Building upon the success of the annual Great Lakes Geometry Conference which is by now a well-established conference held in the Great Lakes region, the PIs propose to bring together experts of toric geometry and of the related areas from the faces of symplectic geometry, algebraic geometry and K""ahler geometry and to provide a common ground where mathematicians share ideas and visions towards the goal of understanding the mirror symmetry of toric varieties in all faces. This will in turn serve a stepping stone towards deeper understanding of Kontsevich's homological mirror symmetry and of Strominger-Yau-Zaslow proposal of Lagrangian torus fibrations on Calabi-Yau manifolds, which have been one of the most active areas of research in geometry and physics of string theory in recent years. While there have been many conferences dedicated to symplectic geometry and mirror symmetry or toric geometry recent years, the PIs are not aware of a conference that brings all of these aspects together in the context of geometry of toric varieties.
The Great Lakes Geometry Conference is by now a well-established conference of geometry and topology held in the Great Lakes region. The conference in the year 2010 is its 11-th anniversary and will be held in the University of Wisconsin at Madison. The main theme of the GLGC 2010 is toric geometry and the related areas which will provide a common ground where mathematicians share ideas and visions towards the goal of understanding the mirror symmetry of toric varieties in all faces. We hope that gathering the experts of different faces in toric geometry and mirror symmetry will encourage collaborations between researchers in the areas. In this conference, the PIs draw the speakers at this conference from a diverse spectrum of active research areas in geometry and mathematical physics. One primary goal of this conference is to expose graduate students and early career mathematicians in the related fields to some recent exciting new developments in this active area of geometry and physics of mirror symmetry and toric geometry. We also hope that the conference will benefit the students and the early career mathematicians at the University of Wisconsin and other Midwestern universities, encourage interaction between the universities in the Midwestern region and beyond, and help graduate students and post-docs to work in these exciting areas.
Building upon the success of the annual Great Lakes Geometry Conference which is by now a well-established conference held in the Great Lakes region, the PIs proposed to bring together experts of toric geometry and of the related areas from the faces of symplectic geometry, algebraic geometry and Kaehler geometry and to provide a common ground where mathematicians share ideas and visions towards the goal of understanding the mirror symmetry of toric varieties in all faces. This will in turn serve a stepping stone towards deeper understanding of mirror symmetry in physics of string theory which have been one of the most active areas of research in geometry and physics of string theory in recent years. While there have been many conferences dedicated to symplectic geometry and mirror symmetry or toric geometry recent years, the PIs are not aware of a conference that brings all of these aspects together in the context of geometry of toric varieties. In this conference, the PIs drew experts into this conference from a diverse spectrum of active research areas in geometry and mathematical physics. One primary goal of this conference was to expose graduate students and early career mathematicians in the related fields to some recent exciting new developments in this active area of geometry and physics of mirror symmetry and toric geometry. There is already an article by one of the principal speakers, D. McDuff ``The topology of toric symplectic manifolds'' (arXiv:1004.3227) which acknowledges the support of this conference grant and communication with another principal speaker, Lev Borisov: quoted from the paper ``This paper owes much to Lev Borisov who sharpened the original version of the finiteness theorem so that it applies to all symplectic manifolds, not just to those with integral symplectic form. ..............The NSF-supported Great Lakes Geometry Conference in Madison, April 2010, provided an excellent forum in which to discuss the results''. The conference also brought about 40 graduate students and early career mathematicians at the University of Wisconsin from various organizations in US and from abroad who engaged in the discussion with the speakers and with other participants and encouraged interaction between the universities in the Midwestern region and beyond, and helped graduate students and post-docs to work in these exciting areas. And many graduate students from University of Wisconsin helped the PI's with various logistics from the registration to various social activities during the conference. This kind of activities will enhance their organizational skills which will be beneficial to their career development in the near future.
