The 16th Hilbert problem, a story of mystery, mistakes and solution

Speaker: 

Professor Oleg Viro

Institution: 

Uppsala University

Time: 

Thursday, March 8, 2007 - 4:00pm

Location: 

MSTB 254

Hilbert's problem of the topology of algebraic curves and surfaces (the
16th problem from the famous list presented at the second International
Congress of Mathematicians in 1900) was difficult to formulate. The way it
was formulated made it difficult to anticipate that it has been solved. I
believe it has, and this happened more than thirty years ago, although the
World Mathematical Community missed to acknowledge this.

Reaction-diffusion equations and biological invasions

Speaker: 

Professor Henri Berestycki

Institution: 

Ecole des hautes etudes en sciences sociales, Paris.

Time: 

Tuesday, February 6, 2007 - 4:00pm

Location: 

MSTB 254

Diffusion, along with transport and reaction effects, is the main factor explaining changes
or transitions in a wide array of situations such as flames, some phase transitions, tumours
or other biological invasions. In these systems, two or several possible states coexist, and
one observes certain states expanding or receding or patterns being formed.

This lecture, meant for a general audience, will describe some mathematical properties of
reaction-diffusion equations as an approach to spatial propagation and diffusion. After
describing the mechanism of reaction and diffusion and giving several illustrations, I will
review some classical results. In the context of ecology of populations, I will then mention
some recent works dealing with non homogeneous media. In this framework, I will describe a
model addressing the question of how a species keeps pace with a shifting climate.

Modelling dynamics of T cells in Type 1 Diabetes

Speaker: 

Professor Leah Keshet

Institution: 

UBC

Time: 

Friday, February 2, 2007 - 3:00pm

Location: 

MSTB 254

Type 1 diabetes (T1D) is an autoimmune disease in which immune cells
target and kill the insulin-secreting pancreatic beta cells.
Recent investigation of diabetes-prone (NOD) mice reveals large cyclic
fluctuations in the levels of T cells (cells of the adaptive
immune system) weeks before the onset of the disease. We extend
a previous mathematical model for T-cell dynamics to account for the
gradual killing of beta cells, and show how such cycles can arise
as a natural consquence of feedback between self-antigen and T-cell
populations. The model has interesting nonlinear dynamics
including Hopf and homoclinic bifurcations in biologically reasonable
regimes of parameters. The model fits into a larger program of
investigation of type 1 diabetes, and suggests experimental tests.

Bodies interacting with and through fluids

Speaker: 

Professor Mike Shelley

Institution: 

Courant Institute

Time: 

Thursday, February 15, 2007 - 4:00pm

Location: 

MSTB 254

The interaction of flowing fluids with free bodies -- sometimes
compliant, sometimes active, sometimes multiple -- constitutes a class
of beautiful dynamic boundary problems that are central to biology and
engineering. Examples range from how organisms locomote in fluids
(which depends strongly on scale) to how non-Newtonian stresses
develop in complex liquids (strongly dependent on the nature of
fluidic microstructure). I will discuss several interesting examples,
emphasizing how they are formulated mathematically so as to yield
models tractable for analysis or simulation, and show how this work
has interacted with experimental studies.

Can one make objects invisible?

Speaker: 

Professor Gunther Uhlmann

Institution: 

University of Washington

Time: 

Thursday, February 22, 2007 - 4:00pm

Location: 

MSTB 254

The subject of invisibility has fascinated people for thousands
of years. There has recently been considerable theoretical and practical
progress in understanding how to cloak objects. We will discuss some of
the recent work on the subject of invisibility which involves using
singular electromagnetic parameters, or singular Riemannian metrics.

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