Question

I am interested in learning Mirror Symmetry, both from the SYZ and Homological point of view. I am taking a reading course in Mirror Symmetry, which will focus on the SYZ side. I know basic Complex geometry, Kahler manifolds, Symplectic manifolds in the geometric side and also reading some material for my course on SYZ conjecture. My major concern is Homological side, about which I have little knowledge.

I am seeking a list of good references for SYZ conjecture, Homological Mirror Symmetry, physics of the theory, modern developments and on its relation to other areas of mathematics and some original papers (preferably in Chronological order).

What are your views about the Claire Voisin's book on Mirror Symmetry. And what is the present status of research in Mirror Symmetry, I mean what type of problems are people working on.

Answer 1

Auroux's notes for a course on mirror symmetry at Berkeley: http://math.berkeley.edu/~auroux/277F09/index.html. They look interesting and they cover a lot of material.

Answer 2

For an understanding of the SYZ conjecture it is necessary to understand the framework of D-branes. I believe that a very good introduction, still unmatched in its comprehensiveness, is the book by Hori et al. on "Mirror Symmetry". This book has been made freely available by the Clay Math Institute and can be downloaded from their website http://www.claymath.org/library/monographs/cmim01.pdf. A more recent reference is the book by Joyce on "Riemannian Holonomy Groups and Calibrated Geometry", which contains a discussion of the SYZ conjecture from a more rigorous point of view.

Answer 3

The book "Dirichlet Branes and Mirror Symmetry" by Aspinwall et. al. seems to fit quite well with your request. It discusses SYZ, Homological Mirror Symmetry and its physical origin.