USRA Summer Seminar
Coordinator: Henri Darmon
Organisational Meeting: Monday, May 2 at 10:00.
Regular meetings: Wednesdays 10:00 to 11:30.
Participants and tentative topics:
Tayeb Aissiou: Shor's quantum factorisation algorithm
Anne-Sophie Charest: Elliptic curve factorisation algorithms
Mathieu Guay-Paquet: Schoof's algorithm for counting points on elliptic curves over finite fields
Ilya Hekimi: Elliptic curve cryptosystems
Louis-Francois Preville-Ratelle: Topics in combinatorial number theory.
Mireille Schnitzer: Primes in arithmetic progressions
Suggested topics for the seminar.
Congratulations on receiving the NSERC Undergraduate Summer Research Award!
I have decided to coordinate the activities of the USRA recipients
working with me by running a weekly seminar, which will be a chance for
people to interact, describe what they are working on,
and discuss questions that arise.
The USRA program is very unstructured: you will be given an office and a
monthly stipend, your sole duties being to learn some new mathematics,
try to come up with a problem that you find interesting, and then make some
progress on it.
These conditions are (dauntingly, perhaps) similar to those of a mathematics
PhD student, and you might not feel completely ready!
Here are some words of advice, which also apply to students embarking on
their PhD studies.
1. This website contains a list of suggestions
for topics that are sufficiently
self-contained that they can be absorbed and explored in a summer.
Try fixing your choice, as early as possible,
on a topic that catches your imagination.
You are free to change your course along the way if,
say, you decide to delve into a sub-topic that
you find intriguing, or even to branch out into something completely
2. You will have to absorb alot of material, much of it on your own.
Don't do this passively. For example, when confronted with a theorem,
put off reading and understanding the proof until you have worked out
a few concrete
examples that illustrate the result, and
can give you a feeling for how it works. This will often
make the proof, when you get to it, seem more natural.
3. Do not isolate yourself.
Being stuck is less discouraging when you can share your
Although you are not required to show up at McGill beyond your
attendance of the weekly seminar, you are encouraged to come to your office
regularly, as this will
allow frequent exchanges with the other USRA recipients.
4. Because of the unstructured nature of the program,
you can only hope to get as much out of the USRA as you put in.
A USRA can be a pleasant, stimulating, and rewarding
experience, and will hopefully allow you to get a taste
of more advanced mathematics, and even
I wish you the best of success
the most of this exciting opportunity!