##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Lisa Carbone

#### UCSD Visitor from Rutgers University

## 2x2 Matrix groups and trees

##### Abstract:

We explore the group of 2x2 determinant 1 matrices with coefficients inthe ring of integers Z as well as an analog obtained by replacing Z by thering of polynomials F[t] where F is a finite field. Decomposition theoremsfor these groups will be obtained using the actions of the groups ontrees, which are connected graphs having no cycles, such as that of degree3 a part of which is pictured above.REFRESHMENTS WILL BE SERVED!

Host: Audrey Terras

### December 11, 2002

### 11:00 AM

### AP&M 2402

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