## Research papers

### Published and accepted for publication

Minimal nondegenerate extensions. With David Reutter.

*Journal of the American Mathematical Society*, to appear. (abstract, arXiv:2105.15167.)Topological Orders in (4+1)-Dimensions. With Matthew Yu. SciPost Phys. 13, 068 (2022). (abstract, arXiv:2104.04534, DOI:10.21468/SciPostPhys.13.3.068.)

On the classification of topological orders.

*Communications in Mathematical Physics*, 393, pp 989–1033 (2022). (abstract, arXiv:2003.06663, DOI:10.1007/s00220-022-04380-3, full-text published version.)Fusion 2-categories with no line operators are grouplike. With Matthew Yu.

*Bulletin of the Australian Mathematical Society*, vol 104, issue 3, pp 434–442, December 2021. (abstract, arXiv:2010.07950, DOI:10.1017/S0004972721000095.)Holomorphic SCFTs with small index. With Davide Gaiotto.

*Canadian Journal of Mathematics*, 2021:1-29. (abstract, arXiv:1811.00589. DOI:10.4153/S0008414X2100002X.)Supersymmetry and the Suzuki chain.

*Tunisian Journal of Mathematics*, Vol 3, No 2, pp 309–359, 2021. (abstract, arXiv:1908.11012, DOI:10.2140/tunis.2021.3.309.)A note on some minimally supersymmetric models in two dimensions. With Davide Gaiotto and Edward Witten. In

*Integrability, Quantization, and Geometry II. Quantum Theories and Algebraic Geometry: Dedicated to the Memory of Boris Dubrovin 1950–2019*, volume 103.2 of*Proceedings of Symposia in Pure Mathematics*, pp 203–222, Amer. Math. Soc., Providence, RI, 2021. (abstract, arXiv:1902.10249, AMS Bookstore.)Galois action on VOA gauge anomalies.

*Progress in Mathematics*volume in honour of Kolya Reshetikhin, 2020. (abstract, arXiv:1811.06495.)Heisenberg-picture quantum field theory.

*Progress in Mathematics*volume in honour of Kolya Reshetikhin, 2020. (abstract, arXiv:1508.05908.)Third homology of some sporadic finite groups. With David Treumann.

*Symmetry, Integrability and Geometry: Methods and Applications*15 (2019), 059. (abstract, arXiv:1810.00463, DOI: 10.3842/SIGMA.2019.059.)Symmetry protected topological phases and generalized cohomology. With Davide Gaiotto.

*Journal of High Energy Physics.*May 2019. (abstract, arXiv:1712.07950, DOI: 10.1007/JHEP05(2019)007.)The Moonshine Anomaly.

*Communications in Mathematical Physics*. February 2019, Volume 365, Issue 3, pp 943–970. (abstract. DOI: 10.1007/s00220-019-03300-2. Published PDF available at https://rdcu.be/bjHMt. arXiv:1707.08388.)H

^{4}(Co_{0};**Z**)=**Z**/24. With David Treumann.*International Mathematics Research Notices*, 2020, no. 21, 7873–7907. (abstract. DOI: 10.1093/imrn/rny219. arXiv:1707.07587.)How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism. With Owen Gwilliam.

*Topology and quantum theory in interaction*, 175–185, Contemp. Math., 718, Amer. Math. Soc., Providence, RI, 2018. (abstract. AMS bookstore. arXiv:1202.1554.)Spin, statistics, orientations, unitarity.

*Algebraic & Geometric Topology*17 (2017) 917–956. (abstract, arXiv:1507.06297, DOI: 10.2140/agt.2017.17.917.)(Op)lax natural transformations, twisted field theories, and the "even higher" Morita categories. With Claudia Scheimbauer.

*Advances in Mathematics*, 307 (2017) 147–223. (abstract, arXiv:1502.06526, DOI: 10.1016/j.aim.2016.11.014.)The quaternions and Bott periodicity are quantum Hamiltonian reductions.

*Symmetry, Integrability and Geometry: Methods and Applications*, 12 (2016), 116, 6 pages. (abstract, arXiv:1603.06603, DOI: 10.3842/SIGMA.2016.116.)Tree- versus graph-level quasilocal Poincaré duality on

*S*^{1}.*Journal of homotopy and related structures*, June 2016, Volume 11, Issue 2, pp 333–374. (abstract, arXiv:1412.4664, DOI: 10.1007/s40062-015-0110-2.)Homological perturbation theory for nonperturbative integrals.

*Letters in Mathematical Physics*, November 2015, Volume 105, Issue 11, pp 1605–1632. (abstract, arXiv:1206.5319, DOI: 10.1007/s11005-015-0791-9.)Reflexivity and dualizability in categorified linear algebra. With Martin Brandenburg and Alexandru Chirvasitu.

*Theory and Applications of Categories*, Vol. 30, No. 23, 2015, pp. 808–835. (abstract, arXiv:1409.5934, published version (open access).)Poisson AKSZ theories and their quantizations. 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.)The fundamental pro-groupoid of an affine 2-scheme. With Alex Chirvasitu.

*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.

*Journal of Mathematical Physics*, 51, 122103 (2010). (abstract, published PDF, DOI:10.1063/1.3503472, arXiv:1004.4305, equation and theorem numbering differs between preprint and published versions).Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics.

*Letters in Mathematical Physics*, November 2010, Volume 94, Issue 2, pp 123–149. (abstract, arXiv:1003.1156, available Open Access from Springer Link at DOI: 10.1007/s11005-010-0424-2).

### Submitted for Publication

Ground-state degeneracy of twisted sectors of Conway Moonshine SCFT. 2023. (abstract, arXiv:2305.05081.)

(3+1)D topological orders with only a

**Z**_{2}-charged particle. 2020. (abstract, arXiv:2011.11165.)Topological Mathieu Moonshine. 2020. (abstract, arXiv:2006.02922.)

Condensations in higher categories. With Davide Gaiotto. 2019. (abstract, arXiv:1905.09566.)

Mock modularity and a secondary elliptic genus. With Davide Gaiotto. 2019. (abstract, arXiv:1904.05788.)

### Other Preprints

Exact triangles, Koszul duality, and coisotopic boundary conditions. 2016. (abstract, arXiv:1608.08598.)

Chains(

**R**) does not admit a geometrically meaningful properadic homotopy Frobenius algebra structure. 2013. (abstract, arXiv:1308.3423.) Published as Tree- versus graph-level quasilocal Poincaré duality on*S*^{1}Peturbative techniques in path integration. Ph.D. Thesis. 2013. (abstract, PDF.) Published as: Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics, The formal path integral and quantum mechanics

On the coordinate (in)dependence of the formal path integral. 2010. (abstract, PDF, arXiv:1003.5730).