We will discuss a complete computation of Savelyev's
homomorphism associated to any coadjoint orbit of a compact Lie
group G, where the domain is restricted to the based loop homology
of G. This gives at the same time some applications to the...
We will discuss the existence of rational (multi)sections and
unirulings for projective families f:X→P1 with at most two singular
fibres. Specifically, we will discuss two ingredients for
constructing the above rational curves. The first is local...
In this talk, I will discuss recent joint work with D.
Cristofaro-Gardiner and B. Zhang showing that a generic
area-preserving diffeomorphism of a closed surface has a dense set
of periodic points. This follows from a result called a “smooth
closing...
In this talk, we prove an upper bound on the average number of
2-torsion elements in the class group of monogenised fields of any
degree n≥3 and, conditional on a widely expected tail estimate,
compute this average exactly. As an application, we...
In this talk, as a continuation of my talk in the Members’
Colloquium but with a specialized audience in mind, I will discuss
in more detail some of the general geometric and dynamical
structures underlying the theoretical aspects of the
restricted...
Traditionally, objects of study in symplectic geometry are
smooth - such as symplectic and Hamiltonian diffeomorphisms,
Lagrangian (or more generally, isotropic and co-isotropic)
submanifolds etc. However, in the course of development of the
field...
In the first half of the talk I will review Gromov's work on
convex integration for open differential relations. I will put
particular emphasis on comparing various flavours of ampleness and,
in particular, I will note that the different flavours...
Let f be an embedding of a non compact manifold into an
Euclidean space and p_n be a divergent sequence of points of M. If
the image points f(p_n) converge, the limit is called a limit point
of f. In this talk, we will build an embedding f of a...
