The SPAMS Schedule - Fall 2010

Welcome to the new, exciting, improved semester at MIT math! Well, we know what you've all been waiting for...

SPAMS! The Simple Person's Applied Math Seminar (or as we like to call it, Awesome Talks + Free Dinner Every Thursday Night) is a long-running seminar series in the MIT Applied Math department, which is run by graduate students, for graduate students. There'll be a talk every Thursday, starting this coming Thursday from 5-6pm in room 2-105, followed by dinner in the Applied Math Lounge.

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And, stay tuned for the unveiling of an upcoming surprise in the common room...

Abstract: No pre-requisites required. I will give a background on the physics of it.

Abstract: As mathematicians, we love it when the pretty and important objects from one area suddenly appear in other domains. This talk will give the story of one such connection. Namely, we will discuss how to find the Bernoulli shift (a fundamental object in dynamical systems) in the dynamics of simple polynomials over the p-adic integers. Along the way, we will study an interesting power series, play with Pascal's triangle, and tell many tall tales.

This talk should be accessible to all graduate students, pure and applied.

Abstract: Set is a simple card game with a surprisingly rich mathematical structure. We will be talking about the mathematics of Set, including the average number of sets in n random cards and how to bound the number of cards you can have without having a set. No knowledge of Set is assumed.

Abstract: Ever been curious how your camera works (and what all the icons on the box mean)? We'll discuss some of the mathematics that go into digital imaging, from color spaces, sensing, and autofocus to compression and denoising.

Abstract: Non-periodic tilings of the plane are a fun curiosity, but there lies at the heart of this topic some deep mathematics which I will try to hint at during this talk. In particular, although one would guess that tilings which are called non-periodic are disorderly, I will show the exact opposite with Roger Penrose's non-periodic tilings. Those tilings display symmetries, have various interesting mathematical features and are quite pretty too! In the hope that the math doesn't get too complicated, ample cute pictures (of tilings and penguins and reptiles, not kittens, sorry!) will be on hand.

Abstract: Learn to create art with rubber bands, and then explore the knot-theoretic limitations of the medium. More specifically, consider the problem of recreating a given graph out of rubber bands, where each edge corresponds to (the two strands of) a single rubber band and each node non-trivially joins all incoming edges. Which graphs are realizable in this way, given that the rubber bands are originally unlinked?

After a few minutes playing with rubber bands, we will provide a complete mathematical answer to the above question, and obtain as a corollary a versatile construction (and verification) for Brunnian links.

Abstract: The classical secretary problem studies the problem of selecting online an element (a "secretary", a "spouse", a "job", etc.) with maximum value in a randomly ordered sequence. This problem has many variations. We will see some of them and also their solutions. As an example of an application we will derive (using math!) what is the earliest age to consider getting married. Of course this depends on the model. There is an optimal age for the case where you are happy with nothing but the best and unhappy in every other scenario. But the answer is *very* different if you value being single over getting married with a suboptimal partner.

Abstract: In this talk, we introduce generating trees, a special kind of recursive structure, and show how they can be used to easily produce nontrivial combinatorial results. The first half of the talk will be a rambling introduction to what combinatorialists like and don't like about recursions, consisting mostly of tangential comments on topics like Somos sequences, linear homogeneous recursions with constant coefficients, and basic differential equations. In the second half of the talk, we'll focus on generating trees, discuss the sort of situation they are useful for, and give a few nontrivial examples from the world of pattern avoidance in permutations.

Abstract: Algebraic statistics is a relatively new subject which uses algebraic geometry, commutative algebra and combinatorics to study problems in statistics. One of the first such connections is represented by Markov bases, introduced by Diaconis and Sturmfels in a paper on contingency table analysis. In this talk, we will define Markov bases and show how to construct them and how they are related to Grobner bases. We will start with the motivating example of testing independence of contingency tables and finish with a description of the Markov bases of this model. No background in statistics or algebraic geometry is required.

Abstract: The combinatorial Hodge decomposition allows us to decompose a directed graph into three simple components. In this talk, we'll go over the necessary background to define the decomposition. We'll show how to use this decomposition to extract global rankings from a set of incomplete and inconsistent pairwise ranking data. If time remains, we might discuss other potential applications of this technique.

No prior knowledge of algebraic topology, of ranking things, or of math is required.

Abstract: Often the first step in data analysis is to cluster data, whereby similar points are grouped together. For example we might cluster consumers based on their grocery purchases. But, how do we choose how many clusters to form? Too many clusters overfit - one for every point - and too few underfit - a single cluster. You want it to depend on the amount and complexity of the data that you have. I'll introduce one approach that takes this into account by using the Chinese Restaurant Process (CRP) and the Dirichlet Process (DP). In the first half of the talk, starting from the basics, I will introduce the CRP and DP and in the second half, I will tell you about a few awesome applications.