Hello,

My name is David Ayotte and I'm a PhD student in mathematics at Concordia 
University in Montreal. My research interests are within the field of 
number theory. More precisely, I study modular forms and their 
generalization to function field, which we call Drinfeld modular forms. In 
the past (for my master thesis), I have also studied questions about 
linking the class number of a quadratic imaginary field with modular forms. 
Thanks to Sagemath and PARI/GP, I was able to do enlightening 
experimentations that complemented my work greatly.

Recently, I started to work on this project of mine about a Sagemath 
module. The goal of my project is to implement Drinfeld modules (which can 
be seen as analogues of elliptic curves for characteristic p function 
fields). Moreover, I am interested in writing functions about Drinfeld 
modular forms. Here's my Github repo: drinfeld-modular-forms 
<https://github.com/DavidAyotte/drinfeld-modular-forms>. Ultimately, I 
would like to implement this functionality directly to Sagemath as there 
are no such functionality yet. You can also refer to my Github page 
<https://github.com/DavidAyotte> for more of my coding projects.

In summer 2017, I participated to the 1-week workshop Sage Days 87 where I 
learned the basics of contributing to Sagemath. The goal of this workshop 
was to develop the p-adics in Sagemath, which were lacking some 
functionality at the time. During this workshop, I worked on some tickets 
which were about fixing a bug or reviewing some contribution. Here's some 
ticket I've worked on:

   - #29330 <https://trac.sagemath.org/ticket/29330>: I reviewed this old 
   ticket recently (this weekend). It is about implementing the method  
   is_skew_hermitian() for matrices.
   - #23473 <https://trac.sagemath.org/ticket/23473>: I fixed this bug: the 
   method is_one() would return "False" for Integers(1)(1) (which is the only 
   element of the zero ring).
   - #23484 <https://trac.sagemath.org/ticket/23484>: I reviewed this 
   ticket about a bug.
   - #20308 <https://trac.sagemath.org/ticket/20308>: I reviewed this 
   ticket about the Zeta function for schemes.
   
These small projects were a good introduction to the development of 
Sagemath. I learned about the git trac command and how to do doctests. 
However, I feel that GSoC would be a fantastic opportunity for me to tackle 
a bigger project and gain more confidence about Sagemath developing as I 
want to continue contributing to it thereafter. 

Best regards,

David Ayotte
PhD Math Student at Concordia University, Mtl
github.com/DavidAyotte


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