Derived Categories in Algebraic Geometry
June 04, 2007 - June 16, 2007
University of Utah
Aaron Bertram (University of Utah), Y.P. Lee (university of Utah), Eric Sharpe (University of Utah and Virginia Tech)
Aaron Bertram (University of Utah)
Andrei Calderaru (University of Wisconsin-Madison)
Patrick Clarke (University of Miami)
Alastair Craw (University of Glasgow)
Eric Sharpe (University of Utah and Virginia Tech)
Over the last several years derived categories have emerged in a remarkable interaction between algebraic geometry and physics. Perhaps the origin of this interaction was a conjecture of Kontsevich for a new picture of mirror symmetry.
Kontsevich's proposed understanding of mirror symmetry, now known as "homological mirror symmetry," recasts mirror symmetry is as an equivalence of categories between the derived category of coherent sheaves on one Calabi-Yau and a derived Fukaya category on the mirror Calabi-Yau.
The first week of this two-week course will focus on the basics of derived categories of coherent sheaves, including the McKay correspondence and derived categories of toric varieties.
The second week will be devoted to more advanced topics, including stability conditions, applications to Landau-Ginzburg models and mirror symmetry. The course will be followed by a Summer Research Conference at Snowbird (see
Prospective participants must apply online at the website http://www.math.utah.edu/dc/app.htm. MSRI will provide funding for several students from MSRI Academic Sponsoring Institutions who are selected through the application process as participants.