2008 Summer Graduate Program

(July 7,2008 - July 25,2008 )

This year the program will focus on Mathematical Bioengineering. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.

The 2008 Summer Program dates are July 7 - 25.

July 7-11, 2008
Lecturer: Richard Bertram, Department of Mathematics, Florida State University
Title: Mathematical Modeling in Neuroscience and Physiology

In these lectures Bertram will discuss examples of how mathematical modeling is used in the areas of neuroscience and physiology. Topics include the dynamics of electrically excitable cells, calcium dynamics and waves, fast and slow time scales, bursting oscillations, phase oscillators, circadian gene oscillations, and synchronization of oscillators. A basic familiarity with ordinary and partial differential equations is assumed. Techniques for the analysis of nonlinear ordinary differential equations using phase plane and bifurcation diagrams will be discussed throughout the series of lectures.

Monday: We will begin with a description of neuron models and mean field models for neural populations. Analysis of these models through phase plane and bifurcation analysis will also be discussed.

Tuesday: We will discuss the biophysical mechanisms for and mathematical analysis of bursting oscillations. Oscillations of this type are frequently observed in nerve and endocrine cells.

Wednesday: The next discussion will be on mathematical descriptions of stochastic systems. We will look at stochastic ion channel fluctuations in nerve cells, and hybrid deterministic models that include noise. We will also discuss ways that noise itself can amplify a signal, such as stochastic resonance.

Thursday: Memory is stored in synaptic couplings between neurons. A synapse is a tiny structure that is the center of many reactions that are key to short term and long term memory. We will discuss mathematical models for the mechanisms of both types of memory.

Friday: Synchronization is a widespread phenomenon in neural populations. We will discuss some of the ways that synchronization has been analyzed mathematically, using the phase oscillator as a mathematical tool for the analysis.

Monday, July 7, 2008
Time Session
Tuesday, July 8, 2008
Time Session
Wednesday, July 9, 2008
Time Session
Thursday, July 10, 2008
Time Session
Friday, July 11, 2008
Time Session
Saturday, July 12, 2008
Time Session
Sunday, July 13, 2008
Time Session
Monday, July 14, 2008
Time Session
Tuesday, July 15, 2008
Time Session
Wednesday, July 16, 2008
Time Session
Thursday, July 17, 2008
Time Session
Friday, July 18, 2008
Time Session
Saturday, July 19, 2008
Time Session
Sunday, July 20, 2008
Time Session
Monday, July 21, 2008
Time Session
Tuesday, July 22, 2008
Time Session
Wednesday, July 23, 2008
Time Session
Thursday, July 24, 2008
Time Session
Friday, July 25, 2008
Time Session
Name Affiliation
Banerjee, Sayanti banerjee.35@osu.edu Mathematics Dept., The Ohio State University
Bergman, Einat einatberg@gmail.com HIT Israel
Bertram, Richard bertram@sb.fsu.edu Math & Institute of Molecular Biophysics, Florida State University
Cracium, Gheorghe craciun@math.wisc.edu Mathematics and Biomolecular Chemistry, University of Wisconsin
Fitak, Robert rfitak@email.arizona.edu University of Arizona
Goddard, Jerome jg440@msstate.edu Math & Stats, Mississippi State University
Haeri, Morteza shaeriho@syr.edu Biomedical Engineering, Syracuse University
Hsiao, Samuel hsiao@bard.edu Mathematics, Bard College
Isaacson, Joseph joseph_issacson@brown.edu Applied Math/Computer Science, Brown University
Joshi, Badal badal@math.ohio-state.edu Mathematics, The Ohio State University
Lavi, Orit laviorit@gmail.com Mathematics, Bar-Ilan University
Luli, Dori luli@mathpost.la.asu.edu Math & Stats, Arizona State University
Ma, Yanping ma@math.psu.edu Mathematics, Pennsylvania State University
McDougal, Robert mcdougal@math.ohio-state.edu Mathematics, The Ohio State University
McGivney, Debra dfmcgivney@gmail.com Mathematics, Case Western Reserve University
Pantea, Casian pantea@math.wisc.edu Mathematics, University of Wisconsin
Park, Hyejin parkh@math.ohio-state.edu Mathematics, The Ohio State University
Pham, Kara karap@math.uci.edu Mathematics, University of California, Irvine
Solovieva, Svetlana svetsolo@list.ru Mathematics and Cybernetics, Moscow State University
Sundling, Kaitlin kemartin2@wisc.edu Mathematics, University of Wisconsin
Thomas, Rachel rachel@math.duke.edu Mathematics, Duke University
Zhuravytska, Svitlana sz38@drexel.edu Mathematics, Drexel University