Lecture Notes from the special session on Algebraic Geometry, Representation Theory and Topological Field Theories, University of Illinois Urbana Champaign, March 2009.

• Matt Ando: Twisted umkehr maps.
• Rina Anno: Stability conditions, Springer fibers, and braids with multiplied threads.
• Chris Brav: The Projective McKay Correspondence.
• Kobi Kremnizer: Localization for singular weights and finite W-algebras.
• David Nadler: Character Sheaves.
• Alexei Oblomkov: On GW/DT Correspondence with Descendents.
• Dmitro Shklyarov: Equivariant topological field theories .
• Matt Szczesny: Moduli problems and localization functors in orbifold CFT .
• Prabhu Venkataraman: The 2-lien of a 2-gerbe .