**Speaker: **Paramita Pramanick

**Date: **2nd october,2018

**Time: **9:15pm-10:15pm

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**Abstract:**

The commutator of two operators A and B is defined as the operator AB-BA**.** In this talk we will start by proving a basic theorem about commutator of matrices : a complex matrix has trace zero if and only if it is a commutator. Then we will prove Kleinecke-Shirokov theorem.If time permits we may discuss limit of commutators and distance from a commutator to the identity.

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**Prerequisites:** Basic Linear Algebra and Introduction to Functional Analysis.

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