Thu, 09/24/2015 - 4:35pm
Lecture 1  "Group representations, their applications and arithmetic" Monday, April 15, 2002  4:00 p.m. - 5:00 p.m.  Physics Building, Room 202 (Refreshments will be served before the talk, at 3:30 p.m.) Representations of symmetric groups are a basic tool in physics and chemistry.  But, in addition, representations of finite groups come up in many other places in science and examples will be given, leading to the "arithmetic" of representations…
Thu, 09/24/2015 - 4:29pm
Monday, March 31, 2003 4:00 p.m. Physics Bldg., Room 202 Scientific publication: a mathematician's viewpoint Abstract: Digital computers have brought enormous changes in the way mathematicians work. One of them relates to an issue which sounds trivial, even though it is not: the art of mathematical typesetting died just as budget problems forced universities to cut back secretarial support. Mathematicians had to learn how to type their own…
Thu, 09/24/2015 - 4:25pm
Monday, April 12, 2004 4:00p.m., Physics Bldg., Room 202 Knots and polynomials Abstract: We will describe certain invariants of knots in three dimensional space and give an impressionistic view of how they relate to physics, algebra and analysis. The notion of subfactor will be introduced. Tuesday, April 13, 2004 4:00p.m., Boyd Graduate Studies, Room 328 The analytic and algebraic flavours of subfactors Abstract: Subfactors are algebras of…
Thu, 09/24/2015 - 4:20pm
Monday, May 2, 2005 4:00p.m., Physics Bldg., Room 202 Basic Twistor Geometry; Physical Motivations Twistor theory is motivated by the idea that the union between space-time structure and quantum-mechanical principles may well involve non-standard quantization procedures. Two guiding principles underlying the twistor approach are holomorphicity (complex analyticity) and non-locality, these seeming to be features that an appropriate "quantized…
Thu, 09/24/2015 - 3:39pm
3 lectures on human & machine learning March 22, 2006 - 3:30pm Student Learning Center 101Title of talk: Learning & intelligence(Lecture for general audience) March 23, 2006 - 3:30pm Student Learning Center 150Title of talk: Fast algorithms for learning March 24, 2006 - 3:30pm Student Learning Center 150 Title of talk: The competing roles of statistics & approximation     Professor Smale has made significant contributions in the…
Thu, 09/24/2015 - 3:28pm
Wednesday, April 11, 2007 3:30 p.m. Physics Bldg., Room 202 Title of talk: Origami, Linkages, and Polyhedra: Folding with Algorithms Abstract: What forms of origami can be designed automatically by a computer? What shapes can result by folding a piece of paper flat and making one complete straight cut? What 3D surfaces can be cut open and unfolded into a flat piece of paper without overlap? When can a robot arm or protein be untangled or folded…
Thu, 09/24/2015 - 3:18pm
Wednesday, March 26, 2008 4:00pm, Physics Bldg., Room 202 Title of talk: Solved and unsolved problems in number theory Abstract: I will survey a few of my favorite problems in number theory, such as Fermat's last theorem (solved) and the rectangular box problem (unsolved).   Thursday, March 27, 2008 3:30pm, Boyd Graduate Studies Bldg., Room 328 Title of talk: Hilbert's tenth problem Abstract: Hilbert dreamed that someday we would have a general…
Thu, 09/24/2015 - 3:08pm
Wednesday, April 15, 20093:30pm, Miller Learning Center, Room 102 Title of talk: Mathematics and the Diversity of Cultures Mathematics has played a vital role in every culture. Looking at the three cultures -- China, India and the West -- one can, to some extent “replay” the history of math from three different starting points. Sometimes one finds that it developed with strong parallels but sometimes with deep differences. The development of…
Thu, 09/24/2015 - 2:59pm
Monday, April 5, 20103:30pm, Room 102Miller Learning Center Title of talk: Curve shortening flow and Mean Curvature flow Abstract: Mean Curvature Flow is the oldest of the geometric flows (Ricci flow being another example of a geometric flow). originates in material science where it has been studied at least since the 1940s. is an example of an evolution equation where a surface (or hyper-surface) moves in the direction where the area locally…
Thu, 09/24/2015 - 2:42pm
From Schubert calculus to equivariant cohomology The aim of this series of lectures is to sketch how the enumerative geometry of the 19th century has grown into the thriving field of equivariant cohomology in the 20th and 21st centuries.    We will begin by sketching the history of the subject, starting from Steiner’s question (posed in 1848): how many conics are tangent to 5 given plane conics?  Answering such questions became a thriving…