Professor Sarah Whitehouse
School of Mathematical and Physical Sciences
Professor of Pure Mathematics
+44 114 222 3870
Full contact details
School of Mathematical and Physical Sciences
J6c
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
-
I obtained my Ph.D. from the University of Warwick in 1994, following a B.Sc. (1990) and M.Sc. (1991) also from Warwick. I spent several years in France, as a Marie Curie post-doctoral researcher at the Université Paris 13 and as a Maître de Conférences at Lens, before coming to Sheffield in 2002.
- Research interests
-
In algebraic topology we use algebra to extract topological or geometric information about spaces. Among the standard tools used to carry out the translation from topology to algebra are generalised cohomology theories. Given such a theory there is an associated algebra of operations, carrying a wealth of structure and information. Prof Whitehouse is particularly interested in studying the structure and properties of these algebras.
A simple, yet still interesting example, is given by complex K-theory. This theory has a strong geometric flavour and yet there is a rich interplay with other areas, such as number theory.
The interplay between topology and algebra leads to ``up to homotopy'' versions of algebraic structures. Prof Whitehouse is interested in A-infinity and E-infinity algebras, arising when one weakens associativity and commutativity conditions.
- Publications
-
Show: Featured publications All publications
Featured publications
Journal articles
- Model category structures and spectral sequences. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. View this article in WRRO
All publications
Journal articles
- Preface for the WITIII proceedings volume. Topology and its Applications, 316, 108098-108098.
- Model category structures on multicomplexes. Topology and its Applications.
- The plethory of operations in complex
topological K-theory. Annals of K-Theory, 6(3), 481-502.
- On the spectral sequence associated to a multicomplex. Journal of Pure and Applied Algebra. View this article in WRRO
- Derived A-infinity algebras and their homotopies. Topology and its Applications, 235, 214-268. View this article in WRRO
- Upper triangular matrices and operations in odd primary connective K-theory. Forum Mathematicum, 27(3), 1435-1378.
- Representations of Derived A-infinity Algebras. Contemporary Mathematics, 641, 1-27.
- Central Cohomology Operations and K-Theory. Proceedings of the Edinburgh Mathematical Society.
- Derived A
∞ -algebras in an operadic context. Algebraic and Geometric Topology, 13(1), 409-440. View this article in WRRO
- Uniqueness of A∞-structures and Hochschild cohomology. Algebraic and Geometric Topology, 11(1), 107-143.
- Discrete module categories and operations in K-theory. Topology and its Applications.
- Infinite sums of unstable Adams operations and cobordism. Journal of Pure and Applied Algebra, 214(6), 910-918.
- Integer-Valued polynomials and K-Theory operations. Proceedings of the American Mathematical Society, 138(6), 2221-2233.
- THE HUNTING OF THE HOPF RING. HOMOL HOMOTOPY APPL, 11(2), 75-132.
- Stable and unstable operations in mod p cohomology theories. ALGEBR GEOM TOPOL, 8(2), 1059-1091.
- The discrete module category for the ring of K-theory operations. TOPOLOGY, 46(2), 139-154.
- Algebraic properties of stably numerical polynomials. J PURE APPL ALGEBRA, 207(3), 607-617.
- Infinite sums of Adams operations and cobordism. MATH Z, 251(3), 475-489.
- Algebras of operations in K-theory. TOPOLOGY, 44(1), 151-174.
- Higher Conjugations and the Yang–Baxter Equation. Journal of Algebra, 251(2), 914-926.
- Operads and Γ-homology of commutative rings. Mathematical Proceedings of the Cambridge Philosophical Society, 132(2), 197-234.
- . Journal of Algebraic Combinatorics, 13(3), 317-326.
- HIGHER CONJUGATION COHOMOLOGY IN COMMUTATIVE HOPF ALGEBRAS. Proceedings of the Edinburgh Mathematical Society, 44(1), 19-26.
- SYMMETRIC GROUP ACTIONS ON TENSOR PRODUCTS OF HOPF ALGEBROIDS. Communications in Algebra, 29(8), 3351-3363.
- On conjugation invariants in the dual Steenrod algebra. Proceedings of the American Mathematical Society, 128(9), 2809-2818.
- The Eulerian representations of ∑n as restrictions of representations of ∑n + 1. Journal of Pure and Applied Algebra, 115(3), 309-320.
- A counterexample to a conjecture of Barr. Theory and Applications of Categories, 2, 36-39.
- The tree representation of ∑n + 1. Journal of Pure and Applied Algebra, 111(1-3), 245-253.
- Homotopy theory of spectral sequences. Homology, Homotopy and Applications (HHA).
- Bases for Cooperations in K-Theory. K-Theory, 23(3), 237-250.
- Model category structures and spectral sequences. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. View this article in WRRO
Conference proceedings papers
- Operads and Γ-homology of commutative rings. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 132(2) (pp 197-234)
Preprints
- Spectral sequences via linear presheaves, arXiv.
- Homotopy theory of spectral sequences, arXiv.
- Model category structures on multicomplexes, arXiv.
- On the spectral sequence associated to a multicomplex, arXiv.
- Model category structures and spectral sequences, arXiv.
- Derived A-infinity algebras and their homotopies, arXiv.
- Representations of derived A-infinity algebras, arXiv.
- Derived A-infinity algebras in an operadic context, arXiv.
- Uniqueness of $A_infty$-structures and Hochschild cohomology, arXiv.
- Model category structures and spectral sequences. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. View this article in WRRO
- Research group
- Grants
-
Past grants, as Principal Investigator
Rigidity Theorems in Stable Homotopy Theory EPSRC Rings Defined by Systems of Congruences and Applications in Topology Leverhulme Stable and Unstable Operations in Higher K-Theory EPSRC
- Teaching interests
-
I am an enthusiastic lecturer with wide experience of undergraduate teaching at all levels. For many years I have taught a popular level 3 Combinatorics module. Other courses I have taught in Sheffield include Algebraic Topology and Groups and Symmetries. Prior lecturing experience includes courses on Metric Spaces and Measure and Integration.I very much enjoy supervising project work. Level 4 MMath project topics I have supervised include Aperiodic Tilings, Integer Vauled Polynomials and Integer Partitions.
- Teaching activities
-
MAS221 Analysis MAS334 Combinatorics