February 9: Michael Northington
Title: Probability and March Madness
Abstract: In this talk, we will cover the basic rules of probability theory and look at a few simple but counter-intuitive results. Also, we will look at an interesting application of probability and statistics where a Markov chain is used to rank college basketball teams. As it turns out, this method, developed by researchers at Georgia Tech, has been successful when compared to other ranking systems (such as RPI, AP poll, ESPN poll, Sagarin rankings, etc.) in predicting the outcome of NCAA tournament games.
February 16: Alex Vlasiuk
Title: A Mathematical Theory of Communication
Abstract: We present some of the ideas from the famous eponymous paper by C. Shannon. A pioneering work of its time (1948), it created several new fields in science and technology. Many powerful modern algorithms, as LZMA compression for example, can be traced to principles formulated by Shannon: they use Markov chains to model the information source. Despite the evolution of data compression and encoding over the past decades, this work can still serve as a remarkably concise and clear introduction to the modern developments.
February 23: Jordan Nikkel
Title: Proofs that everyone should see at least once
Abstract: Math is a language in which we can say many different things. Sometimes we need to build extensive context and vocabulary, but there are plenty of intriguing statements and whose truth we can prove with very little above what you already know. In this talk, we will focus on a series of interesting math problems with elegant, short, and varied solutions, including touring the famous bridges of Königsberg, finding irrational numbers whose exponentiation is rational, and using functions to compare different sizes of infinity.
March 1: Zach Gaslowitz
Title: Fun and Games
Abstract: Come enjoy an evening of fun as we learn how to play, and how to win, some simple pen-and-paper games. We’ll study Nim, Hex, Sprouts, and perhaps a few others, exploring some neat ideas in combinatorial game theory as we try to work out winning strategies. Play later with your friends and family! Guaranteed to make everyone like you.
March 15: José Gil-férez
Title: Speaker: Banach, Tarski, the Sun, and the Pea
Abstract: In a chaotic ever-changing world, one approaches Mathematics in search of stability and eternal truth. We imagine Mathematics as the realm in which everything occupies a precise position, all uncertainty disappears, and we can verify our ideas about how the world should be, if it were ideal. But, we bring with us our prejudices and, despite of the fact that in many occasions Mathematics confirm our intuitions, sometimes we encounter controversial results. Infinity, in particular, seems to be a source of unintuitive findings: there are no more natural numbers than even numbers, we cannot list all the real numbers, … This is only natural, since our intuitions are based mainly (if not exclusively) on finite experiences. But some controversial discoveries do not seem to be related to any infinite process; one of these is Banach-Tarski Theorem: we can divide a sphere in a finite number of pieces, move these pieces (without deformations) and put them back together in a way that we obtain two spheres of the same radius than the original one. An equivalent statement is the following: we can divide a sphere of the size of a pea into finitely many pieces and rearrange them (without deformations) in a way that we obtain a sphere of the size of the Sun. We will explore this theorem and try to understand its significance.
March 22: Victor Falgas-Ravry
Title: A measure of surprise: entropy and its applications
Abstract: Entropy, in its information-theoretic incarnation, was introduced by Claude Shannon in 1948 as a measure of randomness — with the name `entropy’ suggested by John von Neumann, who pointed out that “nobody knows what entropy really is, so in a debate you will always have the advantage”. In this talk I will outline the basic notions and properties of entropy, as well as some of its surprising applications.
April 5: Yuri Bakhturin
Abstract: I would like to talk about the ways people extend the notion of numbers. This includes matrix algebras, division algebras, vector algebras. All these are widely used in Mathematics and its applications.
March 29: Sayan Das
Title: Beam me up, Scotty!
Abstract: Would you like to construct a portable transwarp beaming device? Or maybe “a one ring to rule them all“? That too while munching on your free pizza?
In my talk I shall show you a glimpse of the magical future, and how math plays a role in it.