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...
Neural networks have been around for many decades. An important
question is what has led to their recent surge in performance and
popularity. I will start with an introduction to deep neural
networks, covering the terminology and standard approaches...
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...
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...