# Browse Dissertations and Theses - Mathematics by Contributor "Rezk, Charles"

• (2016-06-21)
We give an explicit construction of extended topological field theories over a manifold taking values in the deloopings of U(1) from the data of differential forms on the manifold. More specifically, for a manifold M, using ...

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• (2016-07-13)
Let E denote a Morava E-theory at a prime p and height h. We characterize the power operations on π0 of a K(h)-local E∞-E-algebra in terms of a small amount of algebraic data. This involves only the E-cohomology of two ...

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• (2018-06-29)
The end goal of this work is to define and study an elementary higher topos. We will achieve this by going through several steps. First we review complete Segal spaces. Then we study various fibrations of complete Segal ...

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• (2010-08-20)
In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\Sigma$, this construction takes the form of a ...

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• (2017-07-11)
A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their ...

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• (2013-02-03)
Let $P_m$ and $D_m$ be the $m^{th}$ level and layer of the Goodwillie-Taylor tower for discrete modules. In \cite{intermont_johnson_mccarthy08} the rank filtration of $D_1F$ is described and the associated spectral sequence ...

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• (2012-02-06)
The origin of these investigations was the successful attempt by myself and coauthors to generalize rational equivalences of two constructions which suggest possible definitions of deRham cohomology of “brave new” rings, ...

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• (2017-11-28)
The equivariant 𝔼∞G operad has the property that 𝔼∞G(n) is the total space for the G-equivariant universal principal Σn bundle. There is a forgetful functor from 𝔼∞G-algebras to 𝔼∞-algebras, where 𝔼∞ is the classic ...

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• (2010-08-20)
Voevodsky showed that there is a motivic spectrum representing algebraic K-theory. We describe an equivalent spectrum that is also a symmetric ring spectrum. A coherence problem occurs when one veriﬁes the symmetry. It is ...

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• (2008)
Recent work of Ando, Blumberg, Gepner, Hopkins and Rezk characterize Einfinity orientations of K-Theory. Their description involves producing measures on the p-adic units with certain moments. In his thesis, Ando produced ...

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• (2017-04-21)
We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring $\mathbb{Z}[q^{\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant ...

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• (2017-07-13)
We define and study the $K$-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of McCarthy, we determine, for a discrete ...

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• (2010-08-20)
Let $\mathcal{C} \colon= \mathds{C}/ \Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of $\mathcal{ O}_{\mathcal{C}^n}$-algebras ...

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• (2011-08-25)
In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel discovered a generalized character theory that proved useful in studying cohomology rings of the form E^*(BG). In this ...

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• (2008)
We then define the units of equivariant spectra in terms of equivariant Gamma-spaces. Thus showing that units of equivariant spectra are equivariant spectra.

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