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CARMA Research Group

Number Theory, Algorithms and Discrete Mathematics

About us

Leader: Florian Breuer

This group covers a wide range of research interests from number theory, combinatorics and theoretical computer science, and in particular the interplay between these fields as well as links to analysis and algebraic geometry.

Topics of interest include: Diophantine analysis and Mahler functions; the arithmetic of global fields including elliptic curves, Drinfeld modules and associated modular forms; special integer sequences and special values of analytic functions; Hadamard matrices; combinatorics, enumeration and the probabilistic method; graph theory, optimal networks and other discrete structures.

There is a strong focus on computational aspects of such topics, including experimental mathematics, visualisation, computational number theory and the analysis of algorithms.

Potential applications of our work range from coding theory and cryptography through group theory, counting points on algebraic varieties to computer networks and even theoretical physics.

People

Members of this research group:

  • Brian Alspach
  • David Bailey
  • Ljiljana Brankovic
  • Richard Brent
  • Florian Breuer
  • Stephan Chalup
  • Tony Guttman
  • Yuqing Lin
  • Jim MacDougall
  • Andrew Mattingly
  • Judy-anne Osborn
  • Joe Ryan
  • Matt Skerrit

Activities

  • Mahler Lecture

    4:00 pm, Monday, 25th Nov 2019
    LSTH, Life Sciences Lecture Theatre
    "Transcendence and dynamics"
       Dr Holly Krieger
    Abstract:
    Many interesting objects in the study of the dynamics of complex algebraic varieties are known or conjectured to be transcendental, such as the uniformizing map describing the (complement of a) Julia set, or the Feigenbaum constant. We will discuss various connections between transcendence theory and complex dynamics, focusing on recent developments using transcendence theory to describe the intersection of orbits in algebraic varieties, and the realization of transcendental numbers as measures of dynamical complexity for certain families of maps.