Teaching
Math 5316, Linear Algebra
Math 3350, Differential Equations
Office hours: MWF 10:00-10:50am.
Research
Papers
- The Batalin-Vilkovisky formalism in noncommutative effective field theory. arXiv:2505.15938.
- Noncommutative effective field theories and the large N correspondence. arXiv:2505.13678.
- A homological approach to the Gaussian unitary ensemble (with
O.Gwilliam and M. Zeinalian). J. Noncommut. Geom. 19 (2025),
no.2, 533-572.
- Large N phenomena and quantization of the
Loday-Quillen-Tsygan theorem (with G. Ginot, O.Gwilliam
and M. Zeinalian). Adv. Math. 409 (2022).
- A Poincaré-Birkhoff-Witt theorem for profinite pronilpotent Lie algebras. J. Lie Theory 29 (2019), no. 3, 611-618.
- On two constructions of an effective field theory. J. Lond. Math. Soc. (2) 94 (2016), no. 1, 314--336.
- The topological quantum field theory of Riemann's theta functions (with R. Gelca). J. Geom. Phys. 98 (2015), 242--261.
- Classical theta functions
from a quantum group perspective (with R. Gelca). New York J. Math. 21
(2015), 93--127.
- Classes
on the moduli space of Riemann surfaces through a
noncommutative Batalin-Vilkovisky formalism. Adv. Math. 243 (2013), 67--101.
- A
nondiagrammatic description of the Connes-Kreimer Hopf
algebra. J. Pure Appl. Algebra 217
(2013), no. 3, 449--469.
- On the
extension of a TCFT to the boundary of the moduli space.
Lett. Math. Phys. 98
(2011), no. 2, 111--132.
- Noncommutative geometry
and compactifications of the moduli space of curves. J. Noncommut. Geom. 4 (2010), no. 2, 157--188.
- Cohomology theories for homotopy algebras and noncommutative geometry
(with A. Lazarev). Algebr. Geom. Topol. 9 (2009),
1503--1583.
- Classes on compactifications of the moduli space of curves through solutions to the quantum master equation. Lett. Math. Phys. 89 (2009), no. 2, 115--130.
- Graph cohomology classes in the Batalin-Vilkovisky formalism (with A. Lazarev). J. Geom. Phys. 59 (2009), no. 5, 555--575.
- Characteristic classes of A-infinity algebras (with A. Lazarev). J. Homotopy Relat. Struct. 3 (2008), no. 1, 65--111.
- Symplectic C-infinity algebras (with A. Lazarev). Mosc. Math. J. 8 (2008), no. 3, 443--475, 615.
- Symplectic A-infinity algebras and string topology operations (with A. Lazarev). Amer. Math. Soc. Transl. (2), Vol. 224, 2008, 147--157.
- A super-analogue of Kontsevich's theorem on graph homology. Lett. Math. Phys. 76 (2006), no. 1, 37--55.
- On the classification of Moore algebras and their deformations. Homology, Homotopy Appl. 6 (2004), no. 1, 87--107.
- Homotopy algebras and noncommutative geometry (with A. Lazarev). arXiv:math/0410621.