Maths Research Associates 2021 Warwick
Lead Research Organisation:
University of Warwick
Department Name: Statistics
Abstract
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Organisations
Publications
Bachmayr M
(2023)
Polynomial approximation of symmetric functions
in Mathematics of Computation
Barucco M
(2024)
Rational circle-equivariant elliptic cohomology of CP(V)
in Homology, Homotopy and Applications
Barucco, M.
(2022)
An algebraic model for rational T2-equivariant elliptic cohomology
Herdegen M
(2024)
? -Arbitrage and ? -Consistent Pricing for Star-Shaped Risk Measures
in Mathematics of Operations Research
Thomas J
(2022)
Body-Ordered Approximations of Atomic Properties.
in Archive for rational mechanics and analysis
| Description | The publication RATIONAL CIRCLE-EQUIVARIANT ELLIPTIC COHOMOLOGY reports a splitting result between the algebraic models for rational T2- and T-equivariant elliptic cohomology, where T is the circle group and T2 is the 2-torus. As an application we compute rational T-equivariant elliptic cohomology of CP(V ): the T-space of complex lines for a finite dimensional complex T-representation V . This is achieved by reducing the computation of T-elliptic cohomology of CP(V ) to the computation of T2-elliptic cohomology of certain spheres of complex representations. The publication 'An algebraic model for rational T2-equivariant elliptic cohomology' reports the construct a rational T2-equivariant elliptic cohomology theory for the 2-torus T2, starting from an elliptic curve C over C and a coordinate data around the identity. The theory is defined by constructing an object ECT2 in the algebraic model category dA(T2), which by Greenlees and Shipley [GS18] is Quillen-equivalent to rational T2-spectra. This result is a generalisation to the 2-torus of the construction [Gre05] for the circle T. The object ECT2 is directly built using geometric inputs coming from the Cousin complex of the structure sheaf of the complex abelian surface X = C × C. We use this construction to compute rational T-equivariant elliptic cohomology of CP(V ): the complex projective space of a finite dimensional complex representation V of T. More precisely we prove that ECT built in [Gre05] and ECT2 satisfy a split condition implying ECT(CP(V )+) _= ECT2(S(V w)+) where S(_) is the sphere of vectors with unit norm and w is the natural representation of T. The rational T2-elliptic cohomology of this space can be deduced from the one on spheres of complex representations SV of T2 that we compute in the construction of ECT2 . |
| Exploitation Route | A future direction, discussed in 'An algebraic model for rational T2-equivariant elliptic cohomology', was the construction of rational T2-equivariant elliptic cohomology ECT2 ? A(T2). A natural question is how to generalize this construction and the construction for the circle ECT ? A(T) to tori of any rank Tk, namely building rational Tk-equivariant elliptic cohomology ECTk ? A(Tk) starting from an elliptic curve C over C and a coordinate te ?OC,e. |
| Sectors | Aerospace Defence and Marine Energy |
| URL | https://link.intlpress.com/JDetail/1844208016011415553 |