The Intersection of Parallel Lines

On Wednesday, February 27, 5:30-6:30 in LGRT 1634, Tobias Wilson will be speaking on “The Intersection of Parallel Lines” (abstract below). As usual, free pizza and soda will be provided.

Hope to see you there!

Abstract:

Two distinct lines in a plane either intersect in exactly one point or
are parallel and never intersect. In this talk, we will reunite those
lonely parallel lines by introducing the notion of projective space.
We will then explore various definitions of projective space and end
by deriving some cool results about curves and tangent lines.

2/20: Kostis Gourgoulias, “Solving optimization problems.. with ants?”

This week, Kostis Gourgoulias will be giving a talk entitled “Solving optimization problems.. with ants?” (abstract below) on Wednesday, Feb. 20th from 5:30-6:30 in 1634. As always, pizza and soda will be provided.

Abstract:
To paraphrase a motto from Numb3rs, ”we all solve optimization problems every day”. From the moment we wake up to the moment we return to bed, we seek to waste as less money and time as possible. And if we happen to be mathematicians, we may also have to solve a couple of optimization problems in math as well. So important is optimization, that one can spend her/his entire
life studying the different methods and then (try to) apply them to different, often extremely hard, problems. Efficient solutions of those problems are worth a lot for both the academic community and the industry. But which method to use? That’s also difficult to answer because there are as many methods as available problems.

So, what do ants have to do with anything? In 1991, Marco Dorigo introduced a new algorithm for solving combinatorial optimization problems (think travelling salesman) based on the behaviour of ants scavenging for food. Apart from being a very cool idea on it’s own, it also helped open up a new branch between mathematics and algorithms, that of swarm intelligence. There are many questions that still have not been answered about how much one can do
with those ideas.

In this talk, we will talk a bit about optimization in general, see what is the idea & the math that Dorigo ”stumbled” onto how it can be turned into an algorithm and what does the algorithm actually do when it runs. What better way to pass the afternoon?

Undergrad Math Seminar, Wed 2/13: Jeff Hatley, “The Birch and Swinnerton-Dyer Conjecture”.

This Wednesday from 5:30-6:30 in LGRT1634, Jeff Hatley will give a talk, entitled “The Birch and Swinnerton-Dyer Conjecture”. The abstract appears below. As always, pizza and soda will be provided.

The Clay Mathematics Institute offers a $1 million prize for the solution
to each of a handful of math problems. This week’s talk will explain one of
them, the Birch and Swinnerton-Dyer Conjecture, which relates the number of
solutions to certain equations, called elliptic curves, to the roots of
certain power series, called L-functions. This talk is for a general
audience.

Undergraduate Math Seminar: This Wednesday, 2/6, 5:30-6:30

The Undergraduate Math Seminar is restarting for the spring semester! We have a great schedule of talks planned, starting this week with Nico Aiello, who will speak on “An Introduction to Secret Keeping and RSA Encryption” (the abstract appears below)

We will meet in LGRT 1634 at 5:30. As always, pizza and soda will be provided.

Abstract: If you’ve got secrets, come learn how to protect them. Be
it trying to ensure the security of a nation, avoid identity theft, or
just keep a diary private, the need for secret keeping is a huge
concern in today’s world. After covering some background material on
modular arithmetic and the Euler phi-function, we will learn the
mathematics behind the RSA encryption method. The talk will be very
interactive – everyone will have a chance to encrypt a word or phrase
(or secret) of their own – and accessible to all. To help with some of
the computation it would be helpful for those who attend to have a
computer or graphing calculator, though it is not necessary.