Michael
Farber
Address:
Department
of Mathematical Sciences
University of Durham
Durham
DH1 3LE
UK
Phone: +44-191-3343095
Fax: +44-191-3343051
|
Address:
University of Durham
|
The
main emphasize of my research is on topology and its applications.
TOPOLOGY is often referred to as "rubber sheet
geometry". A few brief
descriptions of what is topology can be found
here (by
Bob Bruner) and here
(by Neil Strickland). More essays about topology
can be found here.
Nowadays
topology is one of the most important areas of mathematics.
Increasingly, it is being applied in many fields of mathematics
(algebra, geometry, dynamics, mathematical physics) and most recently
in other disciplines such as computer science, engineering,
economics.
My own work touches some traditional topological topics (e.g. the Morse theory, the knot theory, the L2- cohomology theory) and also new applications of the methods of algebraic topology in engineering, in the study of robot motion planning algorithms. In particular, I showed how one may predict instabilities in the behavior of a robot knowing the topology (e.g. the cohomology algebra) of the robot's configuration space. In 2003 I organized a conference "Topology and Robotics" which was supported and hosted by the ETH Zurich (Switzerland); an article about this conference was published in "Science". Applications of topology in computer science are part of a newly created field called Computational Topology. The second conference of this type Topology and Robotics 2006 also took place in Zurich in July 2006. Minisymosium on Topological Robotics will be a part of the International Congress on Industrial and Applied Mathematics ICIAM 07.
Recently I also used methods of algebraic topology (the Morse theory) in the study of convex billiards; see my papers in the "Duke Mathematical Journal" and in "Topology" published in 2001 and 2002.
A
nother
line of my current research is topology of closed 1-forms. This field
was initiated by S. P. Novikov in 1981 who created a version of the
Morse theory where instead of functions one deals with closed 1-forms
and their zeros. In my recent work I constructed a new theory which
uses closed 1-forms and homotopy invariants of new kind in dynamics.
This new theory is able to predict existence of homoclinic cycles in
dynamical systems. This material is described in my recent monograph
"Topology
of closed 1-forms". A
conference "Topology
of closed 1-forms" took
place in December 2004.
List
of my recent publications
Durham Junior Topology Seminar
Durham Pure Mathematics Web Page
Lecture Course "Topology and Robotics", Malaga October 29 - 31, 2007
Lecture course “Configuration spaces and robot motion planning algorithms”, Montpellier June 2008
Minisymposium "Applied Algebraic Topology", ECM 2008
Postgraduate Projects in
Topology
A
vague description of projects for postgraduate research in topology
which I am able to offer can be found here.
Conference "Prospects
in Mathematics" January
8 -11, 2009. Conference
photo can be found here.
Funding Organisations etc:
Mathematical Organizations:
Mathematical Information Servers:
Other Mathematical Sites:
General:
