Chloe Martindale

I am a number theorist currently working as a Postdoc at Technical University of Eindhoven in the group of Prof. dr. Tanja Lange. I am currently working on pairing-based cryptography and the discrete logarithm problem for elliptic curves as part of the USEIT project. My other research interests include Hilbert modular forms, genus 2 and 3 curves with complex multiplication, and isogeny graphs.

Research

  • PhD thesis: Isogeny Graphs, Modular Polynomials, and Applications (draft), supervised by Marco Streng
  • Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication, Sean Ballentine, Aurore Guillevic, Elisa Lorenzo Garcia, Chloe Martindale, Maike Massierer, Benjamin Smith, and Jaap Top
  • Contact information:

    Office: 6.097a MetaForum, Technische Universiteit Eindhoven
    Telephone: +31-40247 2541
    E-mail: chloemartindale (at) gmail (dot) com
    Address: MetaForum building, 5612 AZ, Eindhoven, The Netherlands
    • Co-supervised Bachelor Thesis of Ivo Kok, 'Rings in which every ideal has 2 generators', Spring 2014, with Marco Streng.
    • Here is a growing list of Hilbert modular polynomials. The theory behind this and the algorithm to compute them is in Chapter 2 of my PhD thesis.
      Examples for totally real field \(\mathbb{Q}(\sqrt{5})\):
      Examples for totally real field \(\mathbb{Q}(\sqrt{2})\):
    • Constructing genus 2 curves over finite fields with a prescribed number of points, (pdf), talk in the DIAMANT Symposium in Breukelen, the Netherlands (June 2017).
    • Counting points on genus 2 curves over finite fields, (pdf), talk in the Number Theory Seminar at l'Insitut Fourier, Grenoble (May 2017).
    • Counting points on genus 2 curves over finite fields, (pdf), talk in the Number Theory Seminar at EPFL, Lausanne (November 2016).
    • Studying genus 2 and 3 curves using isogeny graphs and modular polynomials, (pdf), talk in the Algebra Seminar at Universiteit Leiden, Leiden (November 2016).
    • From conic sections to isogeny graphs, (slides), Colloquium talk at University College Dublin (June 2016).
    • Modularity of Elliptic Curves over \(\mathbb{Q}\), (pdf), talk in the Elliptic Curves Seminar at Universiteit Leiden, Leiden (April 2016).
    • Counting points of Jacobians of Genus 2 curves over large finite fields, progress report on a joint research project at AGC2016, led by Ben Smith and Jaap Top, AGC2016, UCLA (February 2016).
    • Isogeny Graphs, (pdf), talk in the PhD Colloquium at Universiteit Leiden, Leiden (October 2015).
    • The theory of canonical lifts, (pdf), Universiteit Leiden (July 2015).
    • The Galois representation associated to modular forms (Part I), (pdf), Universiteit Leiden (May 2015).
    • An algorithm for computing Hilbert modular varieties (pdf), LFANT Seminar, IMB, Université de Bordeaux (September 2014).
    • Elliptic curves and jacobians of curves of genus 2, talk on master thesis supervised by Prof. E. Victor Flynn, University of Oxford (April 2013).