Thursday, 25th December 2003, 4:00 pm

Mathematics Building, Lecture Hall 2

Professor Alexander Goncharov

(Brown University and MPI, Bonn)

"Positivity and higher Teichmuller theory"

** Abstract: **
Let S be a compact two dimensional surface with boundary.
We define two moduli spaces closely related to representations of the fundamental group of S to
a split algebraic group G, e.g. G=SL(m). We equip them with distinguished collections
of coordinate systems such that the corresponding transition functions are
subtraction free. Thus we can define the points of the corresponding moduli spaces with
coefficients in positive numbers, or, more generally, in any semifield.

For G=SL(2) we recover this way the classical Teichmuller spaces and, taking points with values in the tropical semifields, Thurston's laminations on S. For general G we get a generalisation of the Teichmuller-Thurston theory. We quantize these spaces using the quantum dilogarithm.

This is joint work with V. Fock, available as math.AG/0311149.

Light refreshments will be served in the faculty lounge at 3:30.

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