Video Lectures

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...

Although it is a crucial pat of our cosmic timeline, Cosmic Dawn—when the first stars and galaxies formed and systematically reionized the intergalactic medium—remains relatively unexplored. By tracing the distribution and state of neutral hydrogen...

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...