# Dissertations and Theses - Mathematics

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• (2019-07-03)
Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the ...

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• (2019-07-10)
Fix a Weierstrass cubic curve $E$, and an element $\sigma$ in the Jacobian variety $\Jac E$ corresponding to the line bundle $\mathcal L_\sigma$. We introduce a space $\mathsf{RS}_{\sigma, n}(E, V)$ of pure 1-dimensional ...

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• (2019-07-09)
We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k), where k is an algebraically closed field of characteristic p > n. Let X be a smooth projective curve over ...

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• (2019-06-03)
This thesis consists of three projects. The first project focuses on the distribution of zeros of linear combinations of derivatives of $L$-functions. We consider a collection of such combinations and prove asymptotic ...

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• (2019-05-28)
Equivariant elliptic cohomology and twisted equivariant K-theory are both related to the representations of loop groups. After making these relationships precise, we propose a map from twisted equivariant elliptic cohomology ...

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