##### Department of Mathematics,

University of California San Diego

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### Food for Thought Seminar

## Harish Kannan

#### UCSD

## Discrete Morse Theory

##### Abstract:

In this talk we shall look at an overview of discrete Morse theory in the context of simplicial complexes. Discrete Morse theory, based on the work by R. Forman, provides a framework to study the ``shape'' (i.e. the topology) of a simplicial complex via discrete Morse functions which are real valued functions defined on the simplices of the complex. The critical simplices, which are determined by the respective discrete Morse function, reveal key topological features of the simplicial complex. This is, in essence, a discrete adaptation of Morse theory in differential topology which allows us to study the topology of a manifold by looking at the differentiable functions on the manifold. The talk will cover the basics of discrete Morse theory with multiple examples and will also discuss possible applications in the context of persistent homology.

### November 15, 2019

### 11:00 AM

### AP&M 5402

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