L. Boi's talk

[Ugo Bruzzo]

This is a brief introduction to the talk that Professor
Luciano Boi (Ecole des Hautes Etudes en Sciences Sociales,
Centre de Mathématiques, Paris) will give tomorrow
(February 28) at 2:30 pm (SISSA, Room D, Main building).

Luciano is a mathematician who works in the epistemology
of geometry, especially in connection with its applications to
Physics, and on topological models in biology. He has
a special interest in the topology of knots and its applications
to molecular biology.

A detailed abstract of his talk follows. Luciano will also give
a talk entitled "When topology meets biology ‘for life’:
Interdisciplinary remarks on the way in which form modulates function"
as a joint seminar with the Interdisciplinary Laboratory for Advance
Studies (next Friday).

    Ugo Bruzzo

===================================


Abstract: The aim of this talk is to make some general remarks on the 
role
of geometrical and topological concepts in the development of 
theoretical
physics, espacially in gauge theory and string theory, and then to show
the great significance of these concepst for a better understanding of 
the
dynamics of physics. We claim that physical phenomena very likely emerge
from the geometrical and topological structure of spacetime. The 
attempts
to solve one of the central problems in twentieth physics, i.e.: how to
combine gravity and the other forces into an unitary theoretical
explanation of the physical world, essentialy depends on the possibility
of building a new geometrical framework conceptually richer than
Riemannian geometry. In fact, it still plays a fundamenatal role in
non-Abelian gauge theories and in superstring theory, , thanks to which 
a
great variety of new mathematical structures has emerged. A very
interesting hypothesis is that the global topological properties of the
manifold's model of spacetime play a major role in quantum field theory
and that, consequently, several physical quantum effects arise from the
non-local metrical and topological structure of these manifold. Thus the
unification of general relativity and quantum theory require some
fundamental breakthrough in our understanding of the relationship 
between
spacetime and quantum processes. In particular the superstring theories
lead to the guess that the usual structure of spacetime at the quantum
scale must be dropped out from physical thought. Non-Abelian gauge
theories satisfy the basic physical requirements pertaining to the
symmetries of particle physics because they are geometric in character.
They profoundly elucidate the fundamental role played by bundles,
connections and curvature in explaining the essential laws of nature.
Kaluza-Klein theories and more remarkably superstring theory showed that
spacetime symmetries and internal (quantum) symmetries might be unified
through the introduction of new structures of space with a different
topology. This essentially means, in our view, that ‘hidden’ symmetries 
of
fundamental physics can be related to the phenomenon of topological 
change
of certain class of (presumably) non-smooth manifolds.