Modeling on Vascular Tumor Growth and Chemotherapy

Min Wu

November 2nd, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

Our research focus on the mathematical modeling and numerical simulations of vascular tumor growth and chemotherapy. We have developed a model by coupling a discrete angiogenesis model and a continuous tumor growth model accounting for vascular and interstitial fluid dynamics (vascular flow, vascular fluid extravasation, interstitial fluid flow and lymphatic drainage), which affects the delivery of nutrients and therapeutical agents during tumor growth/treatment. The talk will discuss over (1) overview of vascular tumor growth, (2) the tumor vascular/interstitial pressure/flow and the related physiological factors, (3) traditional drug transportation, chemotherapy and the physical barrier therein (4) the novel treatment strategy.

About the Speaker

Min is a fifth year graduate student in math and spent her first year in MCSB program. She received her B.S at Nanjing University, China. Besides study and research, she enjoys spicy food on a daily basis. When she has spare time, she likes to doodle/paint in the sunny afternoon alone, watch cartoon/drama series, or sing/yell with friends in those dark karaoke boxes dancing on the sofa.

Advisor and Collaborators

Min's advisor is John Lowengrub.

Weil Image Sums and Counting Image Sets Over Finite Fields

Joshua Hill

October 19th, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

We investigate a series of related problems in the area of incomplete Weil sums where the sum is run over a set of points that produces the image of the polynomial. We establish a bound for such sums, and establish some numerical evidence for a conjecture that this sum can be bounded in a way similar to Weil's bounding theorem.

To aide in the average case, we investigate the problem of the cardinality of the value set of a positive degree polynomial (degree $d > 0$) over a finite field with $p^m$ elements. We show a connection between this cardinality and the number of points on a family of varieties in affine space. We couple this with Lauder and Wan's $p$-adic point counting algorithm, resulting in a non-trivial algorithm for calculating this cardinality in the instance that $p$ is sufficiently small.

About the Speaker

Josh likes finite fields and long walks on the beach. While not doing math with finite fields on the beach, he reclines on a throne made of math books and gestures with a licorice pipe.

Advisor and Collaborators

Joshua's advisor is Daqing Wan.

Making Yourself Heard with Algebraic Coding

Robert Campbell

April 20th, 2011 - 4:00 - 4:50pm - RH 306

Abstract

We will be exploring coding theory looking at both classic and modern results including basic asymptotic bounds. We will see how algebra can help us in the construction of 'good codes.' We will explore a sampling of examples from algebraic coding. We will conclude with an in depth look at algebraic codes generated from cubic hypersurfaces.

About the Speaker

TBA

Advisor and Collaborators

Robert's advisor is Vladimir Baranovsky.

Lattice Gas Cellular Automata Modeling of Lineage Dynamics and Feedback Control

Shabnam Moobedmehdiabadi

February 23rd, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

This study is important in understanding the mechanism and dynamics of some biological problems such as tumor invasion and wound healing. Firstly, we describe microscopically the model and we derive the corresponding mesoscopic approximation, via the mean field assumption. In the following, we upscale our model providing a PDE which serves as a macroscopic manifestation of the underlying cellular interactions. We focus on investigating the speed and the structure of the invasion front, using the above mentioned approximations, as functions of the underling cell phenotypes and microenvironmental factors (i.e. nutrients).

About the Speaker

Shabnam received her Masters degree in Mathematical Sciences in May 2005 at Claremont Graduate University and her bachelors degree from Sharif Institute of Technology (Tehran, Iran).

Advisor and Collaborators

Shabnam's advisor is John Lowengrub.

Using PDEs in Geometry and Topology - The Hodge Theorem

Lihan Wang

February 9th, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

As one of the deepest and most beautiful theorems in geometry, the Hodge theorem builds a bridge between Riemannian metric and topological invariants. It gives an isomorphism between the space of harmonic p forms on a Riemannian manifold and the p de Rham cohomology group of a smooth structure. By the de Rham theorem, we see the isomorphism between the space of harmonic p forms and p real singular cohomology group.

The Hodge theorem is a good example of how PDEs help us understand geometric structure and even topological structure. In this talk, we will give an introduction to this theorem, explain the idea behind it, and give some applications in Riemannian geometry.

About the Speaker

Lihan loves running for long time, just running, even without music. She also enojys swimming in the early morning and seeing the sun coming out.

Advisor and Collaborators

Lihan's advisor is Peter Li.

Can Mathematics Help Us Understand the Motion of Fluids?

Adam Larios

January 26th, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

One of the most difficult problems in mathematics and physics is to find an accurate, practical description of turbulent flows. Turbulence is ubiquitous in nature, occurring in very diverse physical settings, such as aerodynamics, geophysics, weather and climate modeling, ocean and atmospheric flows, star formation, blood flow in the heart, and many others. This problem is not only untenable by current mathematical tools, but direct numerical simulation of detailed turbulent flows has proven to be computationally prohibitive, even using the most powerful state-of-the-art computers. A major piece of the puzzle of understanding these phenomena is widely believed to lie in a system of nonlinear PDEs known as the Navier-Stokes equations, which are the subject of one of the seven $1,000,000 Clay Millennium Prize problems. I will discuss give an introduction to the Navier-Stokes equations and discuss their relationship to turbulence and the Millennium problem.

About the Speaker

Adam swing dances with the best of them.

Advisor and Collaborators

Adam's advisor is Edriss Titi.

Independence and Large Cardinals

Zac Faubian

January 12th, 2011 - 4:00 - 4:50pm - RH 440R

Abstract

In this introductory mathematical logic talk, we will give describe large cardinals and their role in independence results.

About the Speaker

Zac plays soccer and football for the UCI Mathletes.

Advisor and Collaborators

Zac's advisor is Martin Zeman.