The dynamics of an inviscid and incompressible fluid flow on a
Riemannian manifold is governed by the Euler equations. Recently,
Tao [6, 7, 8] launched a programme to address the global existence
problem for the Euler and Navier-Stokes equations...
This talk is based on a joint work with Thomas Kragh. Using the
generating function theory we split inject homotopy groups of
pseudo-isotopy and/or h-cobordism spaces into various spaces of
Legendrian manifolds, e.g. the space of Legendrian unknots...
For a polynomial f∈ℚ[x], Hilbert's irreducibility theorem
asserts that the fiber f−1(a) is irreducible over ℚ for all values
a∈ℚ outside a "thin" set of exceptions Rf. The problem of
describing Rf is closely related to determining the
monodromy...
For the Bargmann--Fock field on Rd with d>2, we prove that
the critical level lc(d) of the percolation model formed by the
excursion sets {f≥l} is strictly positive. This implies that for
every l sufficiently close to 0 (in particular for the nodal...
A locally testable code (LTC) is an error correcting code that
admits a very efficient membership test. The tester reads a
constant number of (randomly - but not necessarily uniformly -
chosen) bits from a given word and rejects words with...
Despite the fact that the 3-body problem is an ancient conundrum
that goes back to Newton, it is remarkably poorly understood, and
is still a benchmark for modern developments. In this talk, I will
give a (very) biased account of this classical...
A locally testable code (LTC) is an error correcting code that
admits a very efficient membership test. The tester reads a
constant number of (randomly - but not necessarily uniformly -
chosen) bits from a given word and rejects words with...
In various areas of mathematics there exist "big fiber
theorems", these are theorems of the following type: "For any map
in a certain class, there exists a 'big' fiber", where the class of
maps and the notion of size changes from case to case.