The definition of the Kauffman bracket skein algebra of an oriented
surface was originally motivated by the Jones polynomial invariant
of knots and links in space, and a representation of the skein
algebra features in Witten's topological quantum...
Harmonic bundles are flat bundles equipped with a pluri-harmonic
metric. They are very useful in the study of flat bundles on
complex projective manifolds. Indeed, according to the fundamental
theorem of Corlette, any semisimple flat bundle on a...
Harmonic bundles are flat bundles equipped with a pluri-harmonic
metric. They are very useful in the study of flat bundles on
complex projective manifolds. Indeed, according to the fundamental
theorem of Corlette, any semisimple flat bundle on a...
I will discuss a connection between monodromy groups of variations
of Hodge structure and the global behavior of the associated period
map. The large-scale information in the period map is contained in
the Lyapunov exponents, which are invariants...
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
A theme that cuts across many domains of computer science and
mathematics is to find simple representations of complex
mathematical objects such as graphs, functions, or distributions on
data. These representations need to capture how the object...
Decomposition theorem for perverse sheaves on algebraic
varieties, proved by Beilinson-Bernstein-Deligne-Gabber, is one of
the most important and useful theorems in the contemporary
mathematics. By the Riemann-Hilbert correspondence, we may
regard...
A theme that cuts across many domains of computer science and
mathematics is to find simple representations of complex
mathematical objects such as graphs, functions, or distributions on
data. These representations need to capture how the object...