Universität zu Köln

Fischer, Greta (2021). Algorithmic Symplectic Packing. PhD thesis, Universität zu Köln.

Preview

PDF Thesis.pdf - Submitted Version Download (712kB) | Preview

Abstract

In this thesis we explore a symplectic packing problem where the targets and domains are $2n$-dimensional symplectic manifolds. We work in the context where the manifolds have first homology group equal to $\Z^n$ and we require the embeddings to induce isomorphisms between first homology groups. In this case, the problem can be related to a combinatorial optimization problem, namely packing certain allowable simplices into a given standard simplex. We design a computational approach to determine the corresponding $k$-simplex packing widths for up to $k = 13$ simplices in dimension four and $k = 8$ simplices in dimension six.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Fischer, Greta greta.fischer90@gmail.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-456546
Date:	2021
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language symplectic packings English symplectic capacities English combinatorial optimization English mixed integer linear programming English semidefinite programming English
Date of oral exam:	12 April 2021
Referee:	Name Academic Title Jünger, Michael Prof. Dr. Geiges, Hansjörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/45654