Homological mirror symmetry is a deep mathematical conjecture
proposed by Maxim Kontsevich at the 1994 ICM in Zürich, and it is about
a certain relationship between the two mathematical areas of symplectic
geometry and algebraic geometry. More precisely, the conjecture states
that there is a derived equivalence between the so-called Fukaya
category in symplectic geometry, and the category of coherent sheaves
which is well-studied in the field of algebraic geometry. The conjecture
is an attempt at understanding mirror symmetry in string theory which is
well-known by physicists.
In this talk I will first go through history and origins of the
conjecture. After that, an introduction to symplectic geometry will be
given and the goal will be to give the audience a feeling of what the
Fukaya category is.