Andrew Tonks

Lecturer in Pure Mathematics (January 2015-August 2021)

Fixed Term Teaching Fellow (August-September 2021)

Contact details

Address:
Department of Mathematics

University of Leicester 
University Road 
Leicester LE1 7RH 
United Kingdom

OfficeCollege House 204 - Building currently closed!
Emailapt12@leicester.ac.uk or  a.p.tonks@gmail.com

Personal details

Websites

My publications list can also be found on my ORCID ID, and preprints can be found on the arxiv. If you have a subscription, reviews of them can be found at mathscinet.

Publications

  • Gálvez-Carrillo, Imma; Neumann, Frank ; Tonks, Andrew. Gabriel-Zisman Cohomology and Spectral Sequences.. Appl. Categ. Structures, 29(1):69–94, 2021.
  • Masuda, Naruki; Thomas, Hugh; Tonks, Andy; Vallette, Bruno. The diagonal of the associahedra. J. Éc. polytech. Math. 8:121–146, 2021.
  • Gálvez-Carrillo, Imma; Kaufmann, Ralph M.; Tonks, Andrew.Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation. Commun. Number Theory Phys. 14(1):91–169, 2020.
  • Gálvez-Carrillo, Imma; Kaufmann, Ralph M.; Tonks, Andrew.Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects. Commun. Number Theory Phys. 14(1):1–90, 2020.
  • Imma Gálvez-Carrillo, Joachim Kock, and Andrew Tonks. Decomposition Spaces and Restriction Species. Int. Math. Res. Notices, 21:7558–7616, 2020.
  • 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.  Many applications to the real world appear, for example, via the techniques of Persistent Homology.

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