Cahit Arf Lecture 2010
John W. Morgan
Stony Brook University, Simons Center for Geometry and PhysicsThe Topology of 3-Dimensional Manifolds
| Date: | December 9, 2010 at 15:00 |
| Place: |
Cahit Arf Auditorium |
Supported by
Abstract
Poincaré launched the subject of 3-dimensional topology in 1904. At the end of a long treatise on 3-manifolds he asked what became known as the Poincaré Conjecture: Is every simply connected 3-manifold homeomorphic to the 3-sphere. This problem sparked a century of work on manifolds of dimensions 3 and higher, work that made topology one of the most dynamic and exciting areas of mathematics during the 20th century. But in spite of all this work, at the end of the 20th century the Poincaré Conjecture still stood unresolved. Then in 2002 and 2003, Grigory Perelman put a series of 3 preprints on the archive that completely resolved this conjecture and the more general conjecture, due to Thurston, about the structure of all 3-manifolds. His approach was to use work of Richard Hamilton concerning what is called the Ricci flow. This is a parabolic evolution equation for a Riemannian metric on a manifold. In this talk we will review the motivating questions and the Ricci flow. After giving this background we will then sketch Perelman’s method of solution.
Cahit Arf Lecture 2009
Ben Joseph Green
University of Cambridgehttp://www.dpmms.cam.ac.uk/~bjg23/
Patterns of Primes
| Date: | October 12, 2009 at 15:40 |
| Place: |
Cahit Arf Auditorium |
Supported by
Abstract
Cahit Arf Lecture 2008
Günter Harder
Mathematisches Institut der Universitat BonnMax Planck Institute for Mathematics Bonn
Cohomology of Arithmetic Groups and Applications to Arithmetic
| Date: | November 1, 2008 at 15:40 |
| Place: |
Cahit Arf Auditorium |
Supported by
Abstract
This is an exposition of the basic notions and concepts which are needed to build up the cohomology theory of arithmetic groups. We are dealing with objects which have a certain degree of complexity and in this text I give some explanation of the background needed to understand the the definitions and the general structural elements of these objects. A complete discussion can be found on my home page
www.math.uni-bonn.de/people/harder/Manuscripts/buch/ chapters 2 to 6.
See the extended abstract.
Cahit Arf Lecture 2007
Hendrik Lenstra
http://www.math.leidenuniv.nl/~hwl/ Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, The NetherlandsEscher and Droste effect
| Date: | September 25, 2007 at 15:40 |
| Place: |
METU Cultural and Conventional Center |
Supported by
Abstract
In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title "Print Gallery". It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees a paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is nor nearly as well known that it contains a hidden "Droste effect", or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank.
Cahit Arf Lecture 2006
Jean-Pierre Serre
http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Serre.htmlVariation with p of the number of solutions mod p of a family of polynomial equations
| Date: | November 18, 2006 at 15:00 |
| Place: |
Cahit Arf Auditorium |
Supported by