# Mathematics Departmental News for 2007

December 31, 2007

## Harvey Mudd College Well-Represented at World’s Largest Fluid Dynamics Conference (2007/11/29)

Three Harvey Mudd undergraduates (Chris Fox ’09, Parousia Rockstroh ’08, and Stephen Rosenthal ’09) and two faculty members (Profs. Rachel Levy and Andrew Bernoff) presented their research at the American Physical Society’s Division of Fluid Dynamics’ Annual Meeting in Salt Lake City, Utah. The fluid dynamics meeting is the largest of its kind, drawing thousands of engineers, physicists, and mathematicians from all over the world.

The students’ research was conducted this past summer in the Applied Mathematics Department at UCLA, in a program headed by Prof. Andrea Bertozzi, UCLA’s Director of Applied Mathematics, who is an enthusiastic advocate of immersing undergraduates in UCLA’s active research communities. The program is in its third year and is currently funded by an NSF Research Training Grant.

Fox and Rockstroh conducted experiments on particle-laden flow under the supervision of UCLA postdoctoral fellow Dr. Thomas Ward. Rosenthal analyzed shock structures in thin liquid films under the supervision of HMC Prof. Rachel Levy.

The mathematics department was also well represented at the meeting. Professors Andrew Bernoff and Rachel Levy each presented talks as well as alumnus Michael Gratton ’02, now finishing his PhD in Mathematics at Duke University.

## Prof. Su Receives NSF Grant (11/2007)

Professor Francis Su recently received a research grant of $114,468 from the National Science Foundation (NSF) for the support of the project entitled “Combinatorial Fixed-Point Theorems, Polytopes, and Preference Sets”.

The grant lasts for three years beginning August 1, 2007, and pushes the value of grants recently reported by the department past the $1 million mark. Su’s research continues the line of work begun in his prior NSF grant from 2003–2007, in which methods from combinatorics, topology and geometry are used to study problems in mathematical economics and the social sciences; in particular, problems related to voting and fair allocation.

Su also gave an invited plenary talk at 2007 MathFest, the national summer meeting of the MAA, held this year in San Jose, California. His talk was the featured MAA Student Lecture, which is open to all participants, but is aimed at students. Titled “Splitting the Rent: Fairness Problems, Fixed Points, and Fragmented Polytopes”, his talk featured the work of Elisha Peterson ’00.

## Profs. Yong and Borrelli Awarded NSF Grant to Improve the Teaching of Ordinary Differential Equations (ODEs) (11/2007)

Assistant Professor Darryl Yong and Emeritus Professor Robert Borrelli were awarded an NSF grant of $499,792 to support the project entitled Online Resources to Improve the Teaching and Learning of Differential Equations: Encouraging the Wide-Spread Use of Modeling and Computing.

The aim of this project is to improve the teaching and learning of ordinary differential equations (ODEs) by facilitating the development, dissemination and widespread adoption of modeling projects and computer experiments. By encouraging the widespread adoption of innovations in the teaching and learning of ODEs, Yong and Borrelli seek to affect the training of a great number of future scientists, not just mathematicians. Every student at HMC must take the equivalent of a full-semester course in ordinary differential equations, regardless of their major.

## Prof. Levy Helps Italian Police (2007/09)

In September, 2007, Prof. Rachel Levy was contacted by the Senior Chief Director of Forensic Chemistry from the Italian state police to help solve a case of attempted arson. The police wanted to estimate the volume of gasoline that was spilled at the scene of the crime based on the surface area of a stain on the asphalt. The Italian detective contacted Prof. Levy because her work focuses on the spreading behavior of thin films of liquid.

Prof. Levy consulted with the US Environmental Protection Agency which tracks gasoline spills in the US and brought in students from her applied-analysis class to conduct experiments. While the problem is complicated by issues of evaporation, absorption into the concrete and irregular spreading patterns (such as rivulets) due to inclines and rough surfaces, a model assuming a uniform film height provided a feasible approximation. The team determined that the volume of gasoline spilled was approximately five liters and earned hearty thanks from the Italian police.

## Prof. Andrew Bernoff Awarded NSF Grant for Collaborative, Multidisciplinary Research Project (2007/09)

Prof. Andrew Bernoff has been awarded an NSF grant for $405,372 for collaboration with an experimental physics group at Kent State University and with chemical engineers and mathematicians at Case Western Reserve University.

The joint theoretical–experimental–numerical project, entitled “Dynamics of Interfacial Domains”, delves into the basic physical behavior of lipid layers at the micron scale; one classical example being the lipid bilayer that forms the exterior wall of most biological cells. Bernoff’s expertise in fluid mechanics and numerical methods has allowed precise simulations that almost exactly reproduce the experiments at Kent State.

Bernoff and his former thesis student, Jacob Wintersmith ’06 have published two papers in collaboration with the experimental group. Wintersmith spent part of last summer with the group at Kent State helping with the experiements and doing data analysis. This grant will allow several more Mudders to work in the lab at Kent State in the coming years.

## Students, Faculty Celebrate Five Years of Involvement in the Park City Mathematical Institute (2007/08)

What do the mountains of Utah, Statistical Mechanics, and Harvey Mudd College have in common? The answer is the Park City Mathematics Institute, a three-week–long summer school in which undergraduates, graduate students, college professors, and secondary-school teachers all work together to both further their mathematical knowledge and to build bridges between these different mathematical communities.

This year, Profs. Darryl Yong and Andrew Bernoff attended the institute, joined by undergraduates Ben Fogelson ’09, Mutiara Sondjaja ’08, and Andrew Leverentz ’08.

Prof. Bernoff led the “Pizza and Problem Solving” seminars, which were attended by over 200 participants. In these seminars, modeled on HMC’s Putnam Seminar, pizza-fueled participants worked collaboratively to solve mathematical problems.

At one of the seminar meetings, Prof. Bernoff was momentarily shocked when the audience began singing “Happy Birthday”!

Prof. Yong helped facilitate the Secondary School Teacher program as part of LAPDOG (Los Angeles Professional Development & Outreach Group) a group he co-founded and leads.

Our three students attended seminars on topics such as Brownian motion, random walks, and percolation theory. The Mudders found time to break away and enjoy the spectacular Utah scenery: Prof. Bernoff even took a group of students to Arches National Monument.

This is the fifth year in which Harvey Mudd Faculty have taken part of PCMI; past participants include Profs.Lisette dePillis, Danny Goroff, Jon Jacobsen, Francis Su, and Lesley Ward. This year Andrew Bernoff joined the organization’s steering committee, which will insure a continued HMC presence at this unique and prestigious institute.

## Mudd Student Takes First Place at National Problem Solving Competition (2007/08)

Theodore Spaide ’09 took first place in the National Problem Solving Competition, held at MathFest, the summer meeting of the MAA, August 3–5, 2007.

A joint major in computer science and mathematics, Ted was the first student among more than fifty competitors to finish six challenging mathematical problems. Finishing in sixth place was Benjamin Preskill ’09, a double major in math and physics.

This year is the second in which an HMC student finished first in this competition. Eric Malm ’05 won first place in 2004. Another Mudder, Greg Minton ’08 earned second place in 2005.

## UCLA-HMC Summer Research Projects (2007/08)

This summer, five students from Harvey Mudd College conducted summer research in the Applied Mathematics Labs of Prof. Andrea Bertozzi at UCLA. The goal of this program is to immerse students in an active research group combining faculty, graduate students and postdoctoral fellows.

Profs. Andrew Bernoff and Rachel Levy from HMC’s mathematics department supervised the students and were impressed by their motivation, diligence and ability to make genuine contributions to the projects.

Kenn Tevin ’08, a rising junior, worked with a group studying the epidemiology of crime.

Chris Fox ’09, a rising junior, and Parousia Rockstroh ’08, a rising senior, worked in tandem in the fluids lab. They contributed to several projects, including image processing for an experiment involving a slurry flow of small particles suspended in a viscous liquid.

Trevor Ashley ’09, a rising junior, worked on both hardware and software for a project tracking groups of small robots.

Stephen Rosenthal ’09, a rising junior, was mentored by new Mudd faculty member Rachel Levy. He created and analyzed numerical simulations of an experiment in which flows of thin liquid films are affected by heat.

By the end of the summer the allure of city life and scientific discovery had charmed most of the students. As a result, most of the students chose to stay at UCLA beyond the required number of weeks and at the time of this writing they are still working on their projects. This is the third year for the combined UCLA-HMC summer research projects; the work is supported by a National Science Foundation grant aimed at cultivating interest and building experiences that will encourage students to pursue careers in the mathematical sciences.

## Prof. Rachel Levy Lecture’s at Bucknell University (2007/03/22)

Prof. Rachel Levy was a distinguished visiting professor at Bucknell University from April 8–14, 2006, and gave two lectures: a general colloquium on the discovery of undercompressive waves in thin liquid films, and a lecture on gravity-driven thin-liquid films with insoluble surfactant—smooth traveling waves.

## HMC Has Top Ten Finish in 2006 Putnam Competition (03/22/2007)

The results of the nationwide 2006 William Lowell Putnam Mathematical Competition have just been announced, and HMC had a great showing, with a Top 10 finish in the team category (out of 508 schools) and many strong individual performances!

Fifty-two HMC students spent a Saturday in December (12/02/2006) taking this very hard six-hour exam, which requires a unique blend of cleverness and problem-solving skills. Nationwide, 3640 students competed, and this year the *median* score was 0 out of a total of 120 points, so it was an especially difficult exam.

This year’s HMC team of Brian Rice, Greg Minton, and Theodore Spaide earned an Honorable Mention (team category) for finishing tenth place of 508 schools.

The top five teams in the 2006 competition were (in order): Princeton, Harvard, MIT, U. Toronto, and U. Chicago. In the Honorable Mention category with Harvey Mudd College were UBC, Brown, Duke, Stanford, and Washington Univ.

In the individual category, two HMC students made the Top 100 List, four made the Top 200 List, and thirteen made the Top 500 List; a great accomplishment given our school size—only six of the 508 schools who competed could claim more students in the Top 500.

Special honors go to the following participants:

Name | Score (/120) | Rank | Honor |
---|---|---|---|

Brian Rice | 59 | 56 | Honorable Mention |

Theodore Spaide | 50 | 92.5 | Top 100 List |

Jonathan Azose | 40 | 140 | Top 200 List |

Peter McLarnen | 38 | 166 | Top 200 List |

In addition, the following students all made the Top 500 List: Steven Ehrlich, Alex Izsak, Fred Johnson, Kenji Kozai, Greg Minton, Maria Pavlovskaia, George Tucker, Daniel Walton, Jason Winerip.

We are proud of all 61 HMC students who sacrificed their time, talent, and energies to compete in this year’s Putnam competition. Please join us in congratulating all those who participated!