Hello everyone,

I'm Pedro Orlando and I am currently doing a double degree between the 
State University of Campinas (Unicamp), Brazil and Télécom Paris, France. 
At Unicamp I was in the last year of my BSc in Applied Mathematics, and now 
I'm specialising in Applied Algebra and Theoretical Computer Science at 
Télécom Paris during the double degree.

The Applied Maths syllabus at Unicamp is quite open-ended and, as such, I 
dedicated about half of my graduation to pure mathematics, and the other 
half to algorithmics.
At Télécom, I've had, most notably, courses dedicated to the implementation 
of graph algorithms and even an entire semester dedicated to using Sage for 
algebraic applications, and with it I gained some experience with its uses.

Albeit never having worked with open-source per se, I'm very passionate 
about it. In terms of experience, however, I have worked for two years as a 
full-stack developer using Python, C++ and other languages (SQL, 
javascript, shellscript, ...), even acting as code maintainer for a while, 
and thus I am quite accustomed to the git workflow of big projects; I have 
even already started getting acquainted with your development flow by 
making a small contribution to a documentation ticket #33271 
<https://trac.sagemath.org/ticket/33271> in Sage.

>From the ideas list, the two topics which have interested me the most were:
- Rewrite exterior algebra and implement Gröbner bases
- Edge connectivity and edge disjoint spanning trees in digraphs

The first idea is very closely related to the subjects I've studied in 
Applied Algebra, with special mention to Gröbner bases which were often 
used during courses (I might need a refresher though). In this topic, I'd 
love further clarification on ticket #32369 
<https://trac.sagemath.org/ticket/32369> for rewriting exterior algebra 
(namely, the starting point: is the problem in the ExteriorAlgebra class in 
algebras/clifford_algebra.py ?). This project might require me to 
understand Cython more deeply, as well as find out how one would go about 
implementing the bonus "ambitious" goal, but I'm up for the task of 
learning these!

As for the second one, I've always been very interested in graph theory and 
their algorithms, this being one of my favourite topics, and it seems to be 
very well documented, discussed and explained in Sage's trac, even 
containing a paper with the related algorithm, so I'm ready to dive 
head-first into all of the discussions relating to this project. Should 
this be of interest to anyone, I have a small project on GitHub 
<https://github.com/scramblerdoodle/MITRO209_densest_subgraph> implementing 
an algorithm for an approximation to the densest subgraph problem in linear 
time.

Cheers and all the best,
Pedro

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