Gross and Siebert have recently proposed an "intrinsic"
programme for studying mirror symmetry. In this talk, we will
discuss a symplectic interpretation of some of their ideas in the
setting of affine log Calabi-Yau varieties. Namely, we
describe...
Given a K3 surface XX over a number field KK, we
prove that the set of primes of KK where the geometric
Picard rank jumps is infinite, assuming that XX has
everywhere potentially good reduction. This result is formulated in
the general framework of...
I discuss graviton non-Gaussianities in models of inflation
where de Sitter isometries are spontaneously broken. First, I
review the different symmetry breaking patterns following Nicolis,
Penco, Piazza, Rattazzi (2015), and discuss which of them...
A theorem of Bernstein identifies the center of the affine Hecke
algebra of a reductive group GG with the Grothendieck
ring of the tensor category of representations of the dual
group G∨G∨. Gaitsgory constructed a functor which
categrorifies this...
Some years ago, I proved with Shulman and Sørensen that
precisely 12 of the 17 wallpaper groups are matricially stable in
the operator norm. We did so as part of a general investigation of
when group C∗C∗-algebras have the semiprojectivity and
weak...
Expander graphs are graphs which simultaneously are both sparse
and highly connected. The theory of expander graphs received a lot
of attention in the past half a century, from both computer science
and mathematics. In recent years, a new theory of...
With gate error rates in multiple technologies now below the
threshold required for fault-tolerant quantum computation, the
major remaining obstacle to useful quantum computation is scaling,
a challenge greatly amplified by the huge overhead imposed...
Valiant (1980) showed that general arithmetic circuits with
negation can be exponentially more powerful than monotone ones. We
give the first qualitative improvement to this classical result: we
construct a family of polynomials P-n in n variables...
One of the earliest fundamental applications of Lagrangian Floer
theory is detecting the non-displaceablity of a Lagrangian
submanifold. Many progress and generalisations have been made since
then but little is known when the Lagrangian submanifold...
