C e n t r e  d e  r e c h e r c h e s  m a t h é m a t i q u e s

 

Une série de conférence
A series of lectures

PROF. ALEXEI MIASNIKOV

The City College
CUNY

 

"SOLVING EQUATIONS IN WORDS"

This is a series of lectures on equations over free groups and free semigroups. In theoretical computer science this topic is known as the unification problem.
I will discuss recent developments in this area related to algebraic geometry over groups, Tarski's problems, and complexity of the unification problem.

Tous les vendredis, du 2 au 30 mars 2001
13h00 ŕ 15h30
McGill University, Burnside Hall, salle 1234

 

Fridays, March 2 to March 30, 2001
1:00 to 3:30pm
McGill University, Burnside Hall, Room 1234

 

 

LE 2 MARS / MARCH 2

1. Equations over free groups I
1.1 Introduction to equations over free groups
1.2 One-variable equations

2. Equations over free groups II
2.1 Malcev's equation
2.2 Quadratic equations

LE 9 MARS / MARCH 9

3. Equations over free groups III
3.1 Approximations
3.2 Reduction to the free semigroup case

4. Equations over free semigroups I
4.1 Quadratic equations
4.2 Periodic solutions

LE 16 MARS / MARCH 16

5. Equations over free semigroups II
5.1 MakaninŐs algorithm
5.2 Complexity

6. Equations over free groups IV
6.1 Elementary transformations
6.2 Coordinate groups
6.3 Fundamental sequences
6.4 Quadratic part

LE 23 MARS / MARCH 23

7. Equations over free groups V
7.1 Entire transformations
7.2 Complexity

8. Equations over free groups VI
8.1 Periodicity
8.2 Construction of trees

 

LE 30 MARS / MARCH 30

9. Equations over free groups VII
9.1 Description of solution sets
9.2 Complexity

10. Equations over free groups VIII
10.1 Elements of algebraic geometry
10.2 Irreducible components
10.3 Dimension

 

Pour de plus amples informations: ACTIVITES@CRM.UMONTREAL.CA