##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Adrián González Casanova

## The Seed-Bank Random Graph

##### Abstract:

Imagine a population evolving over time, with genetic information being passed down from generation to generation, while evolution shapes it. The inherently random nature of this process makes it an ideal subject to be studied using stochastic processes, particularly Markov processes. Now, imagine if the system had memory, meaning genetic information could be inherited from many generations in the past. In such cases, we refer to a "seed bank."

Seed banks can break the Markovian nature of the process. In this presentation, we will explain how to overcome this difficulty. Furthermore, we will describe the connections between seed bank models, stochastic delay differential equations and the fractional Brownian motion.

### June 1, 2023

### 11:00 AM

APM 6311 with live streaming via Zoom.

Contact poagarwal@ucsd.edu for Zoom info

Research Areas

Probability Theory****************************