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...
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...
Abstract: A rather notorious mistake occurs p. 217 in the proof
of Lemma 6.3 of the book "Simple algebras, base change, and the
advanced theory of the trace formula" (1989) by J. Arthur, L.
Clozel. E. Lapid and J. Rogawski (1998) proposed a proof...
