We study CM cycles on Kuga-Sato varieties over X(N) via theta
lifting and relative trace formula. Our first result is the
modularity of CM cycles, in the sense that the Hecke modules they
generate are semisimple whose irreducible components are...
In this talk I will discuss two undetected populations of black
holes. In the faraway Universe, the first lensed z > 6 quasar
(J0439+1634) was recently discovered. We predicted that the
observed population of quasars should contain many mildly...
I'll describe a method for analyzing the first-order theory of
an arithmetic group using its congruence quotients. When this
method works, it gives a strong form of first-order rigidity
together with a complete description of the collection of...
The query model is one of the most basic computational
models. In contrast to the Turing machine model, fundamental
questions regarding the power of randomness and quantum computing
are relatively well-understood. For example, it is
well-known...
We will discuss the first steps in an approach to proving
homological mirror symmetry for Looijenga pairs through tropical
Lagrangian sections. Namely, we will see how to construct these
Lagrangian sections from tropical data corresponding to line...
The honest answer to the question is that I actually do not
know. I will therefore rather talk about several famous examples
that are widely called "h-principle results" and try to explain
some of the ideas behind the ones I am most familiar with.
