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!

An Introduction to the Analytic Theory of Numbers

Speaker: 

Mustafa Said

Institution: 

UC Irvine

Time: 

Wednesday, October 28, 2009 - 5:00pm

Location: 

RH 440R

I will start by giving a brief history of the subject and continue by presenting some important results in the field such as the "prime number theorem," and the mathematicians that contributed to these results. I will go on and give a very general discussion about the "Riemann Zeta Function," and discuss its importance in the field and mathematics in general. I will also touch upon some open problems such as the "Riemann Hypothesis," and "The Circle Problem." I will end my talk by discussing some recent and important results in the field such as the "Tao - Green" theorem on arithmetic progressions of prime numbers.

From Mars to Morphogen, a Journey in Applied Mathematics

Speaker: 

Professor Frederick Wan

Institution: 

UCI

Time: 

Wednesday, October 14, 2009 - 5:15pm

Location: 

RH 440R

Professor Fred Wan will describe some highlight of his 50 years long journey in applied mathematics research at four institutions. He will touch on scientific topics such as mechanics, economics, and the biology of Morphogens that guide tissue development.

How big is infinity?

Speaker: 

Professor Matt Foreman

Institution: 

UC Irvine

Time: 

Wednesday, April 8, 2009 - 5:00pm

Location: 

RH 594

Is infinity plus one equal to one plus infinity? What is infinity times
zero? Is infinity even a number? What are numbers anyway? Are there
different sizes of infinity? How does infinity come up in ordinary
mathematics? Do we need infinity to add real numbers?

I will survey these puzzles and give some rigorous answers.

Finite Markov Chains and the Casino Game Craps

Speaker: 

Chris O'Grain

Institution: 

UCI

Time: 

Wednesday, March 4, 2009 - 5:00pm

Location: 

RH 594

In any casino, the craps table often has the loudest and most excited crowd. This is because when the shooter wins, everyone wins. Its also because craps offers some of the best odds in the entire casino, giving players the best chance to win money. In this talk, the rules of craps will be explained. Also, the concept of markov chains will be introduced, and a finite markov chain will be used to model the game of craps.

CT Scans and Image Registration

Speaker: 

Edward Castillo

Institution: 

UCI

Time: 

Wednesday, April 9, 2008 - 5:00pm

Location: 

MSTB 256

Radiotherapy is the most common form of treatment for lung cancer patients.
Thoracic specialists develop radiation treatment plans based on CT (computed
tomography)
scans of the lungs. These treatment plans specify the amount of radiation to be
delivered to the patient, as well as which areas of the lungs to irradiate.

Using mathematical and computational tools, my collaborators and
I have developed a software package which can be used to improve the radiation
treatment
planning process. The software is based on a well studied problem in image processing
referred to as "image registration".

In this talk, I will discuss the relationship between image registration and
radiation treatment planning, as well as the types of math and computational tools
required to do research in this field.

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