Is 2,394,129,303,223,424,108,132,089 Prime?

Speaker: 

Alexander Abatzoglou

Institution: 

UC Irvine

Time: 

Wednesday, March 3, 2010 - 5:00pm

Location: 

RH 440R

Primality testing and finding large prime numbers has significant applications to cryptography. In this talk I will discuss a deterministic, polynomial time algorithm for determining if an integer is prime developed by Agrawal, Kayal, and Saxena. Here polynomial time means that there exists constants c,d such that the number of operations to determine if the given integer is prime is less than c log^d(n) where n is the number we are testing for primality.

Pythagorean Triples and Elliptic Curves: A Synthesis of Algebra and Geometry

Speaker: 

Barry Smith

Institution: 

UC Irvine

Time: 

Wednesday, February 24, 2010 - 5:00pm

Location: 

RH 440R

We examine methods to produce triples of integers which are the sides of a right triangle (i.e., (3,4,5), (5,12,13), or (8,15,17)). Multiplication of complex numbers will make an appearance, the first example of the interplay between algebra and geometry. We will then learn about elliptic curves, which provide a similar, but much more intricate, synthesis of algebra and geometry. Elliptic curves are a current area of intense research in mathematics and computer science, playing a central role in modern cryptology and in the recent proof of Fermat's Last Theorem.

Skolem's Paradox: The Universe is Countable

Speaker: 

May Mei

Institution: 

UC Irvine

Time: 

Wednesday, February 3, 2010 - 5:00pm

Location: 

RH 440R

We will informally discuss a seemingly paradoxical consequence of the Lwenheim-Skolem theorem: if ZFC is consistent, there is a countable model of set theory. We will reexamine our intuitive notion of uncountablity and reach a mathematically satisfying resolution.

Pizza and soda will be served!

A completely accessible and historically motivated introduction to The Theory of Partitions

Speaker: 

Dennis Eichhorn

Institution: 

UCI

Time: 

Wednesday, January 20, 2010 - 5:00pm

Location: 

RH 440R

Title: A completely accessible and historically motivated introduction to The Theory of Partitions and its connections to number theory, combinatorics, group theory, continued fractions, statistical mechanics, complex analysis, patience, chess, and ping-pong.

Abstract: In this talk, we take a whirlwind tour of the theory of partitions. Beautiful results from this area's rich history will be presented, and the connections between partition theory and many other fields will be discussed. The talk will be aimed at the partition-theoretically uninitiated, and should be accessible to everyone.
* Pizza and soda will be served!

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