FANOSEARCH is an ongoing collaboration (myself, V. Golyshev and a group in England), that started in 2009.
Mirror Symmetry and Fano Manifolds (Fanosearch Manifesto)
Minkowski Polynomials and Mutations
Quantum Periods for 3-Dimensional Fano Manifolds
Quantum Periods For Certain Four-Dimensional Fano Manifolds
Alessio Corti's 4 Lectures on Extremal Laurent Polynomials in Grenoble (July 2011).
Sergey Galkin's 5 Lectures on Fano Mirrors (only first 2 available) in Anmyundo (June 2011).
Vasily Golyshev's presentation and two lectures.
Mirror symmetry for Fano threefolds:
+Part a. Quantum differential equations of Fano threefolds
+Part b. Minkowski ansatz for mirror symmetry for Fano threefolds
+Part c. Gorenstein toric degenerations of Fano threefolds [cf. Christophersen-Ilten 1202.0510]
7. 15-21 Dec 2012, MPIM Bonn: Galois representations and pencils of Calabi-Yau motives
6. 23-28 Mar 2012, MPIM Bonn: Motivic structures on quantum cohomology: progress reports
5. 14-16 Dec 2011, Freie Universitaet Berlin: Extremal Laurent Polynomials and Fano Varieties
4. 22-26 Feb 2011, Imperial College London: Fano Varieties and Extremal Laurent Polynomials
3. 17-20 Sep 2010, Imperial College London: Fano Varieties and Extremal Laurent Polynomials
2. 13-14 Sep 2010, MPIM Bonn: Quantum motives: realizations, detection, applications
1. 19-21 Oct 2009, Warwick: Extremal Laurent Polynomials -- new approaches to mirror symmetry and classification of Fanos