University of Illinois at Urbana-Champaign
Letter from the Department Chair
This spring has ushered in the changes in the world outside that are near and dear to us all; the annual miracle of the greening of the earth can make an optimist of the greatest pessimist. This spring has also brought other changes. After a year and a half of hard work, Professor Daniel Grayson has resigned from his administrative role as chair of our department. We are searching for a new chair of the department. In the meantime, Dean Sarah Mangelsdorf asked me to serve as Interim Chair, a job that I agreed to do knowing how much I wanted to support our truly wonderful department, even though taking up this task would require me to at least temporarily stop the enjoyable work that I had been doing.
Our department is undergoing a metamorphosis. While most of our colleagues who have been teaching and doing research here for years are still around, many of them have retired in order to focus their time on what they really most want to do. At the same time, many new faculty members have joined our ranks in the last ten years. The balance of research interests among our faculty members is shifting. More and more we see interdisciplinary work being the focus. By this I mean both research that is interdisciplinary in linking mathematicians with engineers and scientists to create new paradigms of how the mathematical sciences can be applied, and also interdisciplinary in the creative regrouping of traditional mathematical fields and techniques into new amalgamations that can yield striking progress in answering difficult and important mathematical questions.
At the same time, our undergraduate student ranks have grown with first year student enrollment increases, leading us to teach a greater number of large classes and also to reorganize our curriculum on many fronts. Our Actuarial Science Program has grown to 270 undergraduate students and 25 graduate students now majoring in this specialization. The number of our graduate students is fairly steady, but the breadth of interests and directions of the careers of our graduate students continues to evolve.
It is an old saying that change is inevitable. But I believe that what will emerge in the future as a result is not inevitable. The outcome will depend on us.
Our department is thinking hard about how it can effectively govern itself, using the chair system to its greatest impact and advantage. We are also asking ourselves how we can best evaluate our research and teaching, seeking to determine what the criteria are that can adequately measure faculty potential, given the increasing focus on interdisciplinary research and collaboration in the mathematical sciences. These intertwined themes of governance and evaluation present us with many challenges. However, they cannot be dealt with once and for all. They will require us to respond with constant attention, flexibility, and renewed energy as the decades go by.
We need your help in this process! Take a look at the breadth of our programs. Ask yourself what you can do to support us. For instance, there is a critical need for funding to support research experiences for undergraduate and beginning graduate students. We sorely need fellowship funds to allow our best and brightest graduate students time to focus exclusively on their research work. We particularly need to identify sources of such funding because our NSF VIGRE grant is ending and other fellowship funds, like the GAANN grants, are proving to be hard to obtain. Moreover, our library, both the traditional archive and the ever more important electronic archive, needs your support to keep it being one of the very best mathematical libraries in the world.
The issues facing our department, and also facing our campus more broadly, are not easy ones to handle. But I know that our department will be able to work effectively to make progress in dealing with these questions. So, with this expression of optimism and hope, as spring matures and summer comes, I wish you all good health and prosperity. May the sun shine on your faces and the wind be at your back.
Joseph Rosenblatt
Interim Chair, Department of Mathematics
In this issue:
- Letter from the Department Chair
- News
- Calcul*rt, a celebration of art and mathematics
- Alumni database update
- Local chapter of Pi Mu Epsilon restarts after 17 years
- New student organization: Illinois Mathematics Community Outreach
- Achievements
- Robert Ghrist to lecture at 2006 ICM
- Scott Ahlgren received LAS Dean's Award for Excellence in Undergraduate Teaching
- UIUC Undergraduate Math Contest
- Department Student Awards
- Faculty News and Conferences
- In memoriam
- Articles
- MATRIX, math club activities
- A little mathematical humor...
by Bruce Reznick
Calcul*rt, a celebration of art and mathematics
The "21st Century Gallery" on the lower level of the Krannert Art Museum presents Calcul*rt, a celebration of art and mathematics, which opened on Thursday, March 9, 2006. The opening took place on the CANVAS and in the newly-formed electronic gallery of the museum. George Francis conducted a walk about the real-time interactive computer animations created by his colleagues and students at the UIUC and UIC Mathematics Departments and the NCSA, EVL and ISL: Donna Cox, Dan Sandin, Lou Kauffman, John Sullivan, Stuart Levy, Camille Goudeseune, Ben Schaeffer, Stan Blank, Ray Idaszak, Glenn Chappell, Chris Hartman, Alexei Bourd, Matt Woodruff.
Thursday, May 4, 2006 will be an "Evening of Mathematical Art" at the Krannert Art Museum. Beginning at 7 p.m., the curators and contributors of Calcul*rt will guide, explain and demonstrate items in the show. At 8 p.m. the audience is invited to join show contributors Donna Cox, George Francis, Hank Kaczamarski, Rose Marshack and Rick Powers in a free flowing discussion on the subject: "How can you tell that it's mathematical art?"
The CANVAS, a joint effort between the Integrated Systems Laboratory of the Beckman Institute at the University of Illinois and the Krannert Art Museum, is a large virtual reality research and exhibition laboratory. Visitors don polarizing stereo glasses and enjoy 3D immersive applications that explore the boundaries between Mathematics, Art, Narrative and Sound.
The exhibit, which will close in June 2006, features many different media exploring the boundaries between mathematics and art. Included are a new electronic net-driven art piece inspired by Richard Powers (Prof., English) and developed by Rose Marshack (Art & Design), Nicholas Duchowski (Mathematics), Abby Watt (Art), Erin Miller (Art & Design) and a new electronic installation by Jonas Downey (MFA, Narrative Media). Mathematically-defined sculptures include wood carvings by Brent Collins, holographic images by Donna Cox and Ellen Sandor, wooden sculptures by Richard Valentin (Argonne), 3D sculptures by Stuart Dickson, silicon bronze sculpture by Helaman Ferguson, and computer-generated 3D sculpture by John Sullivan and Ben Grosser.
Help needed for update of alumni database
The Graduate Office database of alumni has close to 1100 entries and goes back to our first Ph.D. graduate in 1903. Our goal is to make this valuable resource as comprehensive and up-to-date as possible. Now you can help! A website has been set up with a convenient form for entering data. We invite all alumni to help us update our records by visiting the site at http://www.math.uiuc.edu/GraduateProgram/alumni_database.html. We welcome all comments or suggestions for improvements. These, as well as any questions you may have, can be sent to aluminfo@math.uiuc.edu.
Local chapter of Pi Mu Epsilon restarts after 17 years
This semester marked the beginning of Illinois's Alpha chapter of Pi Mu Epsilon after a seventeen year hiatus. National past President Robert Smith from Miami University spoke and outlined the rich tradition of the Alpha chapter. Over twenty new members were inducted to continue that tradition, and meetings have begun to set the focus for this new group on campus. A second induction ceremony was held April 10 for those unable to attend the earlier ceremony.
Pi Mu Epsilon offers a great opportunity to be recognized for continued excellence and achievement in mathematics through promoting scholarly activity. With that in mind, one of our goals is to end the state of Illinois's publication drought in the Pi Mu Epsilon Journal. Through Pi Mu Epsilon, we hope to raise the profile of mathematics and the University of Illinois by linking excellent students and rewarding outstanding achievement. See their website for more information at www.math.uiuc.edu/PME or contact PME President Noel DeJarnette at ndejarne@uiuc.edu or Alison Champion in the UIUC Undergraduate Office at abc@math.uiuc.edu.
New student organization: Illinois Mathematics Community Outreach
Last semester an intrepid group of students began a program dubbed the Mathematics Traveling Road Show. Their goal was to bring interesting activities to middle and high school students in order to raise the profile of mathematics and the University of Illinois while also providing useful professional experience for the volunteers. Last semester they taught lessons to a seventh grade class at Edison Middle School, and with the help of toothpicks and gumdrops, they explored platonic solids and relationships such as similarity and scaling factors. Despite the humble beginnings, last semester was considered a success and they have been asked back to Edison as well as being invited to St. Joseph-Ogden Middle School.
Out of this endeavor has sprung the student organization "University of Illinois Mathematics Community Outreach" (UIMathCo). This organization will incorporate the Mathematics Traveling Road Show and new activities as well as other programs like meeting with high school math clubs to talk about the transition to university level mathematics. We believe that these types of opportunities will not only give back to the community, but will also provide excellent opportunities for volunteering and professional development. Our goal is the continued growth of student involvement-not every member must present activities in the classroom. We are always looking for new ways to get University of Illinois students linked with local schools. The more members we have the more new ideas and ways to get involved. For more information about UIMathCo, contact Noel DeJarnette at ndejarne@uiuc.edu.
Ghrist to lecture at 2006 ICM
Ghrist to lecture at 2006 ICM Robert Ghrist has been invited to deliver a section lecture at the 2006 International Congress of Mathematicians (ICM) in Madrid, Spain. Ghrist is an Associate Professor of Mathematics and a Research Associate Professor in the Coordinated Science Laboratory at UIUC. His 1995 Ph.D. in Applied Mathematics from Cornell University was preceded by a 1991 B.S. in Mechanical Engineering from the University of Toledo, Ohio. He has held positions at the Georgia Institute of Technology, the University of Texas, Austin, the Institute for Advanced Study, and Princeton University.
Professor Ghrist's research is in "Topological Methods in Applied Mathematics." The theme of Ghrist's work is that beneath many common systems arising in engineering or computer science applications, there lies a hidden richness of geometric and topological structure, waiting to be discovered and exploited. By elucidating this structure, one sets up a bridge for 'technology transfer' from Core Mathematics to Core Applications.
Examples of this technology transfer in Ghrist's work include:
1. Using the topology of knots and links to classify periodic orbits of differential equations;
2. Using geometric group theory to coordinate reconfigurable systems ranging from metamorphic robots to protein chains;
3. Using symplectic and contact topology to force hydrodynamic instability in inviscid fluid flows;
4. Using Alexandrov geometry to solve pursuit-evasion problems on complicated, non-convex domains;
5. Using algebraic topology to solve global problems in sensor networks without localization.
The work that Ghrist will be speaking about at the ICM is a joint project with R. Vandervorst [VU Amsterdam]. In this project, the authors consider nonlinear partial differential equations which are of "parabolic" type. Such equations model processes as diverse as the diffusion of heat or the propagation of a rumor. In settings where the equations are truly nonlinear, very complex dynamics can ensue, frustrating the analysis.
Ghrist and Vandervorst use an oblique approach. They first translate the dynamical problems to a problem involving "braids"-the topological objects one normally associates with long hair. Topologists have long known that braids form an algebraic structure-a group-and that the algebra interacts with the topological pleating of braids in a deep manner. By leveraging these structures, the authors can squeeze deeper algebraic information out of the differential equations, previous treatments of which amount to counting integers as opposed to counting braid types. This additional algebraic structure dovetails with a very powerful Morse theory to establish an algebraic and topological "hierarchy" of braids which arise in parabolic differential equations. In the end, a sophisticated yet computable "Homotopy Braid Index" encodes this rich structure in a manner useful in applications for detecting when certain solutions exist and with what frequency.
Spatially discretized solutions to PDEs (such as are common in numberical analysis) possess a braid-theoretic duality which mirrors Alexander duality in homology.
Lifting a collection of solutions to a scalar partial differential equation from their graphs to 3-d yields a topological braid.
Ahlgren receives LAS Dean's Award for Excellence in Undergraduate Teaching
Ahlgren receives LAS Teaching Award Scott Ahlgren has been awarded the LAS Dean's Award for Excellence in Undergraduate Teaching. Ahlgren's educational activities span the range of instructional levels, from high school outreach programs through introductory undergraduate courses to advanced undergraduate and graduate courses in his research specialty. He has begun training and mentoring both graduate students and postdoctoral fellows. Finally, he has devoted considerable time and energy toward the goal of bringing mathematics "to the masses" through public lectures.
Ahlgren has appeared on the Incomplete List of Teachers Ranked as Excellent by their Students four times for both graduate and undergraduate courses. Comments from current and former students emphasize Ahlgren's effectiveness in the classroom. Most frequently, students recall his excitement and enthusiasm, his patience and understanding, and his exceptionally clear and concise explanations.
During the past four years Ahlgren has taught four-day short courses in number theory at the University High School in connection with their "Agora Days" program. During the summers of 2003 and 2005 he directed (together with Craig Russell of University High) the "High School Math Days" program. Ahlgren mentions that one of his proudest moments came when a student in this program, who had previously professed a disinterest in mathematics, declared at its conclusion that he now wanted to become a mathematician.
Ahlgren, an Associate Professor, received his Ph.D. from the University of Colorado at Boulder in 1996. He joined the faculty at Illinois in 2001. His research specialty is number theory. He is an expert in the use and application of modular functions, and his research related to this topic has appeared in the top journals in the field.
