Thesis supervisor: Tibor Jordán
Location of studies (in Hungarian): ELTE TTK Matematikai Intézet Abbreviation of location of studies: ELTE
Description of the research topic:
Rigidity and flexibility of structures is an exciting research area in the intersection of geometry, algebra, and combinatorics. Mathematicians have been interested in the rigidity of frameworks since Euler's conjecture from 1776, which stated that 3-dimensional polyhedra are rigid. The conjecture was verified for convex polyhedra by Cauchy in 1813 and for generic polyhedra by Gluck in 1975. Connelly constructed a counterexample to Euler's original conjecture in 1982. Interest and developments in rigidity have increased rapidly since the 1970's, motivated initially by the combinatorial characterization of rigid two-dimensional generic bar-and-joint frameworks by Laman in 1970, and also by applications in many areas of science, engineering and design.
Combinatorial rigidity refers to the part of rigidity theory which is concerned with those results and problems where the underlying combinatorial structure of the frameworks plays a key role. Maxwell pointed out, already in the 19th century, that one can deduce necessary conditions for the rigidity of a bar-and-joint framework by using properties of its underlying graph. Furthermore, the applications have encouraged mathematicians not only to develop theoretical results but also fast algorithms, e.g. for determining whether a given framework is rigid. These types of problems also made the combinatorial aspects (graph algorithms, combinatorial optimization) even more central.
Results of this field are often useful in other areas of discrete geometry as well.
The goal is to contribute to rigidity theory and its applications by new results in combinatorial rigidity.
Required language skills: English (at least B2 level) Further requirements: Familiarity with the basic concepts and methods of discrete mathematics (graph theory and/or matroid theory), linear algebra,and geometry.
Deadline for application: 2017-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
Login
