## MSRI-UP 2007 research topic: Computational Science and Mathematics.

**Research leader/advisor: Dr. Juan Meza, Lawrence Berkeley National Lab**

**Prerequisites:** Participating students should have already taken the Calculus sequence and a course in Linear Algebra. A course in numerical analysis would be helpful. For maximum benefit, it would be useful if the students have taken a course in physics, chemistry or biology.

**Overview of the summer program:**

The MSRI-UP summer program is designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.

During the summer, each of the 12 students participants will

- participate in the mathematics research program under the direction of Dr. Meza
- complete a research project done in collaboration with other MSRI-UP students
- give a presentation and write a technical report on his/her research project
- attend a series of colloquium talks given by leading researches in their field
- attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences; and
- learn techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships

After the summer, each student will:

- have an opportunity to to attend a national mathematics or science conference where students will present their research.
- be part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies.
- be contacted regarding future research opportunities

**Topic description:**

Computational science is now widely considered to be the third pillar of science alongside experiments and theory. The purpose of this research program is to give students a brief introduction to the most widely used mathematical techniques for solving some of the most challenging scientific problems today. We will draw from current problems being worked on at Lawrence Berkeley National Laboratory including the search for dark energy, climate modeling, nanoscience, and biology. The program will describe the mathematical underpinnings of the scientific applications and discuss the necessary mathematical algorithms needed to solve the problems. For each topic, the lectures will be structured so that a domain scientist from LBNL will discuss the problem and outline the main scientific questions. This will be followed by a set of lectures that describe how to formulate the problem mathematically and what numerical algorithms are needed to solve the problem. We will then address open areas where further research is needed to be able to address the future needs of the scientists.

Possible research projects that students may be involved in are:

- nonlinear eigenvalue algorithms for material sciences
- optimization methods for nanoscience simulations
- machine learning algorithms for feature detection in supernova searches and hurricane
- studies of climate change
- combinatorial algorithms for detecting vulnerabilities in power grid networks
- partial differential equations for combustion and supernova simulations
- fast algorithms for data mining in large scientific data sets

The projects will use the existing computational facilities at MSRI and Berkeley Lab . The students will also have access to the National Energy Research Scientific Computing (NERSC) Center, the flagship scientific computing facility for the Office of Science in DOE.

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