Fall 2006 Schedule of Speakers

 

Date	Location	Speaker	Topic
October 19, 2006	Fowler 309 4:30 pm	Lisette de Pillis Harvey Mudd College Ami Radunskaya Pomona College	Mathematical modeling of cancer growth, the immune response and treatment
	Abstract : Cancer is a term referring to a cluster of diseases, all with the common feature that a sub-population of an individual's own cells has mutated and begun to grow uncontrollably. It is believed that a healthy individual may keep potentially cancerous cells from developing into a health-threatening malignancy through a complicated network of immune responses and mechanisms built into the cell cycle that recognize aberrant cells and control their proliferation. The treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. In particular, chemotherapy has had limited success because of the high toxicity ofmost treatments to many cells that are crucial to the normal functioning of the patient. Therefore, much attention has recently been focused on immunotherapy, i.e. methods of strengthening a patient's own immune response to cancerous cells. Mathematical models of tumor growth in tissue, the immune response, and the administration of immunotherapy can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. The inherent complexity of the immune system and the spatial heterogeneityof human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. These include modeling behavior over vastly different time scales, optimization in high-dimensional spaces, and fitting large sets of dependent parameters to data. In this talk we will present an overview of the evolution of our mathematical and computational work in this area.
November 16, 2006	Fowler 309 4:30 pm	Bob Pelayo California Institute of Technology	Knots, Surfaces, and their Invariants
	Abstract: Knot Theory is one of the many interesting and intuitive subfields of Low-Dimensional Topology. This theory is essentially the study of how circles (knots) can lie in 3-space. We will study the (surprisingly difficult) question of how to decide if two knots are the same or different. Knot Theory is further enriched by studying (2-dimensional) surfaces that have these (1-dimensional) knots as their boundaries. We will further discuss how to attach numbers and even polynomials (called invariants) to knots to help in the task of distinguishing them.  This talk will be largely intuitive and rely heavily on pictures and geometric imagination. However, we will demonstrate many powerful tools used to expand mathematicians' knowledge of low-dimensional spaces.
November 30, 2006	Fowler 309 4:30 pm	Susan Martinosi Harvey Mudd College	An Operations Research Approach to Homeland Security
	Since the terrorist attacks of September 11, 2001, homeland security policy has remained a focus of national attention. Intense debate has surrounded some of the security measures implemented in the wake of the attacks as well as the allocation of national resources to security. We develop mathematical models to address some prominent problems in homeland security, such as the effectiveness of particular security measures in the context of aviation security, and optimal resource allocation using game theory. (Portions of the talk represent joint work with Arnold Barnett, Daniel Walton).