We introduce an SFT-type invariant for Legendrian knots in R^3,
which is a deformation of the Chekanov-Eliashberg differential
graded algebra. The differential includes components that count
index zero pseudoholomorphic disks with up to two positive...
One of the earliest achievements of mirror symmetry was the
prediction of genus zero Gromov-Witten invariants for the quintic
threefold in terms of period integrals on the mirror. Analogous
predictions for open Gromov-Witten invariants in closed...
We prove an effective equidistribution theorem for
semisimple
closed orbits on compact adelic quotients. The obtained error
depends polynomially on the minimal complexity of intermediate
orbits and the complexity of the ambient space. As an...
The second lecture features the nuts and bolts of the invariants
from first lecture, which we call foundations. We explain the
structure theorem for foundations of ternary matroids, which is
rooted in Tutte's homotopy theorem. We show how this...
Lecture Series Framework: A unifying framework for
F1-geometry, tropical schemes and matroid theory. In this series of
3 lectures, I will present a recent approach towards F1-geometry
and its links to tropical geometry, matroid theory,
Lorentzian...
In this talk we will discuss some aspects of the question: given
a group, what is the range of Furstenberg entropy of ergodic
stationary actions of it? For the special linear group and its
lattices, constraints on this spectrum come from Nevo-Zimmer...
The question of asbolute continuity, with respect to the
reference measure, of the harmonic measure on a domain with rough
boundary has been the object of many important results. Here we ask
about the similar question, but where the Dirichlet...
Symplectic manifolds exhibit curious behaviour at the interface
of rigidity and flexibility. A non-squeezing phenomenon discovered
by Gromov in the 1980s was the first manifestation of this. Since
then, extensive research has been carried out into...
The Brunn-Minkowski inequality is a fundamental result in convex
geometry controlling the volume of the sum of subsets of ℝn.
It asserts that for sets A,B⊂ℝn of equal volume and a
parameter t∈(0,1), we have |tA+(1−t)B|≥|A| with equality iff A=B
is...
The analytic de Rham stack is a new construction in Analytic
Geometry whose theory of quasi-coherent sheaves encodes a notion of
p-adic D-modules. It has the virtue that can be defined even under
lack of differentials (eg. for perfectoid spaces or...
