Algebra Seminar[ Edit ]
Given two permutations A and B which "almost" commute, are they "close" to permutations A' and B' which really commute? This can be seen as a question about a property the equation XY=YX. Studying analogous problems for more general equations (or systems of equations) leads to the notion of "locally testable groups" (aka "stable groups").
We will take the opportunity to say something about "local testability" in general, which is an important subject in computer science. We will then describe some results and methods developed (in a work in progress), together with Alex Lubotzky, to decide whether various groups are locally testable or not.This will bring in some important notions in group theory, such as amenability, Kazhdan's Property (T) and sofic groups.
Type:  Seminar 

Name:  Algebra Seminar 
Title:  Equations in permutations and group theoretic local testability 
Speaker:  Oren Becker 
Place:  Amado 719, Technion 
Abstract:  
Given two permutations A and B which "almost" commute, are they "close" to permutations A' and B' which really commute? This can be seen as a question about a property the equation XY=YX. Studying analogous problems for more general equations (or systems of equations) leads to the notion of "locally testable groups" (aka "stable groups"). We will take the opportunity to say something about "local testability" in general, which is an important subject in computer science. We will then describe some results and methods developed (in a work in progress), together with Alex Lubotzky, to decide whether various groups are locally testable or not.This will bring in some important notions in group theory, such as amenability, Kazhdan's Property (T) and sofic groups. 

SubmittedBy:  Yakov Karasik, yaakov@tx.technion.ac.il 
EventLink:  Event № 455 
The uinvariant of a field is the maximal dimension of a nonsingular anisotropic quadratic form over that field, whose order in the Witt group of the field is finite. By a classical theorem of Elman and Lam, the uinvariant of a linked field of characteristic different from 2 can be either 0,1,2,4 or 8. The analogous question in the case of characteristic 2 remained open for a long time. We will discuss the proof of the equivalent statement in characteristic 2, recently obtained in a joint work by Andrew Dolphin and the speaker.
Type:  Seminar 

Name:  Algebra Seminar 
Title:  Linked Fields of Characteristic 2 and their uInvariant 
Speaker:  Adam Chapman 
Place:  Amado 719, Technion 
Abstract:  
The uinvariant of a field is the maximal dimension of a nonsingular anisotropic quadratic form over that field, whose order in the Witt group of the field is finite. By a classical theorem of Elman and Lam, the uinvariant of a linked field of characteristic different from 2 can be either 0,1,2,4 or 8. The analogous question in the case of characteristic 2 remained open for a long time. We will discuss the proof of the equivalent statement in characteristic 2, recently obtained in a joint work by Andrew Dolphin and the speaker. 

SubmittedBy:  Yakov Karasik, yaakov@tx.technion.ac.il 
EventLink:  Event № 439 
Type:  Seminar 

Name:  Algebra Seminar 
Title:  Galois group of local fields, Lie algebras and ramfications 
Speaker:  Victor Abrashkin 
Place:  Amado 719, Technion 
Files:  Abstract 
SubmittedBy:  Yakov Karasik, yaakov@tx.technion.ac.il 
EventLink:  Event № 440 