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Dissertations and Theses  Mathematics
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(20190703)Motivic DonaldsonThomas (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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(20190710)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 1dimensional ...
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(20190709)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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(20190603)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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(20190528)Equivariant elliptic cohomology and twisted equivariant Ktheory 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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