Cahit Arf Lecture 2016 by Andre Neves

Andre Neves

Imperial College
http://wwwf.imperial.ac.uk/~aneves/

Min-max Methods in Geometry

Date:  (To Be Announced)
at xx:xx
Place:

Cahit Arf Auditorium
Department of Mathematics
Middle East Technical University
Ankara, Turkey

Supported by

Abstract

Min-max methods were first introduced in Geometry by Birkhoff in 1920 and the theory was later expanded by Almgren in the 60's and Pitts in the 80's. Recently it has been used by Fernando Marques and myself to prove the Willmore conjecture, the Freedman-He-Wang conjecture, and a old conjecture of Yau in the positive Ricci curvature setting. I will survey these results, talk about new developments, and mention some new directions.

Cahit Arf Lecture 2015 by Vladimir Voevodsky

Vladimir Voevodsky

Institute of Advanced Study
http://www.math.ias.edu/~vladimir/Site3/home.html

Univalent Foundations of Mathematics

Date: April 21, 2015
at 15:40
Place:

Cahit Arf Auditorium
Department of Mathematics
Middle East Technical University
Ankara, Turkey

Supported by

Abstract

Today's mathematics is using foundations which have been developed in the late 19th - early 20th century. Since these foundations had been completed mathematics has grown from a field advanced by a few outstanding minds to a large enterprise involving tens of thousands of mathematicians. On this new scale of existence it is becoming impossible for mathematics to rely entirely on the old peer-review model of ensuring the correctness of the results. Univalent Foundations are new foundations of mathematics invented with the intention of being usable for the development of computer proof assistants that will facilitate the crafting and verification of complex mathematical constructions.

Cahit Arf Lecture 2012 by David E. Nadler

Arf Lectures 2012

David E. Nadler

Northwestern University,
University of California, Berkeley

Traces and loops

Date: November 08, 2012
at 15:40
Place:

Cahit Arf Auditorium
Department of Mathematics
Middle East Technical University
Ankara, Turkey

Supported by

Abstract

This talk will focus on the interplay between two basic notions originating in algebra and topology. In algebra, there is the trace of a matrix, important for its equality with the sum of the eigenvalues of the matrix. In topology, there are the loops on a space, which play a central role in the computation of homotopy groups and in the structure theory of spaces. There is a well-developed understanding of the intimate relation between traces and loops coming from non-commutative geometry and mathematical physics. We will explain how modern formulations elucidate fundamental identities in geometry and representation theory.

Cahit Arf Lecture 2010 by John W. Morgan

John W. Morgan

Stony Brook University, Simons Center for Geometry and Physics

The Topology of 3-Dimensional Manifolds

Date: December 9, 2010
at 15:00
Place:

Cahit Arf Auditorium
Department of Mathematics
Middle East Technical University
Ankara, Turkey

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.