Copyright 201x | Duplication of this product and its content in print or digital form for the purpose

of sharing with others is prohibited without permission from Society for Advancement of Hispanics/Chicanos and Native Americans in Science (SACNAS).

## ap_078 UNIVERSAL DEFORMATION RINGS AND SEMIDIHEDRAL GROUPS

- Roberto Soto ;

Room 505

UNIVERSAL DEFORMATION RINGS AND SEMIDIHEDRAL GROUPS

__Roberto Soto__, Frauke Bleher.

The *University of Iowa, Iowa City, IA*.

To gain a better understanding of a given mathematical object, such as a representation of a group, it is often useful to study the behavior of this object under small perturbations. The theory of such perturbations, also called deformations, is useful in both pure and applied mathematics, and it has led to the solution of many long-standing problems. One particular such problem in pure mathematics is given, for example, by Fermat's last theorem, which was proved (after over 300 years) by Wiles and Taylor using universal deformation rings of group representations. Our goal is to study universal deformation rings of representations of semidihedral groups. A semidihedral group is a non-abelian group whose order is a power of 2. More precisely, for every power of 2 that is at least 16, there are exactly 4 isomorphism classes of non-abelian groups whose order is that power. The semidihedral groups make up one of these classes. We will give a description of all representations of a given semidihedral group that are guaranteed to each have a universal deformation ring. This description follows from the work of Carlson and Thevenaz on endo-trivial representations. We will then discuss how we can determine the universal deformation rings of these representations. Our methods include the use of character theory and decomposition numbers.

### 2014 SACNAS AbstractsExit

### Search

### More Information

### Thanks to Student Presentations Sponsors

- American Society for Biochemistry and Molecular Biology
- American Chemical Society
- Biophysical Society
- Botanical Society of America
- Foundation of Earth Science
- Genetics Society of America
- Maryland Sea Grant
- NOAA Fisheries Service
- St. Jude Children's Resarch Hospital
- Society for Industrial and Applied Mathematics
- Society of Actuaries
- The University of Kansas- Department of Geology
- University of the Incarnate Word Rosenberg School of Optometry
- USDA- Agricultural Research Service