Abstracts for Seminar on Algebra, Geometry and Physics

Seidel-Thomas twists are autoequivalences of the derived category D(X)
of an algebraic variety X. They are the mirror symmetry analogues of Dehn
twists along Lagrangian spheres on a symplectic manifold. Given an object
E in D(X) with numerical properties of such a sphere, Seidel and Thomas
defined the spherical twist of D(E) along E and proved it to be an
autoequivalence. It has been understood for a while that this should
generalise to the notion of the twist along a spherical functor into
D(X). In full generality this was obstructed by some well-known

In this talk I will report on a joint project with H. Ruddat, D. Treumann and E. Zaslow, which constructs a 'skeleton' for  affine hypersurfaces in toric ambient space, and proves that
there exists a retraction of the hypersurface onto it. The skeleton, which is a half-dimensional CW complex, will be defined using toric data. Defining the retraction will involve techniques from log geometry. If time permits I will discuss applications to homological mirror symmetry for
degenerate Calabi-Yau hypersurfaces, with toric components.

Zipf's law was discovered as an empirical probability distribution
governing the frequency of usage of words in a language.  Later
it was observed in many other situations. As Terence Tao recently remarked,
it still lacks a convincing and satisfactory mathematical explanation.

In this talk I suggest that at least in certain cases, Zipf's law can be explained as
a special case of   the  a priori distribution introduced and studied by L.~Levin.
The Zipf ranking corresponding to diminishing frequency appears then as the

We define a jet-space analogue of the BV-Laplacian, avoiding
delta-functions and infinite constants; instead we show that the main
properties of the BV-Laplacian, which is a necessary ingredient in the
quantisation of gauge-invariant systems of Euler-Lagrange equations, and
its relation to the Schouten bracket originate from the underlying
jet-space geometry.