In a previous work with Felix Schlenk, we showed that an
analogue of the phenomenon of Lagrangian barriers holds in the
contact framework in S3 : there exist (explicit) Legendrian
complexes of arcs in S3 that have short Reeb chords to many...
Ideas from tame geometry have recently begun to find their way
into quantum field theory and string theory, suggesting that
consistent effective theories and their observables may admit
definable descriptions of finite complexity. In this talk I...
Hilbert, motivating his list of 23 problems, mentions the
arithmetical formulation of the concept of the continuum in the
works of Cauchy, Bolzano and Cantor, and the discovery of
non-Euclidean geometry by Gauss, Bolyai and Lobachevsky, as...
Why is it so hard to prove P != NP, or even to prove
super-linear circuit lower bounds? While we often blame a lack of
combinatorial ingenuity, the bottleneck might be more fundamental:
the logical strength of our mathematical tools.
Hilbert, motivating his list of 23 problems, mentions the
arithmetical formulation of the concept of the continuum in the
works of Cauchy, Bolzano and Cantor, and the discovery of
non-Euclidean geometry by Gauss, Bolyai and Lobachevsky, as...
We present a general framework for derandomizing random linear
codes with respect to a broad class of properties, known as local
properties, which encompass several standard notions such as
minimum distance, list-decoding, list-recovery, and perfect...
I will talk about a joint work with Antoine Sedillot. We study
sup-norms of sections of metrized line bundles for families of
arithmetic varieties. Using Riemann-Zariski spaces we obtain
formulas that imply new definability results in the context
of...
Constructing completions of period mappings with
significant geometric and Hodge-theoretical meaning is an important
topic in Hodge theory and its applications. There are rich theories
for the classical case in which the period domain is
Hermitian...
The anabelian phenomenon may be viewed as an arithmetic analogue
of Mostow rigidity: it predicts that certain varieties can be
reconstructed from their arithmetic fundamental groups. A
celebrated result of S. Mochizuki shows that hyperbolic
curves...
