##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Marius Junge

#### UIUC

## Graphs and sublaplacians from an operator algebra perspective.

##### Abstract:

Motivated by quantum information theory, we study log-Sobolev inequalities for matrix valued functions on finite graphs and compact Lie groups. Using tools from noncommutative geometry we find a surprising link between graph Laplacians and sublaplacians on the orthogonal group. Simple combinatorial tools, namely the existence of a spanning tree, then allows us to find concrete lower bounds for spectral gaps. Joint work with H. Li and N. LaRacuente.

### January 16, 2020

### 3:00 PM

### AP&M 6402

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