2nd degree (Master)
Coordinator Office Hours:
Prof Jake Solomon
Mirror Symmetry is a correspondence between complex geometry on one manifold and symplectic geometry on another manifold. This correspondence provides a heuristic for formulating the solution of problems previously considered intractable. Mirror symmetry has been proved in many examples by calculating both sides independently. It remains to provide a mathematically rigorous explanation of why the phenomenon of mirror symmetry exists. This seminar will discuss recent work that sheds light on this question.
Learning outcomes - On successful completion of this module, students should be able to:
Students should become acquainted with current work on mirror symmetry.
Teaching arrangement and method of instruction:
See course description and additional reading material.
Additional Reading Material:
Mohammed Abouzaid, "Homological mirror symmetry without corrections"
Andrei Caldararu, Junwu Tu, "Computing a categorical Gromov-Witten invariant"
Kevin Costello, "The Gromov-Witten potential associated to a TCFT"
Background on Mirror Symmetry:
Maxim Kontsevich, "Homological Algebra of Mirror Symmetry"
Andrew Strominger, Shing-Tung Yau, Eric Zaslow, "Mirror Symmetry is T-Duality"
Background on the Fukaya Category:
Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, "Lagrangian Intersection Floer Theory: Anomaly and Obstruction"
Paul Seidel, "Fukaya Categories and Picard-Lefschetz Theory"
End of year written/oral examination 0 %
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Participation in Tutorials 0 %
Project work 0 %
Assignments 100 %
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Research project 0 %
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