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Prof. Dr. Jesus De Loera (UC Davis, USA)

John-von-Neumann-Professor SS 2013

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Zentrum Mathematik, M9
Technische Universität München
D-85747 Garching bei München
Office: 02.04.039
Tel.: +49 89 289-16886
Fax: +49 89 289-16859
E-Mail: deloera (at) math.ucdavis.edu
Homepage at UC Davis 
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John-von-Neumann Lecture

"Algebraic and Geometric Techniques for Optimization"

DESCRIPTION:

  • Optimization 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).

  • In these introductory lectures I will present these new approaches to all senior students. Topics to be included are: Convex and linear optimization (topological tools for on the simplex method, differential geometry and curvature for the central paths of interior point methods), Integer programming and Combinatorial optimization (Graver bases, Generating functions, Nullstellensatz for combinatorial problems), Nonlinear Global Optimization (sum of square methods, semidefinite programming, compressed sensing, cone programming and hyperbolic geometry).

Research Unit M9


Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
Germany
phone:+49 89 289-16858
fax:+49 089 289-16859
sekretariat-m9ma.tum.de

Professors

Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics

News

April 2018
Case Studies 2018: Save the date: Case Studies poster presentation on May 25th, 2018, final workshop on July 7th, 2018.