Student Colloquium
We only get as many Student colloquiums as there are students willing to present their research. Because of this, we do not have a scheduled time for Student Colloquiums. Instead, when there will be a Student Colloquium, we will notify you through email and update the calendar.
Check out videos of our student colloquia on YouTube!
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General 


UPCOMING COLLOQUIA:
None....yet.
Previous Colloquia:
November 3rd, 2011
Introduction to Prime Number Theory and the Riemann Hypothesis by Camilo Montoya (Part 2)
September 6, 2012
Several complex variables, the local equivalence problem, and invariants of real hypersurfaces by Camilo Montoya
The theory of holomorphic functions in the complex plane is known for its strong classical results. However, as functions of several complex variables are considered, these wellknown results fail to translate smoothly. This exposition covers some of the historical developments in the theory of several complex variables, including an introduction to ndimensional complex space and holomorphic functions, the local equivalence problem, real hypersurfaces, pseudoconvexity, Segre varieties, and various other known biholomorphic invariants of real hypersurfaces in R^n. Some results obtained during the summer research classifying unique hypersurfaces will be mentioned.
October 27th, 2011
Introduction to Prime Number Theory and the Riemann Hypothesis by Camilo Montoya (Part 1)
An introduction to Prime Number Theory and the Theory of the Riemann Zeta Function. We begin by examining prime numbers and their distribution, introducing the primecountingfunction Pi(x), its role in the Prime Number Theorem, and the discovery of the relationship between prime numbers and the Riemann zeta function due to Euler. We present an overview of Riemann's exact formula for Pi(x), the importance of the zetazeros in the distribution of the primes, and proceed to the study of the Riemann zeta function and the Riemann Hypothesis. We derive the functional equation, introduce the critical strip and zerofree regions, and prove Hardy's theorem that the zeta function has an infinity of zeros on the critical line.
October 13th, 2011
New Approaches in Poll Aggregation and Political Forecasting by David Shor
I'll try to give an introductory background about the mathematics behind polling and then move on to a brief summary of practical difficulties with election modeling in the real world. For the 2010 US midterm elections, I made district and state level predictions for House/Senate/Governor. My mean error was half that of America's favorite polling nerd, Nate Silver.
October 6th, 2011
Representations of String Links and Tangles by Christian Bueno
The string link monoid is generalizes the braid group by allowing the strands of braids to loop and knot. We consider two representation on string links that extend the Burau representation of the braid group. The first, due to X. S. Lin, is defined probabilistically via sums of weighted paths along strands of the link. The second is a combinatorial/topological representation defined by recursively applying the Conway skein relation to the string link, resolving it into braids on which the representation takes the familiar form of Burau. We show that these two representations agree over many nontrivial string links, supporting a conjecture by T. Kerler that these representations are identical. In further investigations, we consider the case of 2strand string links in depth, relating it to the theory of rational tangles. Lastly we give one consequence of the conjecture, namely, a formula relating the Alexander polynomial of a link closure to its matrix entries under the representation.
September 22nd, 2011
Graph Theoretic Properties Arising from Hurwitz Equivalence in Symmetric Groups by Alejandro Ginory
We investigate the braid group action on tuples of transpositions in the symmetric group on letters, , which we shall refer to as Hurwitz moves. Specifically, we will be considering the  tuples whose entries generate a subgroup of that acts transitively on and where . We then define a graph whose vertices are the tuples described above and whose edges are determined by the action of the standard generators of on the vertices. We present a method for describing the order of the vertex set of , establish lower and upper bounds for the diameter of (especially the asymptotic behavior for fixed and large ), and introduce an algorithm, linear in , for transforming one into another through Hurwitz moves.
September 15th, 2011
Fictitious Forces by Douglas Laurence
September 8th, 2011
Representations of String Links and Tangles by Christian Bueno
The string link monoid is generalizes the braid group by allowing the strands of braids to loop and knot. We consider two representation on string links that extend the Burau representation of the braid group. The first, due to X. S. Lin, is defined probabilistically via sums of weighted paths along strands of the link. The second is a combinatorial/topological representation defined by recursively applying the Conway skein relation to the string link, resolving it into braids on which the representation takes the familiar form of Burau. We show that these two representations agree over many nontrivial string links, supporting a conjecture by T. Kerler that these representations are identical. In further investigations, we consider the case of 2strand string links in depth, relating it to the theory of rational tangles. Lastly we give one consequence of the conjecture, namely, a formula relating the Alexander polynomial of a link closure to its matrix entries under the representation.
September 1st, 2011
Construction of the Natural Numbers by Eric Wawerczyk
The Natural Numbers are the fundamental objects of mathematics. The history of math begins with the concept of number and ever since their discovery, the Natural Numbers have had a sacred place. The mathematicians of the 1900's developed Axiomatic Set Theory in order to bring rigor to the idea of sets. The colloquia introduces the axioms of Peano Arithmetic and the axioms of Zermelo Frankel Set Theory to prove the existence of the Ordinals and verify their acceptance of Peano's axioms.