The Discrete Fourier Transform
Giulio Genovese
This talk will cover the discrete Fourier transform and some applications to the real world.
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Combinatorics of the Real Line
Or: Topics in Analysis that Analysts Don't Know
John Bourke
One may view the real numbers as various set-theoretic objects more accessible to (infinite) combinatorics. This approach allows one to deduce curiosities about sets of measure zero and meagre sets.
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A Sojourn through Complexity Theory
Rachel Esselstein
People have been interested in tilings for many centuries. Ancient cultures decorated palaces and pottery with beautiful mosaics. Even mathematicians have found beauty in the mathematics of tilings. Roger Penrose actually patented his set of tiles, which he proved had no rigid symmetries.
In this talk, I will discuss tiling the hyperbolic plane with a collection of tiles. We will define an algorithm for determining whether we can tile the hyperbolic plane using every tile in our collection. Furthermore, we will show that our problem is NP-complete.
This talk will be accessible to undergraduates at all levels.
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The Spectrum of an Element in a Banach Algebra
Jonathan Brown
[No abstract]
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An Introduction to Computability Theory and Reverse Math
Jared Corduan
I will be giving an introduction to computability theory and reverse math. In particular, we will be considering Stephen Simpson's 'Main Question': "Which set existence axioms are needed to prove the theorems of ordinary, non-set-theoretic mathematics?"
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Closed Geodesics on Surfaces of Revolution
Greg Petrics
In this talk we will classify all types of geodesic behavior on surfaces of revolution, and then classify all surfaces of revolution with infinitely many closed geodesics. In the process we will sketch an entirely elementary proof to a special case of Bangert's Theorem, which states that every differentiable S2 contains infinitely many closed geodesics. We will focus on the intuitive aspects of the theory, and focus on building intuition through the use of MAPLE.
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The Multidimensional Frobenius Problem
Enrique Trevino
[Abstract]
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Worms
Elizabeth Moseman
We define a pre-order on finite sequences of reals with the idea of "scheduling" sequences optimally. We identify and count words which are equivalent in this pre-order. With this notion we can study a form of percolation.
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On the Chromatic Polynomial of Some Sequences of Graphs
Amir Barghi
By briefly introducing chromatic polynomial and its properties, we will compute chromatic polynomials of some sequences of graphs such as C4 x Pn and C5 x Pn.
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Title TBA
Matt Mahoney
[No abstract]
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