# Mathematics Colloquium | Siddharth Mulherkar

## April 6 @ 4:30 pm - 5:30 pm

- This event has passed.

### Event Details

__Speaker:__**Siddharth Mulherkar**

ASP, Department of Mathematics, Ashoka University

**Title:**

*Operator Monotone Functions and Applications***:**

__YouTube__

*https://youtu.be/*O1OdQaup3W8

**For any two Hermitian matrices $A,B$, we shall say that $A \leq B$ if $B-A$ is positive semi-definite. Note that $\leq$ is a partial order on the space of positive definite matrices. For any interval I \subseteq \R we say that $f:I \rightarrow \R$ is \matrix monotone of order $n$ if for all $n \times n$ Hermitian matrices $A,B$ we have $f(A) \geq f(B)$ whenever $A \geq B$ and $\sigma(A) \cup \sigma(B) \subset I$. If $f$ is matrix monotone for all $n$ then we say that $f$ is matrix monotone or operator monotone. We give various characterizations of operator monotone functions and outline some applications to matrix inequalities. This talk will be expository in nature.**

__Abstract:__