#### Presentation Title

A Journey Towards Understanding Extension Theorems on Sobolev Space

#### Presenter Status

Ph. D Mathematics, Assistant Professor of Mathematics

#### Presentation Type

Oral Presentation

B

Chan Shun 108

#### Start Date

18-5-2017 2:45 PM

#### End Date

18-5-2017 3:05 PM

#### Presentation Abstract

In terms of application, no area of mathematics is more widely used than partial differential equations (PDE). Understanding such equations is thus of the utmost importance. One such method for studying PDE is to use various spaces of function solutions, such as Sobolev space. In this talk I address a critical estimate for Sobolev space functions, which is called an extension. This will include the motivation and prerequisites for the Sobolev space of functions as well as brief synopsis of the results from my doctoral research in extension theorems. This talk should be accessible to anyone with a thorough experience in undergraduate mathematics.

#### Biographical Sketch

Christopher "Ryan" Loga teaches as an Assistant Professor of Mathematics at Southwestern Adventist University in Keene, TX. Prior to moving to Texas, he spent his whole life in East Tennessee where he attended Southern Adventist University in Collegedale for his undergraduate studies. This is also where he met his wife Amanda. He also recently concluded his graduate studies at the University of Tennessee in Knoxville where he earned his Ph.D in mathematics. Besides teaching and researching mathematics, Ryan also enjoys writing, playing guitar, and gaming.

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May 18th, 2:45 PM May 18th, 3:05 PM

A Journey Towards Understanding Extension Theorems on Sobolev Space

Chan Shun 108

In terms of application, no area of mathematics is more widely used than partial differential equations (PDE). Understanding such equations is thus of the utmost importance. One such method for studying PDE is to use various spaces of function solutions, such as Sobolev space. In this talk I address a critical estimate for Sobolev space functions, which is called an extension. This will include the motivation and prerequisites for the Sobolev space of functions as well as brief synopsis of the results from my doctoral research in extension theorems. This talk should be accessible to anyone with a thorough experience in undergraduate mathematics.