Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems

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The use of concepts borrowed from topology has led to major athances in t, heorctical physics in recent years. hl quailt, uni field theory. the pionvering work \>?. Skyrme and follow ups on classical solut, ions of Yalig AIills Higgs t, heories has lead to the discovery of t, he lion peturbati~e sectors of gauge theory. Topology has also found its way into colidensed matter physics. Clas sification of defects in ordered media bg 11oinotop~ theorg is a well known example (see e.g. Kleman and Toulouse. Les Kouches XXXV, 1980). More recent, ly. topology and condensed matter physics have again met in t, hc realm of the fract, ioiial cluantml Hall effect. Experimental progress in molecular beam epitaxy techniques leading to high mohilit? samples al lowed the disco\, ery of this reniarkablc and now1 phenomelloii. Th~se cle veloprnents lead also to the at, t, rib~~tion of the 1998 Nobel Prize in physics to Laughlin, Storrner and Tsui. The rlotions of fractional charge as well as fractional statistics ran be interpreted by a topological interaction of infinite rauge. So it is natural to find in the Les Houclles series a school devoted to quantum Hall physics. intcrinediate st, atistics and Chem Sirnons theory. This session also included some one dimensional physics topics like t, he Ca, logero Sutkerland model and some Lut, t, inger liquid physics. Polymer physics is also related to topology. 111 this field topological const, rairlts may be described by concept, ^ from knot theory and statist'ical physics. Hence this session also included Brownian motion theory related to knot theory.