Lopata Hall, Room 101
Nonlinear Optimization, Dimension Reduction, Representation Theory, Reproducibility
Reducing the number of variables in optimization problems is one of the key approaches to reducing the problem to a manageable size, and often brings up Important extra insights into the problem at hand. There are settings where one can remove exponentially many variables. This is instrumental for packing problems, e.g. such that arise in error-correcting codes and other similar settings such as crossing numbers of networks and graphs.
We review a number of our results in this area, both theoretical and implemented in software, some of them relying on group representation theory. Time allowing, we will touch upon questions of reliability and reproducibility of computer-aided theoretical results.
Dmitrii Pasechnik is a Senior Research Fellow in the Department of Computer Science, University of Oxford, and Stipendiary Lecturer and Senior Research Fellow in Pure Mathematics at Pembroke College, Oxford. He received his Diploma in computer science from Moscow National University of Science and Technology in 1989, and his PhD in Mathematics (with Distinction), from the University of Western Australia in 1996. His research interests include Computer Algebra, Scientific Computation, Computational Complexity, Optimization (nonlinear and linear) and its applications, Moment Problems, Algebra, Algebraic Geometry, Combinatorics, Graph Theory, Group Theory (including computational).
Organizer / Host: Roch Guerin