# 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 $$\mathbb{Q}(\sqrt{2})$$:
• 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).