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.