Dr Andrew Baker
- Honorary Senior Research Fellow (School of Mathematics & Statistics)
email:
Andrew.J.Baker@glasgow.ac.uk
School of Mathematics & Statistics, Mathematics & Statistics Building, University Place, Glasgow, G12 8QQ
https://orcid.org/0000-0002-9369-7702Research interests
My main research interests are in Algebraic Topology, especially stable homotopy theory. Other interests include Hopf algebras, Hopf algebroids and formal groups, Galois theory of commutative rings, number theory and homological algebra.
Research groups
Publications
2022
Baker, A. (2022) Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory. arXiv, (doi: 10.48550/arXiv.2212.00437) (Unpublished)
Baker, A. (2022) Locally Frobenius algebras and Hopf algebras. Technical Report. arXiv. (Submitted)
Baker, A. (2022) On P-algebras and their duals. Technical Report. arXiv. (Unpublished)
2021
Baker, A. (2021) On the dual of a P-algebra and its comodules, with applications to comparison of some Bousfield classes. Technical Report. arXiv. (Submitted)
2020
Baker, A. (2020) Homotopy theory of modules over a commutative $S-algebra: some tools and examples. arXiv, (Unpublished)
Baker, A. (2020) Power operations in K-theory completed at a prime. Tbilisi Mathematical Journal(Spec 6), pp. 33-49.
Baker, A. and Bauer, T. (2020) The realizability of some finite-length modules over the Steenrod algebra by spaces. Algebraic and Geometric Topology, 20(4), pp. 2129-2143. (doi: 10.2140/agt.2020.20.2129)
2018
Baker, A. (2018) Iterated doubles of the Joker and their realisability. Homology, Homotopy and Applications, 20(2), pp. 341-360. (doi: 10.4310/HHA.2018.v20.n2.a17)
Baker, A. (2018) Characteristics for E∞ ring spectra. Contemporary Mathematics, 708, pp. 1-17. (doi: 10.1090/conm/708)
2017
Baker, A. (2017) E∞ ring spectra and elements of Hopf invariant 1. Boletín de la Sociedad Matemática Mexicana, 23(1), pp. 195-231. (doi: 10.1007/s40590-016-0096-8)
2015
Baker, A. (2015) Power operations and coactions in highly commutative homology theories. Publications of the Research Institute for Mathematical Sciences, 51(2), pp. 237-272. (doi: 10.4171/PRIMS/154)
2014
Baker, A. and Richter, B. (2014) Some properties of the Thom spectrum over loop suspension of complex projective space. Contemporary Mathematics, 617, pp. 1-12. (doi: 10.1090/conm/617)
2013
Baker, A. (2013) BP: close encounters of the E∞ kind. Journal of Homotopy and Related Structures, 9(2), pp. 257-282. (doi: 10.1007/s40062-013-0051-6)
2012
Baker, A.J. , Richter, B. and Szymik, M. (2012) Brauer groups for commutative S-algebras. Journal of Pure and Applied Algebra, 216(11), pp. 2361-2376. (doi: 10.1016/j.jpaa.2012.03.001)
Baker, A. (2012) On the cohomology of loop spaces for some Thom spaces. Geometry and Topology, 18, pp. 59-74.
Baker, A. (2012) Calculating with topological André-Quillen theory, I: homotopical properties of universal derivations and free commutative S-algebras. arXiv, (Unpublished)
Baker, A. (2012) Frobenius Green functors. arXiv, (Unpublished)
2011
Baker, A. and Richter, B. (2011) Galois theory and Lubin-Tate cochains on classifying spaces. Central European Journal of Mathematics, 9(5), pp. 1074-1087. (doi: 10.2478/s11533-011-0058-3)
2009
Baker, A. (2009) L-complete Hopf algebroids and their comodules. Contemporary Mathematics, 504, pp. 1-22.
Baker, A.J. and Richter, B. (2009) New Topological Contexts for Galois Theory and Algebraic Geometry (BIRS 2008). Series: Geometry and topology monographs, 16. Mathematical Sciences Publishers. (doi: 10.2140/gtm.2009.16)
2008
Baker, A. and Richter, B. (2008) Galois extensions of Lubin-Tate spectra. Homology, Homotopy and Applications, 10(3), pp. 27-43.
Baker, A. , Gilmour, H. and Reinhard, P. (2008) Topological Andre-Quillen homology for cellular commutative S-algebras. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 78(1), pp. 27-50. (doi: 10.1007/s12188-008-0005-9)
Baker, A. and Richter, B. (2008) Quasisymmetric functions from a topological point of view. Mathematica Scandinavica, 103(2), pp. 208-242.
Baker, A. and Richter, B. (2008) On the cooperation algebra of the connective Adams summand. Tbilisi Mathematical Journal, 1, pp. 33-70.
Baker, A. and Richter, B. (2008) Uniqueness of E-infinity structures for connective covers. Proceedings of the American Mathematical Society, 136(2), pp. 707-714. (doi: 10.1090/S0002-9939-07-08984-8)
2007
Baker, A. and Richter, B. (2007) Realizability of algebraic Galois extensions by strictly commutative ring spectra. Transactions of the American Mathematical Society, 359, pp. 827-857.
2005
Baker, A. and Richter, B. (2005) Invertible modules for commutative S-algebras with residue fields. Manuscripta Mathematica, 118(1), pp. 99-119. (doi: 10.1007/s00229-005-0582-1)
Baker, A. and Richter, B. (2005) On the Gamma-cohomology of rings of numerical polynomials and E-infinity structures on K-theory. Commentarii Mathematici Helvetici, 80(4), pp. 691-723. (doi: 10.4171/CMH/31)
2004
Baker, A.J. and May, J.P. (2004) Minimal atomic complexes. Topology, 43(3), pp. 645-665. (doi: 10.1016/j.top.2003.09.004)
Baker, A. and Richter, B. (Eds.) (2004) Structured Ring Spectra. Series: London Mathematical Society Lecture Note Series. Cambridge University Press: Cambridge, UK. ISBN 9780521603058
Baker, A. and Lazarev, A. (2004) Topological Hochschild cohomology and generalized Morita equivalence. Algebraic and Geometric Topology, 4, pp. 623-645. (doi: 10.2140/agt.2004.4.623)
2002
Baker, A. (2002) Matrix Groups: An Introduction to Lie Group Theory. Series: Springer undergraduate mathematics series. Springer: London, UK. ISBN 9781852334703
Baker, A. and Jeanneret, A. (2002) Brave new Hopf algebroids and extensions of MU-algebras. Homology, Homotopy and Applications, 4(1), pp. 163-173.
2001
Baker, A. (2001) On the Adams E2-term for elliptic cohomology. In: Greenlees, J.P.C. (ed.) Homotopy Methods in Algebraic Topology : Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, June 20 - 24, 1999. Series: Contemporary mathematics (271). American Mathematical Society: Providence, USA, pp. 1-15. ISBN 9780821826218
Baker, A. and Lazarev, A. (2001) On the Adams spectral sequence for R–modules. Algebraic and Geometric Topology, 1, pp. 173-199. (doi: 10.2140/agt.2001.1.173)
Baker, A. and Tamanoi, H. (2001) Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras. In: McKay, J. and Sebbar, A. (eds.) Proceedings on Moonshine and Related Topics. Series: CRM proceedings & lecture notes (30). American Mathematical Society: Providence, USA, pp. 1-13. ISBN 9780821828793
Articles
Baker, A. (2022) Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory. arXiv, (doi: 10.48550/arXiv.2212.00437) (Unpublished)
Baker, A. (2020) Homotopy theory of modules over a commutative $S-algebra: some tools and examples. arXiv, (Unpublished)
Baker, A. (2020) Power operations in K-theory completed at a prime. Tbilisi Mathematical Journal(Spec 6), pp. 33-49.
Baker, A. and Bauer, T. (2020) The realizability of some finite-length modules over the Steenrod algebra by spaces. Algebraic and Geometric Topology, 20(4), pp. 2129-2143. (doi: 10.2140/agt.2020.20.2129)
Baker, A. (2018) Iterated doubles of the Joker and their realisability. Homology, Homotopy and Applications, 20(2), pp. 341-360. (doi: 10.4310/HHA.2018.v20.n2.a17)
Baker, A. (2018) Characteristics for E∞ ring spectra. Contemporary Mathematics, 708, pp. 1-17. (doi: 10.1090/conm/708)
Baker, A. (2017) E∞ ring spectra and elements of Hopf invariant 1. Boletín de la Sociedad Matemática Mexicana, 23(1), pp. 195-231. (doi: 10.1007/s40590-016-0096-8)
Baker, A. (2015) Power operations and coactions in highly commutative homology theories. Publications of the Research Institute for Mathematical Sciences, 51(2), pp. 237-272. (doi: 10.4171/PRIMS/154)
Baker, A. and Richter, B. (2014) Some properties of the Thom spectrum over loop suspension of complex projective space. Contemporary Mathematics, 617, pp. 1-12. (doi: 10.1090/conm/617)
Baker, A. (2013) BP: close encounters of the E∞ kind. Journal of Homotopy and Related Structures, 9(2), pp. 257-282. (doi: 10.1007/s40062-013-0051-6)
Baker, A.J. , Richter, B. and Szymik, M. (2012) Brauer groups for commutative S-algebras. Journal of Pure and Applied Algebra, 216(11), pp. 2361-2376. (doi: 10.1016/j.jpaa.2012.03.001)
Baker, A. (2012) On the cohomology of loop spaces for some Thom spaces. Geometry and Topology, 18, pp. 59-74.
Baker, A. (2012) Calculating with topological André-Quillen theory, I: homotopical properties of universal derivations and free commutative S-algebras. arXiv, (Unpublished)
Baker, A. (2012) Frobenius Green functors. arXiv, (Unpublished)
Baker, A. and Richter, B. (2011) Galois theory and Lubin-Tate cochains on classifying spaces. Central European Journal of Mathematics, 9(5), pp. 1074-1087. (doi: 10.2478/s11533-011-0058-3)
Baker, A. (2009) L-complete Hopf algebroids and their comodules. Contemporary Mathematics, 504, pp. 1-22.
Baker, A. and Richter, B. (2008) Galois extensions of Lubin-Tate spectra. Homology, Homotopy and Applications, 10(3), pp. 27-43.
Baker, A. , Gilmour, H. and Reinhard, P. (2008) Topological Andre-Quillen homology for cellular commutative S-algebras. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 78(1), pp. 27-50. (doi: 10.1007/s12188-008-0005-9)
Baker, A. and Richter, B. (2008) Quasisymmetric functions from a topological point of view. Mathematica Scandinavica, 103(2), pp. 208-242.
Baker, A. and Richter, B. (2008) On the cooperation algebra of the connective Adams summand. Tbilisi Mathematical Journal, 1, pp. 33-70.
Baker, A. and Richter, B. (2008) Uniqueness of E-infinity structures for connective covers. Proceedings of the American Mathematical Society, 136(2), pp. 707-714. (doi: 10.1090/S0002-9939-07-08984-8)
Baker, A. and Richter, B. (2007) Realizability of algebraic Galois extensions by strictly commutative ring spectra. Transactions of the American Mathematical Society, 359, pp. 827-857.
Baker, A. and Richter, B. (2005) Invertible modules for commutative S-algebras with residue fields. Manuscripta Mathematica, 118(1), pp. 99-119. (doi: 10.1007/s00229-005-0582-1)
Baker, A. and Richter, B. (2005) On the Gamma-cohomology of rings of numerical polynomials and E-infinity structures on K-theory. Commentarii Mathematici Helvetici, 80(4), pp. 691-723. (doi: 10.4171/CMH/31)
Baker, A.J. and May, J.P. (2004) Minimal atomic complexes. Topology, 43(3), pp. 645-665. (doi: 10.1016/j.top.2003.09.004)
Baker, A. and Lazarev, A. (2004) Topological Hochschild cohomology and generalized Morita equivalence. Algebraic and Geometric Topology, 4, pp. 623-645. (doi: 10.2140/agt.2004.4.623)
Baker, A. and Jeanneret, A. (2002) Brave new Hopf algebroids and extensions of MU-algebras. Homology, Homotopy and Applications, 4(1), pp. 163-173.
Baker, A. and Lazarev, A. (2001) On the Adams spectral sequence for R–modules. Algebraic and Geometric Topology, 1, pp. 173-199. (doi: 10.2140/agt.2001.1.173)
Books
Baker, A.J. and Richter, B. (2009) New Topological Contexts for Galois Theory and Algebraic Geometry (BIRS 2008). Series: Geometry and topology monographs, 16. Mathematical Sciences Publishers. (doi: 10.2140/gtm.2009.16)
Baker, A. (2002) Matrix Groups: An Introduction to Lie Group Theory. Series: Springer undergraduate mathematics series. Springer: London, UK. ISBN 9781852334703
Book Sections
Baker, A. (2001) On the Adams E2-term for elliptic cohomology. In: Greenlees, J.P.C. (ed.) Homotopy Methods in Algebraic Topology : Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, June 20 - 24, 1999. Series: Contemporary mathematics (271). American Mathematical Society: Providence, USA, pp. 1-15. ISBN 9780821826218
Baker, A. and Tamanoi, H. (2001) Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras. In: McKay, J. and Sebbar, A. (eds.) Proceedings on Moonshine and Related Topics. Series: CRM proceedings & lecture notes (30). American Mathematical Society: Providence, USA, pp. 1-13. ISBN 9780821828793
Edited Books
Baker, A. and Richter, B. (Eds.) (2004) Structured Ring Spectra. Series: London Mathematical Society Lecture Note Series. Cambridge University Press: Cambridge, UK. ISBN 9780521603058
Research Reports or Papers
Baker, A. (2022) Locally Frobenius algebras and Hopf algebras. Technical Report. arXiv. (Submitted)
Baker, A. (2022) On P-algebras and their duals. Technical Report. arXiv. (Unpublished)
Baker, A. (2021) On the dual of a P-algebra and its comodules, with applications to comparison of some Bousfield classes. Technical Report. arXiv. (Submitted)