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# Pi Mu Epsilon Conference

# April 10–11 2015

Peter Engel Science Center

Saint John's University

## Invited Speaker: Dr. Ami Radunskaya (Pomona College)

**DDEs, DCs and Doses: Mathematical approaches to designing cancer vaccines.**

8:00 pm Friday, April 10th in Pellegrene Auditorium

Dendritic cells (DCs) are a promising immunotherapy tool for boosting an individual's immune response to cancer. In this talk, we develop a mathematical model using differential equations and delay-differential equations (DDEs) to describe the interactions between dendritic cells, other immune cells and tumor cells.

In order to design an efficient treatment strategy, clinicians need to answer three questions: How much? How often? Who will respond? Our model, along with mathematical tools from control theory and dynamical systems, can be used to suggest answers to these questions. This work is just one example of possible collaborations between mathematicians and researchers in other disciplines: a few other examples will be introduced, illustrating the synergy between modeling challenges and mathematical discoveries.

This talk is designed for a general math audience: no knowledge of immunology is assumed.

**Chaos and Noise: a look at stochastic difference equations.**11:30 am Saturday, April 11th in Pellegrene Auditorium

Many biological and physiological processes involve self-regulating mechanisms that prevent too much growth while ensuring against extinction. The rate of growth is often random (``noisy"), possibly affected by fluctuations in the environment. Some questions that we'd like to answer are: what happens to the system in the long term?

Does the system have a well-defined average? How does this long-term average compare to the long-term behavior of the deterministic (not random)

system? What can we say about the distribution of ``survival times", i.e. the distribution of times until the system reaches a particular

value?

In this talk we answer these questions for a family of maps on the unit interval that model self-limiting growth. We then look at more complicated systems and make several conjectures.

**Biographical Sketch of Ami Radunskaya**

A California native, Professor Radunskaya received her Ph.D. in Mathematics from Stanford University under the supervision of Prof. Donald Ornstein. She is a faculty member of the Department of Mathematics at Pomona College in Claremont, California specializing in ergodic theory, dynamical systems, and applications to various "real-world" problems. Some current research projects involve mathematical models of cancer immunotherapy, designing time-release tablets, and studying stochastic dynamical systems in order to understand how people balance. Professor Radunskaya believes strongly in the power of collaboration and that everyone can learn to enjoy mathematics. She has been a strong supporter of women in mathematics, serving on the Executive Committee of the Association for Women in Mathematics, and taking on leadership roles in several national mentoring programs. She is the President of the EDGE Foundation, and co-director of the EDGE (Enhancing Diversity in Graduate Education) program, which won a "Mathematics Program that Makes a Difference" award from the American Mathematics Society in 2007. Professor Radunskaya was awarded an Irvine Fellowship for Excellence in Faculty Mentoring in 2004, she delivered the Falconer Lecture at MathFest in 2010, and she received a Wig Award for Excellence in Teaching in 2012.

**Upcoming Conference Speakers**

- 2015 Ami Radunskaya

**Former Conference Speakers**

- 2014 Hal Schenck
- 2013 Annalisa Crannell (Videos: Friday's Lecture, Saturday's Lecture)
- 2012 Kenneth Millett
- 2011 William Dunham
- 2010 Claudia Neuhauser
- 2009 Joe Gallian
- 2008 (Conference cancelled due to weather)
- 2007 Carlos Castillo-Chavez
- 2006 Edward Burger
- 2005 Jennifer Quinn
- 2004 Frank Farris
- 2003 Colin Adams
- 2002 David Bressoud
- 2001 Underwood Dudley
- 2000 Sam Patterson
- 1999 Robert L. Devaney
- 1998 Richard Guy
- 1997 Ron Graham
- 1996 Frank Morgan
- 1995 Carl Pomerance
- 1994 Philip Straffin
- 1993 Thomas Banchoff
- 1992 Judith Grabiner
- 1991 Raymond Smullyan
- 1990 Joan Hutchinson
- 1989 Richard Askey
- 1988 Sherman Stein
- 1987 Reuben Hersh
- 1986 Peter Hilton
- 1985 I.N. Herstein
- 1984 Ruth Struik
- 1983 Joan Fisher Box, George Box
- 1982 Alfred Willcox (in conjunction with the North Central Section Meeting)
- 1981 Doris Schattschneider, Leonard Gillman, Don Koehler
- 1980 Mary Ellen Rudin
- 1979 Paul Halmos

**Lectures will be geared toward a general audience**

*Funding for travel to SJU Pi Mu Epsilon conference is provided by NSF grant DMS‐0846477 through the MAA Regional Undergraduate Mathematics Conferences program,http://**www.maa.org/RUMC*