Search result: Catalogue data in Autumn Semester 2019

Mathematics Master Information
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Electives: Pure Mathematics
Selection: Geometry
401-4531-69LFour-ManifoldsW4 credits2VG. Smirnov
AbstractMaking 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.
ObjectiveThis introductory course has but one goal, namely to familiarize the students with the basics in the Seiberg-Witten theory.
ContentThe 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 / NoticeSome knowledge of homology, homotopy, vector bundles, moduli spaces of something, elliptic operators would be an advantage.
401-3057-00LFinite Geometries II
Does not take place this semester.
W4 credits2GN. Hungerbühler
AbstractFinite geometries I, II: Finite geometries combine aspects of geometry, discrete mathematics and the algebra of finite fields. In particular, we will construct models of axioms of incidence and investigate closing theorems. Applications include test design in statistics, block design, and the construction of orthogonal Latin squares.
ObjectiveFinite geometries I, II: Students will be able to construct and analyse models of finite geometries. They are familiar with closing theorems of the axioms of incidence and are able to design statistical tests by using the theory of finite geometries. They are able to construct orthogonal Latin squares and know the basic elements of the theory of block design.
ContentFinite geometries I, II: finite fields, rings of polynomials, finite affine planes, axioms of incidence, Euler's thirty-six officers problem, design of statistical tests, orthogonal Latin squares, transformation of finite planes, closing theorems of Desargues and Pappus-Pascal, hierarchy of closing theorems, finite coordinate planes, division rings, finite projective planes, duality principle, finite Moebius planes, error correcting codes, block design
Literature- Max Jeger, Endliche Geometrien, ETH Skript 1988

- Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983

- Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press

- Dembowski: Finite Geometries.
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