Alastair Hamilton
Department of Mathematics and Statistics
Texas Tech University
Lubbock, TX 79409-1042

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Teaching

Math 4324, Introduction to Topology

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Research

My current research interests involve connections between noncommutative geometry, quantum field theory and the study of moduli spaces of Riemann surfaces. Recently, I have become interested in connections to low-dimensional topology and the invariants of Reshetikhin and Turaev. All my papers are available from the arXiv.

Papers

• Large N phenomena and quantization of the Loday-Quillen-Tsygan theorem (with G. Ginot, O.Gwilliam and M. Zeinalian). arXiv:2108.12109.
  
• 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). math.QA/0410621.