Mathematical Biology

The Graduate Summer School bridges the gap between a general graduate education in mathematics and the specific preparation necessary to do research on problems of current interest. Candidates should have completed basic graduate courses in... {to be determined for 2005.} In general, these students will have completed their first year, and in some cases, may already be working on a thesis. While a majority of the participants will be graduate students, some postdoctoral scholars and researchers may also be interested in attending.

The main activity of the Graduate Summer School will be a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures will not duplicate standard courses available elsewhere. Each course will consist of lectures with problem sessions. Course assistants will be available for each lecture series. The participants of the Graduate Summer School meet three times each day for lectures, with one or two problem sessions scheduled each day as well.

Course Titles and Descriptions:

The 2005 Summer Session in Mathematical Biology will consist of seven graduate level modules.  On any day during the summer session, three models will be offered.  Graduate students are asked to take no more than two of the three modules offered per day, and attend computer labs, pencil and paper exercises, a group project and associated research lectures.  A student involved in two modules will have approximately five hours a day of formal lectures as well as several more hours of associated projects and excercises.  Those students who choose to attend all three modules will participate in shorter versions of the computer lab/exercises.

Mark Lewis, University of Alberta

Introduction to Biological Dynamics

A foundational module in which the basic tools of nonlinear dynamical systems, such as ordinary and partial differential equations and difference equations will be addressed.  Each lecture will focus on the interplay between mathematical tools and biological needs.

James Keener , University of Utah

Introduction to Biological Dynamics

A foundational module in which the basic tools of nonlinear dynamical systems, such as ordinary and partial differential equations and difference equations will be addressed.  Each lecture will focus on the interplay between mathematical tools and biological needs.

Alex Mogilner, University of California at Davis

Cell and Tissue Physiology

Lecture module regarding the usage of mathematical models to deduce the structure and function of cells (e.g. cytoskeleton) and tissue (e.g. myocardium.)

David Earn, McMaster University

Epidemiology and Disease

Lecture module designed to discuss the interplay of mathematics and epidemiology to understand and propose controls for diseases such as malaria, influenza and SARS.

Helen Byrne, University of Nottingham

Cancer

Lecture module to discuss how cancer tumor formation and angiogenesis can be understood with complex spatial models.   These models are now at a stage where they can describe the different stages of cancer progression.  New mathematical approaches can be used to look for methods of controlling cancer.

Paul Bressloff, University of Utah

Neurobiology

Lecture module designed to discuss this new area of mathematical analysis.  Subjects will include feedback in neural networks, and patterns in the visual cortex.

James Cushing, University of Arizona

Ecological Dynamics

Lecture module to show how ecological systems can exhibit very complex temporal and spatial dynamics; this is a particularly rich area for the interplay of mathematical models and biological data.

Leon Glass, McGill University

Fixed Points and Topological Approaches to Biological Dynamics

This will be a set of lectures focusing on qualitative analysis and topological approaches to the study of biological dynamics. Suggested topics include:

Differential Equations - Linear Stability Theory: Using correlated random dot patterns to study vision and illustrate dynamics; Poincare-Hopf classification of vector fields in N dimensions
Phase Resetting: Topology of resetting curves; discontinuities in resetting experiments modeled by ordinary and partial differential equations
Entrainment of Biological Oscillations: Circle maps fixed points and continuation of Arnold tongues; fixed points and Arnold tongues from periodic forcing of 2
dimensional oscillators
Genetic Networks: Poincare maps, fixed points and limit cycles in N dimensions
Phase Maps: Supernumerary limb regeneration; excitable media on compact, oriented 2 dimensional manifolds

A number of computer exercises will be suggested, many from a recent book based on summer school lectures Nonlinear Dynamics in Physiology and Medicine eds. Beuter, Glass, Mackey, Titcombe. I would also suggest a series of research level problems and projects that would be suitable for work during the summer school.

Participants in the Graduate Summer School also may wish to become involved in the Undergraduate Program, attend parts of the Research Program, or participate in the programs of the Education component. Graduate students are expected to participate in Institute-wide activities such as the "Cross Program Activities" and may be asked to contribute some time to volunteer projects related to running the Summer Session.

A limited number of graduate students who have not completed the basic courses may attend. These students will attend some graduate level courses and may be involved as teaching assistants in other programs or work as audio-visual assistants.

The Graduate Summer School is supported by National Science Foundation grant no. 0437137.