Dr. Jason Bell

Department of Mathematics, University of Waterloo

A video of this lecture

can be found HERE.

Game Theory and the Mathematics of Altruism

Game theory is a branch of mathematics that deals with strategy and
decision making and is applied in economics, computer science, biology,
and many other disciplines as well. We will discuss some of the basic
points of game theory and discuss the so-called iterated prisoner dilemma,
a game that is of central importance in the study of cooperation between
individuals. We will then describe various strategies to this game and explain why altruism is something that can evolve naturally.
Read more about Dr. Bell's talk in the UCCS Communique.


Dr. Joseph Watkins

Department of Mathematics &
Interdisciplinary Program in Statistics
University of Arizona   

A video of this lecture
can be found HERE.

Secrets From Deep Human History

Spectacular advances in the technologies that produce genetic data and

continued advancement in probability theory and statistical inference have combined to
dramatically alter our understanding of deep human history. For example, the sequencing
of ancient DNA from Neanderthal bones in Croatia and in Denisova Cave in the
Altai Mountains
came with new inferential strategies that led to the finding of their
genetic signatures in
modern humans. In this talk, we will explore the extent to which
similar events took place in
Africa where we have not yet found any ancient human
remains to be sequenced.

Comparisons with primate genomes provide a second look at deep human history.
Thus, we will
spend a few minutes to introduce the steps our group is taking to
examine how evolutionary
pressures have impacted the human genome.



Dr. Jerry L. Bona
University of Illinois at Chicago

Mathematics and the Ocean

Jerry L. Bona received his PhD in 1971 from Harvard University under supervision of Garrett Birkhoff and then worked at the Fluid Mechanics Research Institute at University of Essex. Subsequently he was faculty member at the University of Chicago, Pennsylvania State University and the University of Texas at Austin, before joining the University of Illinois at Chicago.

He is well-known for his contributions to the fields of fluid mechanics, partial differential equations and computational math and has been active in other branches of pure and applied mathematics, ocean engineering and economics. Read more about Dr. Bona in the UCCS Communique.

Describing various aspects of the Earth's oceans using mathematics goes back to the 17th century. Some of the world's greatest mathematicians and physicists have been involved in this enterprise.

The lecture will begin with a cursory sketch of some of the more important milestones in the mathematics of the ocean. We will then move on to indicate briefly an example taken from water wave theory of how mathematical models are created.

We then turn to some of the more spectacular applications of the theory. 
This will involve us in tsunami propagation, rogue waves and near-shore zone sand bars
and beach protection, as time permits.

Dr. Omer Angel

University of British Columbia

A video of this lecture
can be found HERE.
Random Planar Maps

A planar map is a planar graph embedded in the plane, considered up to continuous
deformations. These object have been studied extensively in combinatorics, physics
(as discrete random surfaces) and more recently probability theory. Much progress
has been made in recent years in understanding the typical structure of these objects,
and glimpses of a deeper theory are visible, particularly conecting the scaling limit of
random planar maps with conformally invariant models of statistical physics.
I will survey some results and conjectures concerning these objects, and discuss 
some recent progress
in understanding percolation and random walks on these
random graphs. 


Dr. William L. Kath
Engineering Sciences &
Applied Mathematics
Neurobiology and Physiology
Northwestern University

A video of this lecture
can be found HERE.

Computational Modeling of Neurons

With its approximately 100 billion neurons and 200 trillion connections, the human

central nervous system is astoundingly complex. Nevertheless, experimental advances
are rapidly revealing new insights about the workings of neurons and the networks in
which they are connected. Simultaneously, computational models of neurons have
grown swiftly in terms of both their capability and utility. When constrained by
experimental data, such models greatly enhance the observations and provide tools
to construct new experimentally testable predictions.

In this talk I will describe how this two-pronged approach has helped explain some
of the function of hippocampal CA1 pyramidal neurons, a group of principal cells in a
region of the brain that is important for the formation of new memories. The models
and experiments indicate that these relatively large neurons integrate and process their
inputs in a two-stage manner, in that they first combine inputs in localized parts of the
dendritic tree before making an ultimate determination whether or not to signal
downstream neurons with an action potential.

Bill Kath is a professor in the Departments of Engineering Sciences and Applied

Mathematics & Neurobiology and Physiology. From 2005-2010 he was the
Co-Director of the Northwestern Institute on Complex Systems at Northwestern
University. His research interests include computational neuroscience, nonlinear
optics, linear and nonlinear wave propagation and nonlinear dynamics. He received the
NSF Presidential Young Investigator Award in 1985, was elected a Fellow of the
Optical Society of America in 2007, and elected a Fellow of the Society for Industrial
and Applied Mathematics in 2010. He has over 150 peer reviewed publication
and 4 US patents.


Dr. Mark J. Ablowitz
Professor of Distinction
College of Arts & Sciences
University of Colorado at Boulder

A video of this lecture
can be found HERE.

Extraordinary Waves: From Beaches to Lasers

Waves are fascinating. There are a class of extraordinary localized waves, called

solitary waves or solitons which were first documented 175 years ago. This lecture
will trace the history of these waves, their associated mathematics and will explain
why mathematics played a crucial role in both historical and modern developments.
Applications range from water waves to giant internal ocean waves to long distance
communications, lasers and Bose-Einstein condensation and more. The discussion
will be general and will leave all equations behind.

Mark Ablowitz is considered a pioneer in the field of applied mathematics, and his

work in the field is among the most highly cited in the world. He is best known for his
landmark contributions to the "inverse scattering transform," or IST, a method
used to solve nonlinear wave equations. Mathematicians and physicists have used
the IST to gain a better understanding of phenomena such as water waves.
Ablowitz joined the CU-Boulder faculty in 1989.