# Baylor Undergraduate Lecture Series in Mathematics

The aim of this lecture series is to bring in mathematicians who are nationally and internationally recognized mathematicians and who have a special penchant for teaching and explaining mathematics. Funds were made available for this lecture series, which began in 2008, by the Baylor administration; special thanks to Dean Lee Nordt and Dean Kenneth Wilkins of the College of Arts and Sciences for their generous support.

## Twelfth Annual Baylor Undergraduate Lecture Series in Mathematics

Speaker: Douglas Arnold

Dr. Douglas Arnold will be the speaker in the twelfth annual Baylor Undergraduate Lecture Series in Mathematics when he visits Baylor University from December 5-6. He is the McKnight Presidential Professor of Mathematics at the University of Minnesota. Professor Arnold was President of the Society for Industrial and Applied Mathematics (SIAM) in 2009 and 2010.

Professor Arnold studied mathematics as an undergraduate at Brown University, gaining his B.A. in 1975. He continued his studies at the University of Chicago, where he received a Ph.D. in 1979. He then moved to work at the University of Maryland, College Park. In 1989, he moved to Penn State University where he occupied a chair until 2002. He became director of the Institute for Mathematics and its Applications (IMA) in Minnesota in 2001.

Professor Arnold's research initially focused on the finite element method for the solution of problems in elasticity. This expanded to take other applications into account, like the collision of black holes. Especially well known is Arnold's development of the finite element exterior calculus, a discrete version of exterior calculus that can be used to analyze the stability of finite element methods. This was the topic of the plenary lecture Arnold gave at the 2002 International Congress of Mathematicians.

Together with a colleague (Jonathan Rogness), Arnold produced a video explaining Möbius transformations which won an honorable mention in a contest sponsored by Science magazine and the National Science Foundation in 2007. The video was watched over a million times at YouTube. Other honors include winning the International Giovanni Sacchi Landriani Prize in 1991, the award of a Guggenheim Fellowship in 2008 and election as a foreign member of the Norwegian Academy of Science and Letters in 2009. In 2012 he became a fellow of the American Mathematical Society. In 2009, he was named a fellow of the Society for Industrial and Applied Mathematics.

Dr. Arnold's lectures and abstracts, with dates and venues, are:

*Thursday, December 5, 2019 at 4:00 pm - BSB D110*

## PUBLIC LECTURE: Computational Mathematics Simulating The World

**Abstract**: In the late 20th century science underwent a revolution as computational science emerged as the third mode of scientific exploration alongside experiment and theory. Computer simulation of physical reality has played an equally transformative role in virtually all areas of technology, affecting many aspects of modern life. We now depend on simulation to design, predict, and optimize natural and engineered systems of all sorts, ranging from mechanical to chemical to electronic, and at scales ranging from atomic to terrestrial to cosmological. Mathematical algorithms have been crucial to these advances, even more so than advances in computer technology. In this talk we will encounter some of the mathematical ideas that have emerged and the ongoing challenges facing computational mathematics in simulating the world.

*Friday, December 6, 2019 at 4:00 pm - MMSci 301*

## DEPARTMENTAL COLLOQUIUM: **Finite Element Exterior Calculus**

**Abstract: **Finite element exterior calculus, or FEEC, is a prime example of a structure-preserving discretization method, in which key mathematical structures of the continuous problem are exactly captured at the discrete level. In the case of FEEC these structures arise from differential complexes and their cohomology, and FEEC applies geometry, topology, and analysis in order to design and analyze stable and accurate numerical methods for the differential equations related to the complexes. We will present an accessible overview of FEEC and some of its applications.