Abstracts for Seminar on Algebra, Geometry and Physics

A very nice feature of quasi-smooth derived schemes (in the sense of Toen-Vezzosi and Lurie) is that they induce a  1-perfect obstruction theory on the underlying scheme. This gives rise to a virtual fundamental class on the underlying scheme. I will discuss in detail how this obstruction theory is induced. This requires reviewing some facts about the Postnikov decomposition and the cotangent complex of simplicial algebras.

This project was motivated by string theory. We study the relation between
the topology of moduli space of curves and that of the Sato-Grassmannian
via the Krichever map. The Krichever map was discovered for solving certain
integrable systems, KdV, K.P.; Segal and Wilson showed that the Krichever
map is an embedding from the moduli space of curves with some geometric
data into the Sato-Grassmannian. We expressed image of the induced map of
the Krichever map in terms of lambda-classes and psi-classes and related

We consider the conjugacy problem and its friends (simultaneous and subgroup conjugacy, double coset
problem etc.) in braid and Garside groups. We show how these problems naturally emerge in non-commutative public key cryptography and how they are related. At the end we consider left self-distributive (LD)
systems and my new idea of non-associative cryptography and apply there P. Dehornoy's shifted
conjugacy (and its generalizations).

 

For any curved differential graded algebra A, Block introduced a dg category
called P_A. When A is the Dolbeaut algebra of a compact complex manifold,
Block proved that the homotopy category of P_A is the bounded derived category
of coherent sheaves on the manifold.  His first paper can be found at
http://arxiv.org/abs/math/0509284

Because P_A is defined without the use of sheaves, its definition is motivated by
non-commutative geometry. After providing some historical context and defining the main