The University of Southampton

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Phone:: (023) 8059 2141
Email:: S.D.Theriault@soton.ac.uk

Professor Stephen Theriault

Professor, Head of Pure Mathematics

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Professor Stephen Theriault is a Professor in Pure Mathematics within Mathematical Sciences at the University of Southampton. He specialises in homotopy theory, a branch of algebraic topology, which is concerned with the classification of topological spaces up to continuous deformation. He has over 50 research publications and served as the topology editor of the journal The Proceedings of the Edinburgh Mathematical Society. He is now the journal's convenor.

Background

2012 - date Reader, University of Southampton

2002 - 12 Lecturer, Senior Lecturer, University of Aberdeen

1999 - 02 Whyburn Postdoctoral Fellow, University of Virginia

1998 - 99 NSERC Postdoctoral Fellow, MIT

1997 - 98 University of Illinois at Chicago

1997 PhD Mathematics, University of Toronto

1991 BSc Mathematics, Dalhousie University

Research

Publications

Teaching

Contact

Research interests

Unstable homotopy theory and its applications to other areas of mathematics and physics. I am particularly interested in the homotopy theory of fundamental spaces, such as spheres, Moore spaces and Lie groups. I am also interested in using methods from homotopy theory to solve problems that arise in other areas; this includes studying moment-angle complexes and polyhedral products in toric topology, complements of coordinate subspace arrangements in combinatorics, gauge groups in mathematical physics, and moduli spaces in algebraic geometry.

Research projects: There are several excellent problems which are suitable for a PhD thesis and subsequent research in the areas described above, particularly in the applications of homotopy theory to other areas of mathematics and physics. If you are interested in studying for a PhD in one of these areas, please contact me.

Research group

Pure Mathematics

Articles

Theriault, S., Kishimoto, D., & Tsutaya, M. (2017). The homotopy types of G₂-gauge groups. Topology and its Applications.

Kaji, S., Sakai, M., & Theriault, S. (2016). Counting the number of homotopy associative multiplications on certain H-spaces. Topology and its Applications, 214, 137-149. DOI: 10.1016/j.topol.2016.10.008

Grbic, J., & Theriault, S. (2016). Homotopy theory in toric topology. Russian Mathematical Surveys, 71(2), 185-251. DOI: 10.1070/RM9704

Theriault, S. (2016). Mod-p homotopy decompositions of looped Stiefel manifolds. Homology, Homotopy and Applications, 18(2), 59-69. DOI: 10.4310/HHA.2016.v18.n2.a3

Theriault, S. (2016). Odd primary homotopy types of SU(n) gauge groups. Algebraic and Geometric Topology, 1-18.

Grbic, J., Panov, T., Theriault, S., & Wu, J. (2016). The homotopy types of moment-angle complexes for flag manifolds. Transactions of the American Mathematical Society, 368(9), 6663-6682. DOI: 10.1090/tran/6578

Kaji, S., Ohsita, A., & Theriault, S. (2015). Mod p decompositions of the loop spaces of compact symmetric spaces. Algebraic and Geometric Topology, 15(3), 1771-1811. DOI: 10.2140/agt.2015.15.1771

Theriault, S. (2015). Moment-angle manifolds and Panov's problem. Research in Math Sciences, 2015(20), 10154-10175.

Grbić, J., Theriault, S., & Wu, J. (2014). Suspension splittings and James-Hopf invariants for retracts of the loops on co-H-spaces. Proceedings of the Royal Society of Edinburgh Section A Mathematics, 144(1), 87-108. DOI: 10.1017/S0308210512000480

Beben, P., & Theriault, S. (2014). The loop space homotopy type of simply-connected four- manifolds and their generalizations. Advances in Mathematics.

Grbić, J., & Theriault, S. (2013). The homotopy type of the polyhedral product for shifted complexes. Advances in Mathematics, 245, 690-715. DOI: 10.1016/j.aim.2013.05.002

Beben, P., & Theriault, S. (2013). The Kahn-Priddy Theorem and the homotopy of the three-sphere. Proceedings of the American Mathematical Society, 141(2), 711-723. DOI: 10.1090/S0002-9939-2012-11337-1

Grbić, J., Theriault, S., & Wu, J. (2012). Decompositions of looped co-H-spaces. Proceedings of the American Mathematical Society, 141, 1451-1464. DOI: 10.1090/S0002-9939-2012-11417-0

Grbić, J., Harper, J., Mimura, M., Theriault, S., & Wu, J. (2012). Rank p ? 1 mod-p H-spaces. Israel Journal of Mathematics, 194(2), 641-688. DOI: 10.1007/s11856-012-0085-1

Theriault, S. D. (2011). 2-primary Anick fibrations. Journal of Topology, 4(2), 479-503. DOI: 10.1112/jtopol/jtr008

Selick, P., Theriault, S., & Wu, J. (2011). Functorial homotopy decompositions of looped co-H spaces. Mathematische Zeitschrift, 267(1-2), 139-153. DOI: 10.1007/s00209-009-0613-9

Gray, B., & Theriault, S. (2010). An elementary construction of Anick's fibration. Geometry & Topology, 14(1), 243-275. DOI: 10.2140/gt.2010.14.243

Theriault, S. D. (2010). Odd primary homotopy decompositions of gauge groups. Algebraic & Geometric Topology, 10(1), 535-564. DOI: 10.2140/agt.2010.10.535

Beben, P., & Theriault, S. (2010). Torsion in finite H-spaces and the homotopy of the three-sphere. Homology, Homotopy and Applications, 12(2).

MATH2003 Group Theory

MATH6137 Homotopy and Homology

Professor Stephen Theriault
Building 54 Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ

Room Number:54/8017

Telephone:(023) 8059 2141
Email:S.D.Theriault@soton.ac.uk

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