From QFT to 2-d Supersymetric TQT:Mirror symmetry between Math and Physic

Theoretical physics is taking an increasing part in the universe of mathematics. After calculus, vector and tensorial analysis, topological theories make their entry into quantum field theories. More precisely, in this domain, topological theories are the most relevant. A fundamental theorem of the Atiyah has important repercussions in several branches of quantum physics in the geometric approach. We can cite the work of Alain Connes on non-commutative geometry, but also all the developments due to Donaldson, E. Witten around Gauge theories, superstring and Mirror Symmetry. We present here an historical survey of some topological field theories, especially Mirror Symmetry to understand the interpenetration between quantum physics and topology.