Number | Title | ECTS | Hours | Lecturers |
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**401-4531-69L** | **Four-Manifolds** | 4 credits | 2V | G. Smirnov |

Abstract | Making use of theoretical physics methods, Witten came up with a novel approach to four-dimensional smooth structures, which made the constructing of exotic 4-manifolds somewhat routine. Today, Seiberg-Witten theory has become a classical topic in mathematics, which has a variety of applications to complex and symplectic geometry. We will go through some of these applications. |

Objective | This introductory course has but one goal, namely to familiarize the students with the basics in the Seiberg-Witten theory. |

Content | The course will begin with an introduction to Freedman’s classification theorem for simply-connected topological 4-manifolds. We then will move to the Seiberg-Witten equations and prove the Donaldson theorem of positive-definite intersection forms. Time permitting we may discuss some applications of SW-theory to real symplectic 4-manifolds. |

Prerequisites / Notice | Some knowledge of homology, homotopy, vector bundles, moduli spaces of something, elliptic operators would be an advantage. |