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Index Theory For Invariant Elliptic Operators On Manifolds With Proper Cocompact Group Actions, Gong Cheng

Arts & Sciences Electronic Theses and Dissertations

In this thesis, we study G-invariant elliptic operators, and in particular Dirac operators, on the space of invariant sections of a Hermitian bundle over a (non-compact) manifold with a proper and cocompact Lie group action. We provide a canonical way to define the Hilbert space of invariant sections for proper and cocompact actions and prove that the G-invariant Dirac operators, and more generally, elliptic operators, are Fredholm for the Hilbert space we constructed. Using the framework developed in this thesis, we give a new proof of a generalized Lichnerowicz Vanishing Theorem for proper cocompact group actions as an application.

Topics In Pt-Symmetric Quantum Mechanics And Classical Systems, Nima Hassanpour

Arts & Sciences Electronic Theses and Dissertations

Space-time reflection symmetry, or PT symmetry, first proposed in quantum mechanics by Bender and Boettcher in 1998 [2], has become an active research area in fundamental physics. This dissertation contains several research problems which are more or less related to this field of study. After an introduction on complementary topics for the main projects in Chap.1, we discuss about an idea which is originated from the remarkable paper by Chandrasekar et al in Chap.2. They showed that the (second-order constant-coefficient) classical equation of motion for a damped harmonic oscillator can be derived from a Hamiltonian having one degree of freedom. …

Algorithmic Trading With Prior Information, Xinyi Cai

Arts & Sciences Electronic Theses and Dissertations

Traders utilize strategies by using a mix of market and limit orders to generate profits. There are different types of traders in the market, some have prior information and can learn from changes in prices to tweak her trading strategy continuously(Informed Traders), some have no prior information but can learn(Uninformed Learners), and some have no prior information and cannot learn(Uninformed Traders). In this thesis. Alvaro C, Sebastian J and Damir K \cite{AL} proposed a model for algorithmic traders to access the impact of dynamic learning in profit and loss in 2014. The traders can employ the model to decide which …

Carlson's Theorem For Different Measures, Meredith Sargent

Arts & Sciences Electronic Theses and Dissertations

Hedenmalm, Lindqvist, and Seip in 1997 [11] revitalized the modern study of Dirichlet

series by defining the space H 2 and considering it as isometrically isomorphic to the Hardy

space of the infinite polytorus H 2 (T ∞ ). This allowed a new viewpoint to be applied to

classical theorems, including Carlson’s theorem about the integral in the mean of a Dirichlet

series. Carlson’s theorem holds only for vertical lines in the right half plane, and cannot be

extended to the boundary in full generality (as shown by Saksman and Seip in [14]). However,

Carlson’s theorem can be shown to …

Regulators On Higher Chow Groups, Muxi Li

Arts & Sciences Electronic Theses and Dissertations

There are two natural questions one can ask about the higher Chow group of number fields:

One is its torsion, the other one is its relation with the homology of GLn. For the first

question, based on some earlier work, the integral regulator on higher Chow complexes

introduced here can put a lot of earlier result on a firm ground. For the second question, we

give a counterexample to an earlier proof of the existence of linear representatives of higher

Chow groups of number fields.

Chapter 1 gives a general picture of the two problems we are talking about. Chapter …