Courses / ActivitiesMirror Symmetry from aspects of mathematics and physics (1)
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During the past 20 years, the Mirror symmetry discovered by string theory had been proved to be one of the most fundamental breakthrough in the study of Calabi-Yau manifolds and 3-dimensional algebraic geometry. Some long standing problems are solved with the help of it. However, its full strength has not yet been fully understood. The major reason is that the full correspondence between physics and mathematics requires many new notions to be rigorously developed. The 2000 Clay Lecture Notes by Vafa et al. is a serious attempt toward this goal. The main focus of this program is to go through it from BOTH the mathematical and physical point of view. For this purpose 3 activities are designed. (1) A spring course entitled "Geometry and topological field theory" by Chin-Lung Wang which should cover Chapters 2, 3, 4, namely an introduction to quantum field theory and proofs, in both physics and mathematics, of classical mirror symmetry in genus 0. (2) An accompanied student seminar which should cover more basic material in mathematics including relevant differential geometry and algebraic geometry, e.g. Chapter 1 and assigned homework, and some further readings. (3) A summer school on the more advanced topics in mirror symmetry including Chapter 5, e.g. the higher genus aspects, and some recent developments.
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Chin-Lung Wang
2011-02-23
09:00:00 - 12:00:00
R304 , Astronomy and Mathematics Building
During the past 20 years, the Mirror symmetry discovered by string theory had been proved to be one of the most fundamental breakthrough in the study of Calabi-Yau manifolds and 3-dimensional algebraic geometry. Some long standing problems are solved with the help of it. However, its full strength has not yet been fully understood. The major reason is that the full correspondence between physics and mathematics requires many new notions to be rigorously developed. The 2000 Clay Lecture Notes by Vafa et al. is a serious attempt toward this goal. The main focus of this program is to go through it from BOTH the mathematical and physical point of view. For this purpose 3 activities are designed. (1) A spring course entitled "Geometry and topological field theory" by Chin-Lung Wang which should cover Chapters 2, 3, 4, namely an introduction to quantum field theory and proofs, in both physics and mathematics, of classical mirror symmetry in genus 0. (2) An accompanied student seminar which should cover more basic material in mathematics including relevant differential geometry and algebraic geometry, e.g. Chapter 1 and assigned homework, and some further readings. (3) A summer school on the more advanced topics in mirror symmetry including Chapter 5, e.g. the higher genus aspects, and some recent developments.