Richard Bertram | Homepage

Associate Professor of Mathematics

Research Interests

Mathematical Physiology

My focus in this area is on the endocrine system. One interest is insulin-secreting pancreatic beta-cells. These are the only cells in the body that secrete the key hormone insulin, and death or disfunction of beta-cells leads to diabetes. I collaborate with mathematical and experimental labs on this project. Another project is the function and neuronal control of prolactin-secreting lactotrophs in the pituitary gland. Prolactin has over 100 functions, but it's primary function is milk production for lactation. I collaborate with an experimental lab on this project.

Mathematical Neuroscience

My primary interest here is the mechanism of synaptic transmission and short-term plasticity. Plasticity is the way that a synapse changes over time to strengthen or weaken a connection to a postsynaptic cell. Short-term plasticity is a form of short-term memory, and is also a mechanism through which information is filtered by the synapse. I have collaborated with several mathematical and experimental labs on this project.

Analysis of Bursting Oscillations

Bursting oscillations, consisting of fast oscillations or spikes followed by a period of quiescence, are prevalent in excitable cells. The biophysical mechanisms driving these oscillations vary from cell to cell, and I have been involved in modeling these mechanisms in several bursting cells. However, bursting oscillations can be studied from a purely mathematical perspective, using techniques from dynamical systems theory. For a number of years now I have been involved in such studies.

Teaching

Biomedical Projects

Students will learn how to write and critically evaluate NSF grant proposals.

Calculus II

Integration techniques, improper integrals, applications of definite integrals, differential equations, analysis of series.