKSZ theories and their quantizations. 2014. In

*Proceedings of the conference String-Math 2013*, volume 88 of*Proceedings of Symposia in Pure Mathematics*, pages 291--306, Providence, RI, 2014. Amer. Math. Soc. (abstract, PDF (published version), arXiv: 1307.5812, DOI: 10.1090/pspum/088.).Peturbative techniques in path integration. Ph.D. Thesis. 2013. (abstract, PDF).

Homological perturbation theory for nonperturbative integrals. 2012. (abstract, PDF, arXiv: 1206.5319).

How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism. With Owen Gwilliam. 2011. (abstract, PDF, arXiv: 1202.1554).

The fundamental pro-groupoid of an affine 2-scheme. With Alex Chirvasitu. 2011.

*Applied Categorical Structures*, Vol 21, Issue 5 (2013), pp. 469–522. (abstract, arXiv: 1105.3104, DOI: 10.1007/s10485-011-9275-y).The formal path integral and quantum mechanics. 2010.

*Journal of Mathematical Physics*, 51, 122103. (abstract, published PDF, DOI:10.1063/1.3503472, arXiv: 1004.4305, equation and theorem numbering differs between preprint and published versions).On the coordinate (in)dependence of the formal path integral. 2010. (abstract, PDF, arXiv: 1003.5730).

Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics. 2010.

*Letters in Mathematical Physics*, 94(2):123–149. (abstract, preprint PDF, arXiv: 1003.1156, available Open Access from Springer Link at DOI: 10.1007/s11005-010-0424-2).Poisson Lie linear algebra in the graphical language. 2009. (PDF, TeX)

One of my more satisfying activities is that I am a reviewer for MathReviews. Of my reviews, two appeared in the September 2012 print addition: MR2742432 (2012i:55005): Stolz and Teichner, Supersymmetric field theories and generalized cohomology, 2011 and MR2752518 (2012i:81001): Baez and Lauda, A prehistory of n-categorical physics, 2011.

Some talks I have given (or will give) are listed below. You can open all abstracts or close all abstracts if you like.

The Stokes groupoids of Gualtieri, Li, and Pym. May 4&6, Math 448: Topics in Geometry and Topology, Northwestern. (abstract, notes)

Some non-dualizable categories. April 17, Representation Theory, Geometry, and Combinatorics, UC Berkeley. (abstract, handout)

Local Poincare duality & deformation quantization. April 2, Center for Geometry and Physics, Institute for Basic Science, Pohang, South Korea. (abstract, handout, video (follow talk link))

Some comments on Heisenberg-picture qft. March 18, Max Planck Institute for Mathematics, Bonn, Germany. (abstract, handout)

Twisted field theories and higher-categorical (op)lax transfors. March 3, Topology Seminar, University of Notre Dame, South Bend, IN. (abstract, handout)

Functorial axioms for Heisenberg-picture quantum field theory. January 12, CRG Geometry and Physics Seminar, UBC, Vancouver, BC. (abstract, handout)

Heisenberg-picture quantum field theory. November 17, Quantum Mondays Seminar, Center for Geometry and Physics, Institute for Basic Science, Pohang, South Korea. (abstract, video (follow talk link))

The CS-WZW correspondence. October 30, CFT Seminar, Northwestern University, Evanston, IL. (abstract, notes)

Poisson AKSZ theories. October 3, Homological Methods in Quantum Field Theory, Simons Center for Geometry and Physics, Stony Brook, NY. (abstract, outline, video, live-TeX'ed notes by Gabriel C. Drummond-Cole)

Lie bialgebra quantization in 2- and 3-dimensional field theory. May 28, Associators, Formality and Invariants Seminar, Northwestern, Evanston, IL. (abstract, notes)

The Jones polynomial and the Temperley--Lieb TQFT. May 9, Graduate Student Seminar, Northwestern, Evanston, IL. (abstract, notes)

Heisenberg-picture TQFTs. May 2, Representation Theory, Geometry, and Combinatorics, UC Berkeley. (abstract, notes)

Poisson AKSZ theory and homotopy actions of properads. February 21, Modern trends in topological quantum field theory, Erwin Schrödinger International Institute for Mathematical Physics. (abstract, handout)

Up-to-homotopy Frobenius structures on manifolds, and how they relate to perturbative QFT. January 22, Topology Seminar, UC Berkeley. (abstract, handout)

Poisson AKSZ theories and quantization. October 24, Geometry Seminar, UT Austin. (abstract, handout)

Poisson AKSZ theories and quantization. October 12, Higher Structures in Algebra, Geometry and Physics, Fall Eastern Sectional Meeting of the AMS, Temple University, Philadelphia. (abstract, handout)

Poisson AKSZ theory, properads, and quantization. October 10, Geometry and Physics, Northwestern, Evanston. (abstract, handout)

A properad action on homology that fails to lift to the chain level. October 10, Geometry and Physics Pre-talk, Northwestern, Evanston. (abstract, handout)

A properadic approach to the deformation quantization of topological field theories. September 25, Algebra and Combinatorics, Loyola University, Chicago. (abstract, notes)

A salad of BV integrals and AKSZ field theories, served over a bed of properads; it comes spiced with chain-level Poincare duality and just a pinch of Poisson geometry. September 10, Research Seminar in Mathematics, Northeastern University, Boston. (abstract, notes)

Star quantization via lattice topological field theory. June 18, String-Math, Simons Center for Geometry and Physics, Stony Brook. (abstract, slides)

Lattice Poisson AKSZ Theory. February 4, Algebraic Geometry Seminar, University of British Columbia. (abstract, handout)

Feynman diagrams for quantum mechanics. October 10–12, Topics in Applied Mathematics, UC Berkeley. (abstract, notes)

Nonperturbative integrals, imaginary critical points, and homological perturbation theory. August 28, New Perspectives in Topological Field Theories, Center for Mathematical Physics, Hamburg. (abstract, notes)

Nonperturbative integrals, imaginary critical points, and homological perturbation theory. August 24, QGM Lunch Seminar, Aarhus. (abstract, notes)

Wick-type theorems beyond the Gaussian. March 2, Representation Theory (and related topics) seminar, Northeastern. (abstract, handout, notes)

Twisted N=1 and N=2 supersymmetry on R^4. February 10, GRASP seminar, UC Berkeley. (abstract, notes)

Notes on Floer / Gromov–Witten TQFT, based on conversations with Zack Sylvan. November 15, Witten in the 80s, UC Berkeley. (notes)

Gauge-fixed integrals for Lie algebroids. November 1, Talks in Mathematical Physics, Universität Zürich & Eidgenössische Technische Hochschule Zürich. (abstract, handout)

Introduction to BV Integrals. November 1, Selected topics in classical and quantum geometry, Universität Zürich. (abstract, handout)

Asymptotics of oscillating integrals via homological perturbation theory. October 19, GRASP seminar, UC Berkeley. (abstract, handwritten notes, too-long typed notes)

BRST Gauge Fixing: I. Introduction to Q-manifolds and BRST. II. Chern-Gauss-Bonnet, Morse Theory, and topological sigma models. October 11-20, Witten in the 80s, UC Berkeley. (abstract, notes I, notes II)

(Topological) duality of Hopf algebras. June 13, Cluster Algebras and Lusztig's Semicanonical Basis, University of Oregon. (abstract, notes)

Homological perturbation and factorization algebras. May 26, Geometry/Physics Seminar, Northwestern University. (abstract, notes)

On Atoms, Mountains, and Rain. April 20, NUMS Seminar, Northwestern University. (abstract)

Feynman Diagrams for Schrodinger's Equation. Feb 15, GADGET Seminar, UT Austin. (abstract, handout)

E

_{2}operad, Gerstenhaber and BV, and Formality. Feb 10, Student String Topology Seminar, UC Berkeley. (abstract, notes, handout)

Crash course in Tannaka-Krein theory. Dec 3, Student Subfactors Seminar, UC Berkeley. (abstract, notes)

Formal calculus, with applications to quantum mechanics. Sept 10, GRASP seminar, UC Berkeley. (abstract, notes).

Introduction to Vassiliev invariants. April 2, GRASP seminar, UC Berkeley. (abstract).

How to quantize infinitesimally-braided symmetric monoidal categories. March 19, Subfactors Seminar, UC Berkeley. (abstract, notes).

The Formal Path Integral in Quantum Mechanics. Feb 26, Subfactors Seminar, UC Berkeley. (abstract, slides).

What the Hell is a Feynman Diagram? Sept 29, Ph.d. seminar, Institut for Matematiske Fag, Aarhus Universitet. (abstract, notes).

On Atoms, Mountains, and Rain. March 31, Many Cheerful Facts, UC Berkeley. (abstract, notes).

Combinatorial Calculus: From Taylor Series to Feynman Diagrams. July 7-12, Canada/USA Mathcamp. (abstract, notes, exercises).

Enriching Yoneda. December 11, QFT Mini Conference, UC Berkeley. (abstract, notes).

Divergent Series. October 18, Many Cheerful Facts, UC Berkeley. (abstract, notes).

I occasionally "Live-TeX" notes from classes and lectures. As with any notes, mine are replete with omissions and errors, undoubtedly; typing does allow me to catch questions from the audience and jokes from the professors, so these are included as well. Needless to say, anything good about the notes, and in particular presentation of the mathematical material, is due to the professor of the class. Anything bad about them, and in particular every inaccuracy, is mine. Use them with care. Also, please e-mail me with corrections: typos are trivial to fix, and mathematical errors should not be allowed to propagate. I was inspired to start typing lecture notes after watching Anton Geraschenko do it, and appreciate his advice.

- Philippe Di Francesco. Chern-Simons Research Lectures: Discrete Integrable Systems and Cluster Algebras, 10-12 April 2012. Prepared slides: Day 1 (8 MB), Day 2 (16 MB), Day 3 (13 MB). Unedited notes from the first two days.
- Denis Bernard. Chern-Simons Research Lectures: Stochastic Schramm-Loewner Evolution (SLE) from Statistical Conformal Field Theory (CFT): An Introduction for (and by) Amateurs, 19-23 March 2012. Prepared notes: arXiv:math-ph/0602049v1. Mildly edited notes.
- David Kazhdan. Chern-Simons Research Lectures: The classical master equation in the finite-dimensional case, 9-13 Jan 2012. Mildly edited notes.
- Jorg Teschner. Chern-Simons Research Lectures: Quantization of Hitchin's Moduli Spaces and Liouville Theory, 17-21 Oct 2011. Unedited notes.
- Fedor Smirnov. Chern-Simons Research Lectures: Correlation functions in integrable Quantum Field Theory, 28 Sept - 4 Oct 2011. Unedited notes. Slides.
R. Borcherds, M. Haiman, N. Reshetikhin, V. Serganova.

*Berkeley Lectures on Lie Groups and Quantum Groups*. Part I: Lie Groups, and start of Part II: Quantum Groups. Edited by T. Johnson-Freyd and A. Geraschenko. (DRAFT. PDF, TeX (tar.gz). Last updated Friday, 27-Sep-2013 13:35:14 CDT.)Chapters 1–6 of the full volume are almost exactly the same as the edited notes from M. Haiman (2008), but there have been some formatting changes. Chapter 7 is based mostly on lectures 20–31 of Anton's notes from the 2006 Tag Team Lie Groups course (PDF). Chapter 8 is drawn from V. Serganova (2010). The first chapter of Part II: Quantum Groups has now been incorporated. Ultimately Part II will consist of between five and six chapters, based on the lectures by N. Reshetikhin (2009) and V. Serganova (2010).

- MSRI, Symplectic Geometry, Noncommutative Geometry and Physics, May 10, 2010 to May 14, 2010. (All slides and transcripts (tar.gz).)
- V. Serganova. Math 261B: Quantum Groups. Spring 2010. (Unedited: PDF, TAR.GZ. Last updated Friday, 27-Sep-2013 13:35:48 CDT.)
- N. Reshetikhin. Math 261B: Quantum Groups. Spring 2009. (Unedited: PDF (size exceeds 800 KB), TAR.GZ (size exceeds 9 MB). Last updated Friday, 27-Sep-2013 13:35:56 CDT.)
- M. Haiman. Math 261A: Lie Groups. Fall 2008. (Edited: PDF, TeX. Unedited: PDF (size exceeds 1 MB), TAR.GZ (size exceeds 6 MB). Last updated Friday, 27-Sep-2013 13:36:13 CDT.)
- M. Rieffel. Math 208: C* Algebras. Spring 2008. (Unedited: PDF (about 600 KB), TAR.GZ (about 4 MB). Last updated Friday, 27-Sep-2013 13:36:22 CDT.)

Please note that the TAR.GZ files include TeX sources and plenty of other detritus: auxiliary files, partly completed problem sets, etc. You are welcome to download them, but I make no promises that the files will load on your computer: that will depend on whether your TeX installation exactly matches mine.

Linked below are the application materials I produced in Fall of 2012 for my postdoc search (which was relatively successful). If you are a PhD student applying to postdocs, be sure to look over applications other than mine — I have very little data on what parts of my applications helped me, and what parts hurt (although nothing hurt so much as to keep me from winning a postdoc). In fact, I recommend looking more widely than just the Secret Blogging Seminar crowd, as theirs are the applications I read before writing mine, and perhaps we've just been propagating the same mistakes.

- NSF Summary
- NSF Project Proposal
- NSF References
- NSF Biographical Sketch
- NSF Data Plan
- MathJobs Cover Letter Template
- MathJobs Project Proposal
- MathJobs Publication List
- MathJobs Teaching Statement

If you are curious, you can read the syllabus for my PhD Candidacy Qualifying Exam (UC Berkeley, 11 June 2009).

I have taught the following classes at Northwestern:

- Spring 2014: Freshman Seminar: Theories of mind and mathematics
- Fall 2013: Math 300: Foundations of Higher Mathematics

I have taught the following classes at UC Berkeley:

- Summer 2009: Math 1B: Calculus
- Spring 2009: Math 1A: Calculus
- Fall 2008: Math 32: Precalculus
- Summer 2008: Math 1B: Calculus
- Spring 2008: Math 53: Multivariable Calculus
- Fall 2007: Math 1B: Calculus

My husband and I are avid cooks. For a while we collected recipes and discussions at Local Seasoning. We are on hiatus right now, but may start up again.

In a previous life, I was a kitchen manager at Columbae House, at Stanford University. Around the same time, I was also a dancer, and I choreographed the Opening Committee performance for the 2007 Stanford Viennese Ball (video).