Charles Epstein - The Kimura Diffusion Equation in Population Genetics, Theory and Numerics
Recorded 24 February 2026. Charles Epstein of the University of Pennsylvania presents "The Kimura Diffusion Equation in Population Genetics, Theory and Numerics" at IPAM's Mathematics of Cancer: Open Mathematical Problems Workshop.Abstract: A standard forward model in population genetics is the Wright-Fisher model, which assumes random mating in a constant population. It models genetic drift, selection and mutation. An important infinite population limit is the Kimura diffusion equation. For a single gene with one 2 alleles the diffusion takes place on the unit interval, and with N alleles in an N-1 simplex. The 1-dimensional case is also important in the study of the allele frequency spectrum. The Kimura operator is degenerate at the boundary of the simplex, so its analysis falls outside of the standard elliptic/parabolic theory. I will discuss some of the analytic properties of the diffusion defined by this operator, joint with Rafe Mazzeo, and recent numerical work in the 1-dimensional case, joint with Jon Wilkening, which produces highly accurate solutions, even in very challenging situations.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/mathematics-of-cancer-open-mathematical-problems/ Receive SMS online on sms24.me
TubeReader video aggregator is a website that collects and organizes online videos from the YouTube source. Video aggregation is done for different purposes, and TubeReader take different approaches to achieve their purpose.
Our try to collect videos of high quality or interest for visitors to view; the collection may be made by editors or may be based on community votes.
Another method is to base the collection on those videos most viewed, either at the aggregator site or at various popular video hosting sites.
TubeReader site exists to allow users to collect their own sets of videos, for personal use as well as for browsing and viewing by others; TubeReader can develop online communities around video sharing.
Our site allow users to create a personalized video playlist, for personal use as well as for browsing and viewing by others.
@YouTubeReaderBot allows you to subscribe to Youtube channels.
By using @YouTubeReaderBot Bot you agree with YouTube Terms of Service.
Use the @YouTubeReaderBot telegram bot to be the first to be notified when new videos are released on your favorite channels.
Look for new videos or channels and share them with your friends.
You can start using our bot from this video, subscribe now to Charles Epstein - The Kimura Diffusion Equation in Population Genetics, Theory and Numerics
What is YouTube?
YouTube is a free video sharing website that makes it easy to watch online videos. You can even create and upload your own videos to share with others. Originally created in 2005, YouTube is now one of the most popular sites on the Web, with visitors watching around 6 billion hours of video every month.
![BriAnna Weldon vs. Julia Pekowitz - Draw W3 - USA Curling National Championships [A]](https://img.youtube.com/vi/ckdcz0C3tfs/maxresdefault.jpg)
![Elizabeth Cousins vs. Christine McMakin - Draw W3 - USA Curling National Championships [D]](https://img.youtube.com/vi/nsm1hpBCkqw/maxresdefault.jpg)
