Lecturer in Pure Mathematics
Contact details
Address:
Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom
Office: College House 204
Email: apt12@leicester.ac.uk
Personal details
Websites
My publications and preprints can be found on the arxiv and on mathscinet, or Google's attempt to model the academic world.
Publications
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Decomposition Spaces and Restriction Species. Int. Math. Res. Notices, :–, 201.
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Decomposition spaces, incidence algebras and Möbius inversion III: The decomposition space of Möbius intervals. Adv. Math., 334:544–584, 2018.
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness. Adv. Math., 333:1242–1292, 2018.
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory Adv. Math., 331:952–1015, 2018.
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Homotopy linear algebra. Proc. Roy. Soc. Edinburgh Sect. A, 148(2):293–325, 2018.
Imma Gálvez, Vassily Gorbounov, Zain Shaikh, and Andrew Tonks. The Berkovits complex and semi-free extensions of Koszul algebras. Ann. Fac. Sci. Toulouse Math. (6) 25(2-3): 363–384, 2016
K Worytkiewicz, K Hess, P-E Parent, A Tonks. Corrigendum to: "A model structure à la Thomason on 2-Cat''. J. Pure Appl. Algebra 220(12):4017–4023, 2016.
Imma Gálvez-Carrillo, Leandro Lombardi, Andrew Tonks. An A∞ operad in spineless cacti. Mediterr. J. Math. 12(4): 1215–1226, 2015
Fernando Muro, Andrew Tonks, and Malte Witte. On determinant functors and K-theory. Publ. Mat., 59:137–233, 2015.
Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. Adv. Math., 254:79–117, 2014.
Fernando Muro and Andrew Tonks. Unital associahedra. Forum Math., 26(2):593–620, 2014.
Imma Gálvez-Carrillo, Frank Neumann, and Andrew Tonks. Thomason cohomology of categories. J. Pure Appl. Algebra, 217(11):2163–2179, 2013.
Imma Gálvez-Carrillo, Frank Neumann, and Andrew Tonks. André spectral sequences for Baues-Wirsching cohomology of categories. J. Pure Appl. Algebra, 216(11):2549–2561, 2012.
Imma Gálvez-Carrillo, Andrew Tonks, and Bruno Vallette. Homotopy Batalin-Vilkovisky algebras. J. Noncommut. Geom., 6(3):539–602, 2012.
I. Gálvez, V. Gorbounov, and A. Tonks. Homotopy Gerstenhaber structures and vertex algebras. Appl. Categ. Structures, 18(1):1–15, 2010.
Kathryn Hess and Andrew Tonks. The loop group and the cobar construction. Proc. Amer. Math. Soc., 138(5):1861–1876, 2010.
Fernando Muro and Andrew Tonks. On K1 of a Waldhausen category. In K-theory and noncommutative geometry, EMS Ser. Congr. Rep., pages 91–115. Eur. Math. Soc., Zürich, 2008.
Fernando Muro and Andrew Tonks. The 1-type of a Waldhausen K-theory spectrum. Adv. Math., 216(1):178–211, 2007.
K. Worytkiewicz, K. Hess, P. E. Parent, and A. Tonks. A model structure à la Thomason on 2-cat. J. Pure Appl. Algebra, 208(1):205–236, 2007.
Carles Casacuberta, Marek Golasinski, and Andrew Tonks. Homotopy localization of groupoids. Forum Math., 18(6):967–982, 2006.
Kathryn Hess, Paul-Eugène Parent, Jonathan Scott, and Andrew Tonks. A canonical enriched Adams-Hilton model for simplicial sets. Adv. Math., 207(2):847–875, 2006.
Imma Gálvez and Andrew Tonks. Differential operators and the Witten genus for projective spaces and Milnor manifolds. Math. Proc. Cambridge Philos. Soc., 135(1):123–131, 2003.
A. P. Tonks. On the Eilenberg-Zilber theorem for crossed complexes. J. Pure Appl. Algebra, 179(1-2):199–220, 2003.
R. Brown, M. Golasinski, T. Porter, and A. Tonks. Spaces of maps into classifying spaces for equivariant crossed complexes. II. The general topological group case. K-Theory, 23(2):129–155, 2001.
Hans-Joachim Baues and Andrew Tonks. On the twisted cobar construction. Math. Proc. Cambridge Philos. Soc., 121(2):229–245, 1997.
Hans-Joachim Baues, Mamuka Jibladze, and Andy Tonks. Cohomology of monoids in monoidal categories. In Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), volume 202 of Contemp. Math., pages 137–165. Amer. Math. Soc., Providence, RI, 1997.
R. Brown, M. Golasinski, T. Porter, and A. Tonks. Spaces of maps into classifying spaces for equivariant crossed complexes. Indag. Math. (N.S.), 8(2):157–172, 1997.
Andy Tonks. Relating the associahedron and the permutohedron. In Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), volume 202 of Contemp. Math., pages 33–36. Amer. Math. Soc., Providence, RI, 1997.
Hans-Joachim Baues and Andy Tonks. On sum-normalised cohomology of categories, twisted homotopy pairs and universal Toda brackets. Quart. J. Math. Oxford Ser. (2), 47(188):405–433, 1996.
Ronald Brown and Andrew Tonks. Calculations with simplicial and cubical groups in AXIOM. J. Symbolic Comput., 17(2):159–179, 1994.
A. P. Tonks. Cubical groups which are Kan. J. Pure Appl. Algebra, 81(1):83–87, 1992.
Research
My research is in the areas of algebraic homotopy and homotopy algebra. That is, I am interested in algebraic and categorical models for the homotopy theory of topological spaces, and in the use of homotopy theoretic methods in algebra and category theory. I work with infinity-groupoids (in both the classical and the modern senses), simplicial objects, and operads.
