##### Department of Mathematics,

University of California San Diego

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### Food for Thought

## Johnny Jingze Li

#### UCSD

## Mathematical Theory for Emergent Effects

##### Abstract:

Emergent effects are commonly understood as novel properties, patterns, or behaviors of systems that are not present in their components, sometimes expressed as “the whole is more than the sum of its parts”. I will discuss a framework that gives a measure of emergent effect as the “loss of exactness” computed from local structures, through category theory, homological algebra and quiver representations, and show that the derived functor that encodes emergent effects is related to information loss. I will also discuss potential connections to neural networks. I can also talk about other maths that could be used for quantifying emergence if you are not that into homological algebra.

### February 16, 2024

### 1:00 PM

APM 2402

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