#### Title of Oral/Poster Presentation

#### Class

Article

#### College

College of Science

#### Department

Mathematics and Statistics Department

#### Faculty Mentor

Andreas Malmendier

#### Presentation Type

Oral Presentation

#### Abstract

A gravitational anomaly is a special type of curvature that is important in string theory. Elliptic curves are very important and ubiquitous in mathematics - for example, it was a special property of some families of elliptic curves that was instrumental in proving the famous Fermat's Last Theorem. In the context of my research, an elliptic curve is a torus defined by a simple polynomial equation. My research shows that every suitably general one parameter family of elliptic curves (called an elliptic fibration with section) has both local and global gravitational anomalies. In my talk, I will explain these anomalies and demonstrate what they represent. Then I will show how to resolve the anomalies. This technique of "resolving anomalies" is fundamental in string theory, and led to a complete revitalization in string theory research.

#### Location

Room 154

#### Start Date

4-10-2019 9:00 AM

#### End Date

4-10-2019 10:15 AM

#### Included in

Gravitational Anomalies & Elliptic Curves

Room 154

A gravitational anomaly is a special type of curvature that is important in string theory. Elliptic curves are very important and ubiquitous in mathematics - for example, it was a special property of some families of elliptic curves that was instrumental in proving the famous Fermat's Last Theorem. In the context of my research, an elliptic curve is a torus defined by a simple polynomial equation. My research shows that every suitably general one parameter family of elliptic curves (called an elliptic fibration with section) has both local and global gravitational anomalies. In my talk, I will explain these anomalies and demonstrate what they represent. Then I will show how to resolve the anomalies. This technique of "resolving anomalies" is fundamental in string theory, and led to a complete revitalization in string theory research.