Essays about: "holomorphic"

Showing result 1 - 5 of 14 essays containing the word holomorphic.

  1. 1. Gromov-Witten invariants via localization techniques

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Noah Dizep; [2023]
    Keywords : Gromov-Witten invariants; enumerative geometry; string theory;

    Abstract : Gromov-Witten invariants play a crucial role in symplectic- and enumerative Geometry as well as topological String Theory. Essentially, theseinvariants are a count of (pseudo)holomorphic curves of a given genus,going through n-marked points on a symplectic manifold. READ MORE

  3. 2. An operator theoretic approach to the Riemann Hypothesis

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Ramon Arjan van de Scheur; [2023]
    Keywords : Riemann hypothesis; Prime number theorem; Prime number theorem for arithmetic progressions; operator theoretic equivalent; compact operator; prime-counting function; Chebyshev function; Laplace transform; Fourier transform; convolution operator; weak topology; strong topology; compact perturbation; Tauberian theorem; Poisson kernel; holomorphic; self-adjoint; spectrum; trace; Mathematics and Statistics;

    Abstract : In 2023 an operator theoretic approach to the Prime Number Theorem was introduced by Olsen. In this thesis this approach is examined and applied to give a new, operator theoretic, proof of a different version of the Prime Number Theorem and of the Prime Number Theorem for arithmetic progressions. READ MORE

  4. 3. An Introduction to Hitchin Systems

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Manuel Neumayer; [2023]
    Keywords : Mathematics and Statistics;

    Abstract : This thesis aims to introduce the tools that are needed to understand — and historically led to the inception of — Hitchin systems. We lay out a basic theory of Hamiltonian systems on symplectic manifolds, and prove the Liouville-Arnold theorem, which states that integrable Hamiltonian systems admit coordinates in which their solution is basically linear. READ MORE

  5. 4. The Uniformization Theorem

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Nikita Zozoulenko; [2021]
    Keywords : complex analysis; riemann surface; analytic functions; holomorphic functions; differential geometry; harmonic; subharmonic; perron; analysis; Mathematics and Statistics;

    Abstract : In this bachelor's thesis we provide a self contained proof of the Uniformization Theorem. It states that a simply connected Riemann surface is conformally equivalent to either the complex plane C, the unit disk D, or the Riemann sphere C^*. READ MORE

  6. 5. Equivariant Mathai-Quillen Formalism

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Yu Hao; [2021]
    Keywords : ;

    Abstract :  Equivariant localization is a technique can be used to reduce the dimensionality of integral for the manifold with a Lie group action on. Such technique can beapplied to simply the calculation of path integral with certain type of symmetries. READ MORE