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Friday, April 15, 2016

1:10 PM - 2:10 PM (ET)

Exley 121

Event Type

Seminar/Colloquium

Contact

Han Li

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=68639

TALK #1: What is an arithmetic group?

Wednesday 4/13 Exley 121 4:15pm-5:15pm

ABSTRACT: We will discuss a few basic properties of "arithmetic groups,'' which are certain groups of matrices with integer entries. By definition, the subject combines algebra (group theory and matrices) with number theory (the integers), but it also has connections with other areas, including the theory of periodic tilings.

The three talks in this series are almost entirely independent of each other, so it will be perfectly feasible to attend any subset.

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TALK #2: Some arithmetic groups that cannot act on the line

Thursday 4/14 Exley 121 4:15pm-5:15pm

ABSTRACT: It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups also cannot act on the line. This problem remains open, but it can be solved in cases where every element of the group is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed.

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TALK #3: What is an amenable group?

Friday 4/15 Exley 121 1:10pm-2:10pm

ABSTRACT: Amenability is a fundamental notion in group theory, as evidenced by the fact that it can be defined in more than a dozen different ways. A few of these different definitions will be discussed, and we will see how amenability arises in the study of arithmetic groups.

To learn more about arithmetic groups (and the role played by amenable groups), download a free copy of the speaker's book from http://arxiv.org/src/math/0106063/anc/