
Lecture Series by V. Voevodsky

NOTE: The date and time for the second lecture have
changed. 
University of Miami
Department of Mathematics
College of Arts and Sciences
Lecture Series
Professor Vladimir Voevodsky
Institute for Advanced Study
Princeton University
will present
Categories, Population Genetics and a Little of Quantum Physics
Thursday, January 6, 2005, 1:00pm
Tuesday, January 11, 2005, 1:00pm 
Thursday, January 13, 2005, 3:00pm
Ungar Room 402
Refreshments served 30 minutes before each talk in Ungar Room 521
All interested persons are welcome to attend.
Abstract:
In these lectures I will tell about my work on two related but separate subjects. The first one is mathematical
population genetics. I will describe a simple model which is useful for the study of the relationship between the
history of a population and its genetic properties. While the positive results obtained in the framework of this model
may have little use because of the model's simplicity the negative results are likely to remain valid for more complex
real world populations.
The second subject can be described as a categorical study of probability theory where "categorical" is understood in
the sense of category theory. Originally, I developed this approach to probability to get a better understanding of
the constructions which I had to deal with in population genetics. Later it evolved into something which seems to be
also interesting from a purely mathematical point of view. On the elementary level it gives a category which is useful
for the work with probabilistic constructions involving complicated combinations of stochastic processes of different
types. On a more advanced level, applying in this context the old idea of a functor as a generalized object one gets a
better view of the relationship between probability and the theory of (pre)ordered topological vector spaces. This
leads to the third topic mentioned in the title. But I am only beginning to understand this connection.
Some Information:
Vladimir Voevodsky
2002 Fields Medalist
Vladimir Voevodsky is a Professor at the Institute for Advanced Study in Princeton. He was awarded 2002 Fields Medal
in Beijing for developing a new cohomology theory for algebraic varieties. The last lead to the proof of Milnor's and
recently of Bloch Kato conjectures.
Voevodsky, whose field within mathematics is algebraic geometry, is known for his work in the homology theory of
schemes, algebraic Ktheory, and interrelations between algebraic geometry and algebraic topology. He has been
concerned with a synthesis of algebraic geometry and homotopy theory, two major branches of modern mathematics. His
interest has moved recently to Math Biology.
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