**Adrianna Gillman, Department of Applied Mathematics, University of Colorado Boulder**

*Fast algorithms group: Accurate, efficient and robust techniques for solving partial differential equations*

Partial differential equations are often used to model physical phenomena. Unfortunately, it is impossible to simply write down the solution to most of the equations. Instead we have to approximate the solutions numerically. My work focusing on the development of numerical algorithms that reduce the computational cost to achieve a desired accuracy. This work involves the development of high order approximation techniques and specialized numerical linear algebra. The resulting methods can be hundreds to thousands of times faster than previously state of the art techniques. In this talk, I will give a high level view of my research, introduce you to current and past group members and give you some insight into how I customize Ph.D. research programs to help my students achieve their career goals.

**François Meyer, Department of Applied Mathematics, University of Colorado Boulder**

*The Analysis of Modern Data Set: A Panoramic View*

As the amount and complexity of data increases, the types of data analytics questions to be answered become more and more sophisticated. The talk will present the recent work of APPM graduate students who have leveraged deep insights from several branches of mathematics to design algorithms that can analyze large and complex datasets. We also describe the impact of this research on scientific application areas, such as geoscience, and neuroscience. The emphasis of the talk will be on the critical role played by these graduate students in the design of mathematical abstractions that are necessary to inform algorithm design.