TY - THES T1 - Noncommutative geometry and quantum group symmetries Y1 - 2007 A1 - Francesco D'Andrea KW - Noncommutative geometry AB - It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world... PB - SISSA UR - http://hdl.handle.net/1963/5269 U1 - 5093 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER -