Feedback, lineages and cancer

Speaker: 

Prof. John Lowengrub

Institution: 

UCI

Time: 

Monday, November 29, 2010 - 5:30pm

Location: 

RH 306

A multispecies continuum model is developed to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression and the development of morphological instability.

*Pizza and soda will be served!

Cryptography and Counting Points on Elliptic Curves

Speaker: 

Nick Alexander

Institution: 

UCI

Time: 

Monday, November 8, 2010 - 5:30pm

Location: 

RH 306

In 2003, the National Security Agency (NSA) payed Certicom, a small Canadian security company, 25 million dollars for the right to use Certicom's elliptic curve cryptography technology. We will introduce elliptic curves and their applications to cryptography and computer security, and suggest why the NSA paid so much. Then we will describe the computationally important "point counting problem", which is necessary for efficient elliptic curve cryptography. We will survey some recent research that "counts points" on certain elliptic curves.

Mathematical Models of Flames

Speaker: 

Joanna Bieri

Institution: 

University of Redlands

Time: 

Monday, October 25, 2010 - 5:30pm

Location: 

RH 306

Many of the mechanisms that govern flame dynamics are complicated and not well understood. Even simple models can give us a lot of information about the stability, shape and location of flames. The goal of this talk will be to discuss the model of an edge-flame in a confined space, or narrow channel. We will begin by talking about the heat equation, a diffusion-type partial differential equation, and the possible boundary conditions for such an equation. Then we will develop a model for a flame in a narrow channel and discuss how we can use numerical methods to find solutions for this system.

*Pizza and soda served!

Predictions of tumor morphological stability and evaluation against experimental observations

Speaker: 

Kara Pham

Institution: 

UCI

Time: 

Monday, October 18, 2010 - 5:30pm

Location: 

RH 306

The hallmark of malignant tumors is their invasion of local tissue and infiltration
of distant organs (metastasis). A defining characteristic of aggressive tumors
is an unstable morphology, including invasive fingers and protrusions. Shape
instabilities (growing protrusions) are associated with local invasiveness, also
often a precursor to tumor metastasis. We study tumor morphological stability
by employing three mathematical models to gain insight into tumor invasion
and metastasis. Using linear theory, we study the tumor morphological stability
described by each model and evaluate the consistency between theoretical
model predictions and experimental data from in vitro 3D multicellular tumor
spheroids. We will discuss the results and show that it is feasible to extract parameter
values from a limited set of data and create a self-consistent modeling
framework that can be extended to the multiscale study of cancer. Numerical
methods are used to simulate the nonlinear effects of stress on solid tumor
growth and invasiveness.

Applying to Graduate School in Mathematics Workshop

Speaker: 

Time: 

Wednesday, October 6, 2010 - 5:00pm

Location: 

RH 440R

* Workshop for Undergraduate Students on preparing for and applying to graduate school. All levels of students are encouraged to attend. The workshop will feature a presentation on what students should do in their Sophomore-Senior years to prepare for graduate studies and how to apply for graduate school. Also, there will be a panel of current UCI students to offer advice on the application process and selecting a school.

Fractals

Speaker: 

Anton Gorodetski

Institution: 

UC Irvine

Time: 

Wednesday, April 28, 2010 - 5:00pm

Location: 

RH 440R

We will consider the notions of fractal and fractal dimension. Examples of
fractals in mathematics (such as Cantor set, Serpinskiy carpet, Julia and
Mandelbrot sets, fractals generated by iterated function systems) and in
real life will be discussed.

How to Count using Generating Functions

Speaker: 

Sho Seto

Institution: 

UC Irvine

Time: 

Wednesday, April 14, 2010 - 5:00pm

Location: 

RH 440R

For n = 1, 2, 3. we can give a geometric argument in proving the formula
1 + 2 + 3 + .. + n = n(n+1)/2
1^2 + 2^2 + .. n^2 = n(n+1)(2n+1)/6
1^3 + 2^3 + + n^3 = (n(n+1)/2)^2
For n >3, there is a method using generating functions to obtain that formula.
We will go over the geometric and generating function arguments.

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.

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