Stability conditions, rational elliptic surfaces and Painleve equations
Abstract
We will describe the space of Bridgeland stability conditions
of the derived category of some CY3 algebras of quivers drawn on the
Riemann sphere. We give a biholomorphic map from the upper-half plane to
the space of stability conditions lifting the period map of a meromorphic
differential on a 1-dimensional family of elliptic curves. The map is
equivariant with respect to the actions of a subgroup of $\mathrm{PSL}(2,\mathbb Z)$ on the
left by monodromy of the rational elliptic surface and on the right by
autoequivalences of the derived category.
The complement of a divisor in the rational elliptic surface can be
identified with Hitchin's moduli space of connections on the projective
line with prescribed poles of a certain order at marked points. This is
the space of initial conditions of one of the Painleve equations whose
solutions describe isomonodromic deformations of these connections.
Normal Forms, Factorability and Cohomology of HV-groups
Abstract
A factorability structure on a group G is a specification of normal forms
of group elements as words over a fixed generating set. There is a chain
complex computing the (co)homology of G. In contrast to the well-known bar
resolution, there are much less generators in each dimension of the chain
complex. Although it is often difficult to understand the differential,
there are examples where the differential is particularly simple, allowing
computations by hand. This leads to the cohomology ring of hv-groups,
which I define at the end of the talk in terms of so called "horizontal"
and "vertical" generators.
11:00
"Model theoretic properties of S-acts and S-poset".
Abstract
An S-act over a monoid S is a representation of a monoid by tranformations of a set, analogous to the notion of a G-act over a group G being a representation of G by bijections of a set. An S-poset is the corresponding notion for an ordered monoid S.
What is persistent homology?
Abstract
Persistent homology is a relatively new tool to analyse the topology of data sets.
We will give a brief introduction and tutorial as preparation for the third talk in the afternoon.
11:00
11:00
Analysis on boundaries of hyperbolic groups
Abstract
We'll survey some of the ways that hyperbolic groups have been studied
using analysis on their boundaries at infinity.