Mini-Course on Lattice Gauge Field Theory and Prismatic Sets

Sala 1.02
Wednesday, 17 September, 2008

Lecture 1: 17 September (Wed): 14h30-15h30 (Room 1.02 )

Bundle Theory:

Firstly I will try to give the idea on the importance of gauge
theory. The purpose of this talk is to give the theory of principal
G-bundles, where G is a Lie group. This talk contains the theory of
connection and curvature in a principal G-bundle. I will mention
trivial bundle and give some examples.

Lecture 2: 18 September (Thu): 14h30-15h30 (Room 1.02 )

Prismatic Sets, Prismatic Triangulation and The Classifying Space:

I will talk about simplicial sets and classifying space. I will
define prismatic sets and study with their various geometric
realizations. I will introduce the prismatic triangulation of a
simplicial map and in particular of a simplicial set. If time
permits, I will give some topological properties of these
triangulations and some related maps. The important thing is to see
a bundle over a simplicial set and construct the transition
functions for a simplex which are generalized lattice gauge fields.
( This part will be given in the last talk with details)
So I hope that I can prepare you with aid of the first two talks
for the last one.

Lecture 3: 19 September (Fri): 14h30-15h30 (Room 1.02 )

Lattice Gauge Field Theory and Prismatic Sets (joint work with Johan L. Dupont):

We study prismatics sets analogously to simplicial sets except that
realization involves prims. Particular examples are the prismatic
subdivision of a simplicial set S and the prismatic star of S. Both
have the same homotopy type as S and in particular the latter we use
to study lattice gauge theory in the sense of Phillips and Stone.
Thus for a Lie group G and a set of parallel transport functions
defining the transition over faces of the simplices, we define a
classifying map from the prismatic star to a prismatic version of
the classifying space of G. In turn this defines a G-bundle over the
prismatic star.


Prof. Bedia Akyar (Dokuz Eylul University, Izmir)