Essays about: "algebraic number theory"

Showing result 1 - 5 of 11 essays containing the words algebraic number theory.

  1. 1. Tensor rank and support rank in the context of algebraic complexity theory

    University essay from KTH/Matematik (Avd.)

    Author : Pelle Andersson; [2023]
    Keywords : linear algebra; tensor product; tensor rank; matrix multiplication; complexity; linjär algebra; tensorprodukt; tensorrang; matrismultiplikation; komplexitet;

    Abstract : Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. READ MORE

  3. 2. Profinite groups

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

    Author : Juan Moreno Poncela; [2023]
    Keywords : Profinite Groups; Infinite Galois Theory; Mathematics and Statistics;

    Abstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE

  4. 3. Cyclotomic Fields and Fermat's Last Theorem

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

    Author : Samuel Runyeon Odeberg; [2021]
    Keywords : pure mathematics; number theory; algebra; algebraic number theory; cyclotomic fields; cyclotomic rings; cycltomic integers; Fermat s last theorem; Mathematics and Statistics;

    Abstract : Number theory is in a sense among the oldest disciplines of mathematics. A running theme is that many number theoretic problems are very easy to state and understand. However, actually solving these problems often requires much work or some very clever trick. READ MORE

  5. 4. Voronoi Cells of Varieties with respect to Wasserstein Distances

    University essay from KTH/Matematik (Avd.)

    Author : Adrian Becedas; [2021]
    Keywords : ;

    Abstract : Voronoi diagrams are partitions of a metric space into Voronoi cells according to distance from points on some set w.r.t. some distance. READ MORE

  6. 5. Scheme Theory & Weak Mordell-Weil for Elliptic Curves Over Number Fields

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

    Author : Carl-Fredrik Lidgren; [2021]
    Keywords : algebraic geometry; schemes; scheme theory; elliptic curves; Mordell-Weil; weak Mordell-Weil; algebraic number theory; arithmetic geometry; number theory; geometry; Mathematics and Statistics;

    Abstract : We provide an introduction to scheme-theoretic algebraic geometry, which studies spaces that are in essence locally solutions to systems of polynomial equations, and prove the weak Mordell-Weil theorem. The weak Mordell-Weil theorem states that for an elliptic curve $E$ over a number field $K$, the quotient $E(K)/mE(K)$ is finite for all $m\geq 2$. READ MORE