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1	Branched Covering Constructions and the Symplectic Geography Problem Hughes, Mark Clifford January 2008 (has links) We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a positive integer λ(s) such that each pair (j,8j+s) with j ≥ λ(s) is realized as (χ_h(M),c_1^2(M)) for some minimal simply-connected symplectic M. The smallest values of λ(s) currently known to the author are also explicitly computed for 0 ≤ s ≤ 99. Our computations in these cases populate 19 952 points in the (χ,c)-plane not previously realized in the existing literature. 4-manifold branched covering symplectic geography symplectic manifold Pure Mathematics
2	Branched Covering Constructions and the Symplectic Geography Problem Hughes, Mark Clifford January 2008 (has links) We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a positive integer λ(s) such that each pair (j,8j+s) with j ≥ λ(s) is realized as (χ_h(M),c_1^2(M)) for some minimal simply-connected symplectic M. The smallest values of λ(s) currently known to the author are also explicitly computed for 0 ≤ s ≤ 99. Our computations in these cases populate 19 952 points in the (χ,c)-plane not previously realized in the existing literature. 4-manifold branched covering symplectic geography symplectic manifold Pure Mathematics
3	Topics Pertaining to the Group Matrix: k-Characters and Random Walks Reese, Randall Dean 01 June 2015 (has links) (PDF) Linear characters of finite groups can be extended to take k operands. The basics of such a k-fold extension are detailed. We then examine a proposition by Johnson and Sehgal pertaining to these k-characters and disprove its converse. Probabilistic models can be applied to random walks on the Cayley groups of finite order. We examine random walks on dihedral groups which converge after a finite number of steps to the random walk induced by the uniform distribution. We present both sufficient and necessary conditions for such convergence and analyze aspects of algebraic geometry related to this subject. k-characters group determinant random walks branched covering Mathematics
4	The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers / 多項式写像のモジュライ空間とその固定点における微分係数 Sugiyama, Toshi 23 July 2018 (has links) 京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13201号 / 論理博第1560号 / 新制\|\|理\|\|1635(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授宍倉光広, 教授泉正己, 教授國府寛司 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM complex dynamics moduli space polynomial map fixed-point multiplier Bezout's theorem intersection multiplicity branched covering 400

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