THE MALLAT FAMILY FUND FOR RESEARCH IN MATHEMATICS
invites you to
a
SPECIAL LECTURE
SERIES
to be presented
by
The lectures will be
held in
Room
232
Technion -
Israel Institute of Technology
Lecture I:
Diffusion
mediated transport with a look at motor proteins
Motion in small live systems has
many challenges. Prominent environmental conditions are high viscosity and
warmth. Not only is it difficult to move, but maintaining a course is rendered
difficult by immersion in a highly fluctuating bath. This holds especially for
the motor proteins responsible for much of eukaryotic cellular traffic. The
situation falls under the rubric of diffusion mediated transport. We give some
brief historical notes, the work of many distinguished scientists, and then turn
to an approach based on the Monge transport problem
(1787) and its modern version, Monge- Kantorovich Theory, which offers us a means of studying
these systems with analysis. We arrive at a precipice: does this help? Can we
say anything about the behavior of the cellular process? An exciting venue for
math in the natural world!
Lecture II:
Analysis
of the multistate transport system
The multistate Brownian motors or molecular rachet mechanisms introduced in the first talk result in
weakly coupled systems of evolution equations, generally speaking. Their
stationary solutions are not in equilibrium and detailed balance conditions fail
to hold. But out of equilibrium status is not sufficient for reliable transport.
We examine this question
Lecture III:
Making
sense of microstructure
Most technologically useful materials are polycrystalline, comprised of many small grains separated by interfaces, called grain boundaries. The energetics and connectivity of this network of interfaces plays a role in many material properties and across many scales of use. Preparing arrangements of grains and boundaries, a texture, suitable for a given purpose is a central problem in materials science: it is the problem of microstructure. Recent years have witnessed a changing paradigm in experimental science: automated data acquisition technologies, now practiced in disciplines as varied as materials science and molecular biology, allow vast interrogation at certain scales. Typically most interesting are those mesoscales rich in information. The yield has been huge amounts of data, demanding novel approaches for interpretation. These advances pose new challenges for our understanding of such systems through mathematical modeling, simulation, and analysis.