John von Neumann Gastprofessur
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Aktuelle Preisträger/innen |
Frühere Preisträger/innen |
Kontakt |
Aktuelle Preisträger/innen
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Prof. Dr. Sergii Koliada, Academy of Sciences, Kiev John von Neumann Vorlesung: Topological dynamics: minimality, entropy and chaos Weitere Informationen Abstrakt zur VorlesungClose Abstrakt der Vorlesung1. Topological transitivity and minimality: Lecture 1 - Topologically transitive maps; Lecture 2 - Minimal maps and minimal spaces; Lecture 3 - Minimal sets on manifolds; 2. Li-Yorke sensitivity and other concepts of chaos: Lecture 4 - On chaotic interval maps; Lecture 5 - Topological chaos and Li-Yorke chaos; Lecture 6 - Li-Yorke sensitivity and weakly mixing maps; Lecture 7 - On Lyapunov numbers; 3. Topological entropy: Lecture 8 - Topological entropy of (nonautonomous) dynamical systems; Lecture 9 - Topological entropy of (nonautonomous) piecewise-monotone dynamical systems on the interval and applications; Lecture 10 - Group homeomorphisms and topological entropy of their elements; 4. Functional envelope of a dynamical system: Lecture 11 - Introduction and topological transitivity; Lecture 12 - Topological entropy of a functional envelope. weitere Informationen |
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Prof. Dr. Jesus De Loera, University of California at Davis, USA John von Neumann Vorlesung: Algebraic and Geometric Techniques of Optimization Weitere Informationen Abstrakt zur VorlesungClose Abstrakt der VorlesungOptimization is a vibrant growing area of Applied Mathematics. Its many successful applications depend on efficient algorithms and this has pushed the development of theory and software. In recent years there has been a resurgence of interest to use 'non-standard' techniques to estimate the complexity of computation and to guide algorithm design. New interactions with fields like algebraic geometry, representation theory, number theory, combinatorial topology, algebraic combinatorics, and convex analysis have contributed non-trivially to the foundations of computational optimization. This course will be an introduction to the new techniques used in Optimization that have foundation in algebra (number theory, commutative algebra, real algebraic geometry, representation theory) and geometry (convex and differential geometry, combinatorial topology, algebraic topology, etc). weitere Informationen |
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Prof. Dr. Marc Noy, Universitat Barcelona John von Neumann Vorlesung: Advanced Topics in Graph Theory weitere Informationen Abstrakt zur VorlesungClose Abstrakt der Vorlesung1. Matchings and coverings. Matchings in bipartite graphs: Hall's theorem. Stable matchings. Matchings in general graphs: Tutte's theorem. Vertex and edge coverings. 2. Connectivity. Structure of 2-connected and 3-connected graphs. Menger's theorem and applications. 3. Planar graphs. Connectivity of planar graphs. Kuratowski's theorem. Duality. Graphs on surfaces. 4. Colourings. The greedy algorithm and Brook's theorem. Edge colouring. List coloring of planar graphs and bipartite graphs. 5. Graph minors. Excluded minors. Planar and series-parallel graphs. Wagner's theorems: excluding K5 or K3,3. 6. Tree-width. Tree-decompositions and partial k-trees. Lower bounds. The excluded grid theorem. Erdös-Pósa property. Complexity issues: Courcelle's theorem. 7. The graph minor theorem. Well quasi-orderings. Kruskal's theorem. Bounded tree-width. Obstructions for surfaces. The structure theorem and the graph minors theorem. Algorithmic consequences. weitere Informationen |
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Prof. Dr. Peter Song, University of Michigan, Ann Arbor, USA John von Neumann Vorlesung: Regularized regression models for high-dimensional data weitere Informationen Abstrakt zur VorlesungClose Abstrakt der VorlesungThis course is intended to provide a systematic introduction to a state- of-the-art toolbox for the regression analysis of high-dimensional data. It begins with the conventional ideas for low dimensional data, including penalized statistical procedures (e.g. ridge regression, splines smoothing and mixed-effects models), shrinkage estimation (e.g. Steins estimation and empirical Bayes), and variable selection criteria (e.g. Akaike information criterion (AIC) and Bayesian information criterion (BIC)). Then the course evolves to several important topics of regression models for high-dimensional data. Numeric implementation and illustration are emphasized throughout the lectures and R software will be extensively used in the course. Topics include: 1. Introduction to penalized statistical procedure and shrinkage estimation 2. Quadratic optimization 3. Model selection based on L0 penalty, AIC, BIC and extended BIC (EBIC) 4. Regression with L2 penalty: Ridge regression, splines smoothing, mixed-effects model 5. Shrinkage estimation: Steins method, and empirical Bayes 6. Regularized regression model with L1 penalty: LASSO, SCAD and others penalties 7. Extensions: Bridge regression, Elastic Net penalty, group LASSO 8. High-dimensional classification: HTC 9. Regularized regression analysis of longitudinal data: SOFARE and other methods This course will be based on my personal lecture notes with supplementary articles and R software packages. weitere Informationen |
Frühere Preisträger/innen
| Wintersemester | Sommersemester |
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| 2012 | |
| Prof. Dr. Ansgar Jüngel, TU Wien | Prof. Dr. Zalman Balanov, University of Texas |
| Prof. Dr. Serguei Popov, University of Campinas, Brasilien | Prof. Dr. Wieslaw Krawcewicz, University of Texas, Dallas |
| Prof. Dr. Wim Schoutens, Universität Leuven, Belgien | Prof. Dr. Sanjoy Mitter, MIT |
| Prof. Dr. Marina Vachkovskaia, University of Campinas, Brasilien | Prof. Dr. Reinhold Schneider, TU Berlin |
| 2011 | |
| Prof. Dr. Harry Joe, University of British Columbia | |
| Prof. Dr. H. N. Mhaskar, California State University, USA | |
| Alle bisherigen John von Neumann Gastprofessuren | |
Kontakt
Wissenschaftliche Leitung: Prof. Dr. Massimo Fornasier
Administration: Lydia Weber
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