Polymath - (Pol’e math) A person of much or varied learning; one acquainted with various subjects of study.
Message from Department Chairman | The Kakeya Needle Problem by Dylan Retsek | Summer Research Program | Honor Roll | Graduates | Alumni News | Noyce Program | Department Photo | New Faculty | Faculty Publications/Conference Talks | IBL Workshop | Math Club | Putnam Math Competition | Mathematical Contest in Modeling | End-of-Year BBQ/Softball | Annual Awards Banquet | Outstanding Students | Commencement | What's New with You? | Credits
Message from Department Chairman Don Rawlings
Aside from the budgetary woes we currently face, there is positive news to report this year. Foremost, we are extremely pleased to have Dr. Amelie Schinck and Dr. Stan Yoshinobu join the ranks of our Mathematics Education faculty. Within our group of math educators there is a sense of rejuvenation and excitement. You’ll find short biographies of Amelie and Stan below. Beginning with the 2009-2011 catalog, our majors will have more curricular choice. We have kept the teaching concentration, revised our general curriculum, and added two new concentrations (one in Applied Mathematics and one in Pure Mathematics). Loosely speaking, our curricular reorganization blends the prescriptive curriculum of 25 years ago (consisting of the applied, finite, and teaching options) with the more flexible general curriculum of recent times. We feel confident that these changes will have broad appeal with our students. In case you have not already noticed, our website <math.calpoly.edu> has had a facelift. Our aim was to make the site more appealing to students. Upon opening the site, you will now find pictures of some recent graduates who embody the spirit and enthusiasm of our students. Also featured is a weekly puzzle (in the quick links section). As some of you may know, our tradition of a weekly puzzle died out a few years ago and was recently revived by Dr. Morgan Sherman. For fun, I invite you to test your skills in solving the weekly puzzles; all correct solutions are acknowledged, and the best are posted. Professors Art DeKleine, Myron Hood, and George Lewis have each completed their participation in the Faculty Early Retirement Program. And Professor Kent Morrison retired as of Spring 2009. We wish all of them the best as they pursue new interests. As always, there is nothing we enjoy more than hearing from you. If you are ever in the area, please drop in and say hello. I also invite you to keep in touch by submitting a note to our newsletter. Finally, I want to express our deep gratitude to those who have supported us through their donations. Your thoughtfulness, much appreciated by students and faculty alike, helps support many important activities in the Department. Thank You!
The Kakeya Needle Problem by Dylan Retsek
A Kakeya set is a plane set K within which a unit segment can be maneuvered so as to
switch the location of its endpoints. Elementary Kakeya sets include the solid disk of
radius 1/2, the deltoid, and the three-cusped hypocycloid. Originally posed in 1917, the
Kakeya problem asks for the Kakeya set of least area.
In 1928, Besicovitch proved the astonishing fact that there is no Kakeya set of least area.
Precisely, given any ε> 0 there exists a Kakeya set of area less than ε. The idea of the
proof is to “parallel park” the needle via an intricate dance of “turns and slides” through
a central “nucleus” of very small area. The Kakeya sets in Besicovitch’s proof are very “spiny” (think of a two-dimensional sea urchin) and not at all convex. If one insists that
K be convex, then one gets a whole
new Kakeya question and answer; the
convex Kakeya set of least area is the
equilateral triangle of altitude one (Pal,
1921). Somewhere between requiring
convexity and making no restrictions
at all is to require that K be star-like.
A plane set K is called star-like if
there exists a distinguished point O
in K such that for any other point in
K the line segment from that point to
O lies entirely within K (imagine a
two-dimensional museum that can be
guarded with a single security camera).
In 1971, Cunningham showed that every star-like Kakeya set has area at least π/108, but
to this day no one knows if this lower bound is sharp! Cunningham’s method of proof is
to center a small disk of radius 1/6 about the distinguished point O of the star-like Kakeya
set K and then keep careful track of how much area the unit segment sweeps out inside
and outside this disk. No matter how one exchanges the location of the endpoints, the
total area is always at least π/108. Under the direction of Dr. Dylan Retsek, Cal Poly
mathematics majors Sean Gasiorek and Tina Woolf generalized the lower bound estimate
for Cunningham’s method of proof by considering disks of arbitrary small radius
R. The lower bound formula they obtained for arbitrary R is L(R)=(R(2R-1)π²)/8, which
indeed has a maximum of π/108 when R=1/6. Thus, π/108 is the maximum lower bound
attainable through Cunningham’s method.
Cal Poly Mathematics Department Summer Research Program 2009
Six Cal Poly Mathematics Department faculty members and 13 undergraduate and graduate mathematics majors worked on research projects during the spring and summer of 2009. These projects were funded by the Cal Poly College-Based Fee Initiative.
Dr. Anton Kaul worked with Cal Poly students
Erin Kelly, Michael Mazzella, and Josh
Pollitz on the project “Shellability in Group
Theory.” In this project, they examined the
behavior of lexicographic shellability in infinite groups. In the course of the investigation,
they proved that local shellability is preserved
under various group theoretic constructions,
including free products and, more generally,
free products with amalgamation.
Dana Duke, JP Horton and Paul Sinz, working
with Dr. Paul Choboter, explored the dynamics
of wind-driven coastal upwelling and
downwelling. Coastal upwelling occurs off
the west coast of North America when winds
drive the near-surface ocean water away from the coast, causing deep water to be drawn up to the surface. Downwelling happens when
winds in the opposite direction push surface
waters toward the coast and down into the
deep ocean. The group used a theoretical
model of upwelling and downwelling that reduces
the dynamics to a set of coupled nonlinear
Partial Differential Equations (PDEs).
The students successfully proved that a certain family of functions solves the PDEs, and
they explored these analytic solutions in detail. The students also performed numerical simulations of upwelling and downwelling with a numerical model that featured more complete dynamics than was included in the theoretical model.
Cal Poly students Casey Kelleher (Math and
Physics) and Mathew Werber (Physics) worked
with Dr. Charles D. Camp on “Pattern Detection
in Climatic Time Series.” The time series of
climatic data records are both short and noisy, often making it difficult to extract information
about the underlying processes creating the
data. The students used new and traditional time
series analysis techniques, such as Empirical
Mode Decomposition and Principal Component
Analysis, to extract the interannual variability
from atmospheric time series and from recent
climate model output. This work was also supported
by an NSF grant.
Toeplitz matrices have all their diagonals (from upper left to the lower right) being constants. The
question of when a Toeplitz matrix is normal was studied more than a decade ago by several authors. Eventually, a simple and elegant answer was given. Hankel matrices have all their skew diagonals (from
lower left to upper right) being constants. The question of when
a Hankel matrix is normal seems much more difficult and is
still open. Based on a recent paper by two Russian numerical
analysts and a general framework for related problems developed
by Professor Caixing Gu and Dr. Linda Patton in 2003,
Dr. Caixing Gu and the graduate student Yu Huang were able
to characterize all five by five normal Hankel matrices during
the summer research.
Perelman’s proof of the Poincare conjecture used Hamilton’s
Ricci flow in an essential way. The Ricci flow can
be thought of as an evolution equation for the metric on
a Riemannian manifold. In many cases, it is known to
converge to a “best” metric, where “best” metric might
mean a metric of constant curvature or one with a lot of
symmetry. During the summer, Dr. Joe Borzellino, with
students Allan Boone and Ryan Ward, looked into the
behavior of the Ricci flow on 2-dimensional Riemannian
orbifolds (a generalization of a Riemannian manifold).
Their goal was to determine to what extent the Ricci flow
converges to the “best” metric. The summer research
was promising, and they hope to get publishable results
with more work.
2008-2009 Honor Roll
| HONOR ROLL OF CORPORATIONS, FOUNDATIONS & ORGANIZATIONS The Department of Mathematics is grateful to the following corporations, foundations, and organizations who made gifts for general and special purposes and for matching gifts. |
||
| Chevron Corporation | Intuit | Northrop Grumman Corporation |
| Cupertino Electric Inc | General Electric Company | Pacific Gas and Electric Company |
| IBM Corporation | Lockheed Martin Corporation | Wells Fargo & Company |
| Intel Corporation | Microsoft Corporation | |
| HONOR ROLL
OF INDIVIDUALS All individuals listed below have brought strength to the Mathematics Department through their financial support and the confidence it represents. The Department recognizes you for your generosity and thoughtfulness. |
||
| President’s Round Table $5,000 - $19,999 | ||
| Donald B. Gibson | ||
| Dean’s Honor Roll $1,000 - $1,999 | ||
| Stephen J. Corcoran and Jacqueline
Wyland Marjorie L. Hanks and *Charles J. Hanks |
Estate of Arthur A. Hiatt Debra L. Magana |
Paul F. and Barbara J. Murphy Elmer F. and Mona R. Reed |
| College Cabinet $500 - $999 | ||
| John L. and Nancy E. Cook Dianne and Donald Jackson |
Victoria L. Flavell Myron and Sue Hood |
Susyn C. and Brian K. Normington Gary M. Schare |
| Department Council $250 - $499 | ||
| Anonymous Donor Jay A. Austin Greg R. and JoAnn V. Beserra Charles A. and Anet Carlin Gary A. Gale Janie and Stu Goldenberg Leah J. Griffith |
Robert J. and Barbara Gulliford Carol S. Judd Sharon M. Kuge Leslie L. Livesay Frank A. Blesi and Susan L. Marietta Craig J. and Leslie V. Nelson Richard O. Parker Jr. |
Sharon D. Raney Cami A. and Terry R. Reece Robert M. Reinsch T. William and Khanh N. Van Oss Susan L. and Andrew P. West David G. and Bernice White |
| College Partners $100 - $249 | ||
| Jeanne C. Barks Robert K. Bohi Irwin W. Boxer Mark J. and Ramona E. Bujulian Eric W. Burdick Joanie M. Carew and Ashley S. Green James V. and Beverly A. Carlson Michael F. and Nancy K. Chase Rose M. De Palma James S. DeGracie Herbert A. and Gloria J. DeKleine Jane M. and Arthur R. Delgadillo Jay B. and Donna J. Fox Randall H. Garacci John L. Glaze |
Jody Ann S. and John W. Jacobs Margret E. Jacoby Edward C. and Awilda B. Jarrett Maria G. Kelly Bob and Lisa M. Kernaghan Kent M. and Nancy N. Kilborn Harmony J. and Thor L. Larsen Nancy E. and Dan E. Littrell Brian M. McCay Elizabeth A. and Ross I. Miyazawa Douglas R. and Karen B. Morgan Stuart and June L. Moy Mary E. and Philip H. Pattengale Robert H. and Carol Schmiederer Ann E. Segesman |
Margery L. Segraves Stuart A. Snyder Richard A. Spohn Carrie A. and Kevin Starbird Lawrence L. Stiles A. William Stillman Jr. Neal R. and Lucille Townsend Gordon S. and Ann H. Umemoto John S. and Ann M. Volk Karen E. Watson Nan L. and Gregory L. Wojcik Nancy E. and Brian C. Wright Richard E. and Peggy S. Wroble Christy M. and Louis A. Yaussi |
Note: Every effort has been made to list our donors correctly. If there is an error, please bring it to our attention immediately. We apologize in advance if there is an omission.
2008-09 Graduates
Bachelor of Science
Elizabeth Ruth Andrews,
Laura Nicole Baldwin*,
Antigone Electra Bennett,
Robert James Brunner,
Kyle Leland Chapman,
Wade Thomas Dillon**,
Aaron Spencer Donley,
Ruth Anne Emerick,
Matthew Charles Forman,
Christopher Joseph Fredericks,
Thomas Kintaro Furukawa,
Mark Aquino Gabaya,
Hunter S. Glanz**,
Robert Paul Gordon,
Tyler Martin Hall**,
Ryan Toddhuntington Koether,
Laura Kathryn Leach*,
Brandy Lynn Little,
Mark Thomas Lydon*,
Sarah Rose Lyons**,
Erin Elizabeth Malloy** ^,
Sean Justin Melling Gasiorek,
Patrick David Perl,
Kasandra Joi Phillis,
Sunny Lynn Sawyer,
Madeline Louise Schroth-Miller,
Kelly Ann Seal,
Aaron B. Shev,
Kyle M. Smith,
William Paul Taylor,
Dustin Tidyman-Jones,
Kathryn Ann Vaughan*** ^,
Shea Llewellyn Williams,
Tina Michelle Woolf*** ^,
Daniel Thomas Young.
Kelsey Ryska Δ
# Cal Poly Scholar;
^ Honors Program;
* Cum laude;
** Magna cum laude;
*** Summa cum laude; Δ Graduating with Distinction
Alumni News
A message from Jeff Duff, MS 1993 (email: jeffduff@air-streams.com), Vice President, Airstreams Renewables, Inc.
Life is very busy in the renewable energy sector. Received my latest copy of Polymath, it was good to see some I still recognize. Family is doing well - wife Chris, Rachel (15.5), Jeremy (14). Running a company has kept me from in-depth mathematics study, but I still keep my pencil sharp. Our company has moved into the realm of technical education and training. Our curriculum is being taught in a number of community and technical colleges, and we have some speaking engagements at various higher ed arenas. If there is any interest in renewable energy, I’d be up for a quick trip to put on a presentation about the opportunities, specifically in Wind Energy. From a math perspective, we have engaged more statistics in the work I have focused on, white papers on our web site. However, most are interested in the general overview of the industry.
An update on Eric Schadt, BS 1991 Mathematics, Applied Mathematics Concentration
Eric received his Ph.D. in Biomathematics from UCLA. He is now the Chief Scientific Officer for Pacific Biosciences in Menlo Park. Recently, the New York Times’ Science section had an article about Dr. Schadt, in which it describes his work in biomathematics. From 1999 until recently, Dr. Schadt worked as the head of genetics and bioinformatics for Rosetta Inpharmatics, a company based in Seattle. Founded in 1996 by Dr. Hood, Dr. Friend and the biologist and Nobel laureate Lee Hartwell, Rosetta was bought by the pharmaceutical giant Merck in 2001 for $620 million. At Merck, the Rosetta team was provided with resources beyond those usually available in academia. Rosetta built one of the fastest supercomputers in the drug industry, running 16 trillion calculations a second. The company now has in clinical trials eight drugs that emerged out of Rosetta’s platform. When Dr. Schadt left Merck, he took on two jobs — as the co-director of Sage with Dr. Friend, and as the chief scientific officer of Pacific Biosciences, a company founded in 2004.
2009 Cal Poly Math Noyce Program
Last June, the directors of the Cal Poly Math Noyce Program, Dr. Todd Grundmeier and Dr. Elsa Medina, offered a three-day workshop for Noyce Scholars. Fifteen Noyce
Scholars from Cal Poly and other universities attended the workshop to discuss pedagogical issues related to the teaching of mathematics and to prepare for the first year of teaching. The directors received an NSF grant of $52,670 to continue offering these workshops in coming years. The photo shows the fifteen Math Noyce Scholars, the directors of the Math Noyce Program, Dr. Todd Grundmeier and Dr. Elsa Medina, as well as the mathematics department chair, Dr. Don Rawlings, and the dean of the College of Science and Mathematics, Dr. Phil Bailey.
2009 Mathematics Department Photo
Row 1 L-R: Lana Grishchenko, Katie Vaughan, Kelsey Prancevic, Jessica
Ellis, Elsa Medina, Caixing Gu, Don Hartig, Jonathan Shapiro
Row 2: Bill Demarest, Sheryl O’Neill, Wade Dillon, Amelie Schinck, Dana
Paquin, Mike Mogull, Don Rawlings
Row 3: Phyllis Brudney, Maureen Rosenberg, Todor Todorov, Sean
Gasiorek, Jim Mueller, Richard Neufeld
Row 4: Carole Simard, Kate Riley, Dylan Retsek, Mike Robertson
Row 5: Ryan Harris, Liz Czapla, Adrienne Riley, Stan Yoshinobu, Yu Huang,
Vince Bonini, Morgan Sherman, Ben Richert, Dave Camp, Paul Choboter
Row 6: Mark Stankus, Todd Grundmeier, Cami Reece, Bill Hesselgrave, Al
Jimenez, Allan Boone, Harvey Greenwald, Steve Agronsky, Joon
Jung, Rob Webb, Joe Borzellino, Anton Kaul, Clint Hahlbeck, Jeff
Liese, Colleen Kirk, Tony Mendes
Introducing New Mathematics Department Faculty
Amélie Schinck is happy to join the Cal Poly Mathematics faculty this fall. Amélie recently completed her Ph.D. in Curriculum and Instruction with a specialty in Mathematics Education from the University of North Carolina at Charlotte. She completed her M.Sc. in Mathematics (Number Theory) at Concordia University in Montréal, Canada. Amélie is committed to the teaching of mathematics, K-12 teacher preparation, and to extending her scholarship in the field of mathematics education. In addition to mathematics and its education, her interests include swimming, hiking, and good food enjoyed with friends.
Stan Yoshinobu started his career in Real Analysis, studying under John Garnett (UCLA). Currently, Stan specializes in Mathematics Education, focusing on teacher preparation and training at both the K-12 and college levels. Stan previously was an associate professor at Cal State Dominguez Hills and a postdoctoral fellow at the University of Arizona. In his free time, Stan enjoys cycling, hiking, watching sports, listening to Jazz, photography and spending time with his family.
Faculty Publications and Conference Talks 2008-2009
- J. Borzellino and V. Brunsden, A Manifold Structure for the Group of Orbifold Diffeomorphisms of a Smooth Orbifold, Journal of Lie Theory, 18 (2008) no. 4, 979-1007.
- J. Borzellino was an invited speaker for the Workshop on Global Riemannian Geometry, Orbifolds, and related topics at Middlebury College, Middlebury, VT, October 2009.
- J. Borzellino was an invited speaker in the Special Session on Global Analysis on Homogeneous Spaces at the AMS 2009 Fall Central section meeting at Baylor University, Waco, TX, October 2009.
- J. Borzellino was an invited speaker in the Special Session on Global Riemannian Geometry at the AMS 2009 Fall Western section meeting at University of California, Riverside, CA, November 2009.
- C.D. Camp, K.K.Tung, and J.Zhou, Constraining model transient climate response using independent observations of solar-cycle forcing and response, Geophy.Res.Lett.,35,L17707,doi:10.1029/2008GL03420.
- C.D. Camp, X. Jiang, S. Pawson, J. E. Nielsen, R.-L. Shia, T. Liao, V. Limpasuvan, and Y. L. Yung, Interannual Variability and Trends of Extratropical Ozone. Part I: Northern Hemisphere, J. Atmos. Sci., 65, 3013-3029, doi:10.1175/2008JAS2665.1.
- C.D. Camp, X. Jiang, S. Pawson, J. E. Nielsen, R.-L. Shia, T. Liao, V. Limpasuvan, and Y. L. Yung, Interannual Variability and Trends of Extratropical Ozone. Part II: Southern Hemisphere, J. Atmos. Sci., 65, 3030-3041, doi:10.1175/2008JAS2793.1.
- C.D. Camp was an invited speaker, 1st PRIMA (Pacific Rim Mathematical Association) Congress, University of New South Wales, Sydney, AU, July 6-10, 2009. Pattern detection in multivariate climatic time series: detecting the inûuence of solar variability on the Earth’s atmosphere.
- C.D. Camp received, as Principal Investigator, GRANT: NSF/ATM-0808375 subcontract Modeling the Influences of the QBO, the Solar Cycle and ENSO on the Strength of the Stratospheric Polar Night Vortex, Subcontracted from Univ. of Washington, Principal Investigator: Ka-Kit Tung. Dates: May 2009 - April 2011, Amount: $65,298.
- A. Kaul and M.E. White, Centralizers of Coxeter elements and inner automorphisms of right-angled Coxeter groups, Int. J. Algebra, Vol. 3, no. 10 (2009), 456-473.
- Dana Paquin, Doron Levy, and Lei Xing, Multiscale Registration of Planning CT and Daily CBCT Images for Adaptive Radiation Therapy, Medical Physics, Volume 36, Number 1, January 2009.
- Lawrence Sze (with Hoang Mai and Ben Ford), Self-conjugate simultaneous p- and q-core partitions and blocks of An, Journal of Number Theory 129 (2009), 858-865.
- Lawrence Sze (with David Aukerman and Ben Kane), On simultaneous s-cores/t-cores, Journal of Discrete Mathematics, Vol. 309, p. 2712-2720, 2009.
- Todor Todorov, Algebraic Approach to Colombeau Theory of Generalized Functions, a seminar talk at University of Vienna (Austria), in the DIANA-Seminar Research Group, June 26, 2009 .
- Todor Todorov and Hans Vernaeve, Power Series in a Non-Standard Setting, International Conference on Logic & Analysis, York (UK), August 3-7, 2009.
- Todor Todorov, Special Colombeau Algebras of Generalized Functions and Non-Standard Analysis, International Conference on Generalized Functions, Vienna (Austria), August 29-September 4, 2009.
IBL Workshop Summer 2009
In July, Mark Stankus, Dylan Retsek, and Stan Yoshinobu (workshop director) attended the 2009 Inquiry-Based Learning Workshop in Austin, Texas. At the weeklong workshop with 23 other mathematicians, Mark, Dylan, and Stan discussed practical ways to implement a student-centered teaching method, called Inquiry-Based Learning (IBL), in undergraduate Mathematics courses. Development and implementation of IBL courses at Cal Poly is planned for the next two years. For those interested in learning more about IBL, please contact Stan Yoshinobu.
Math Club Activities by Jose Valdez
The Math Club held bi-weekly meetings to discuss upcoming events, trips, and t-shirt ideas. They came up with a t-shirt “Why Math?” which is shown here. Their big trip of the year was to Big Sur where they camped out for a weekend. They would also have game-nights frequently at Kyle Chapman’s house. Most Fridays, the Math Club joined the Physics Club to play some kind of sport such as dodgeball, volleyball, indoor soccer, or ultimate frisby.
Putnam Math Competition 2008
In December 2008, the Cal Poly team of Kyle Chapman, Paul Coombs, and Thomas Furukawa, along with eight other Cal Poly students, participated in the Putnam Competition. The team placed 74th out of 545 teams entered in the competition. The high scorer from Cal Poly was Kyle Chapman, with a score of 22, followed by Paul Coombs, with 19 points.
Mathematical Contest in Modeling 2009
Cal Poly, led by coach Jonathan Shapiro, had two teams in the Mathematical Contest in Modeling. Team 5730 consisted of Kevin Lamb, Kyle Chapman, and Megan Evans. Team 5731 consisted of Allan Boone, Erin Kelly, and Alex Eames. Each team tackled the problem of designing more efficient traffic circles. Each team was given a “Successful Participant” designation. You can see all of the results of the Mathematical Contest in Modeling at COMAP.
End-of-Year BBQ and Softball
The Faculty Team won this round, 11-8. This stopped the Undergraduate Team’s winning streak at one and could be the beginning of another good streak for the Faculty side. Additional photos are available at End-of-year BBQ and Softball.
Sixth Annual Math Awards Banquet
This year's Annual Math Awards Banquet was held on Thursday, May 21, 2009 at Cafe Roma. Additional photos are available at Math Awards Banquet.
Outstanding Students
Outstanding students were recognized at the Math Awards Banquet. Additional Photos are available at Math Awards Banquet.
Commencement Fall 2008 and Spring 2009
Additional Photos are available at Commencement Fall 2008 and Spring 2009.
What’s New With You?
We would love to hear from you! Please drop us a line and let us know what you’d like to share in the “Alumni News” of Polymath. Include your name, graduation year, degree received (B.S./ M.S.), e-mail address, web page, current job title and employer, professional and/or personal news, and whether it is okay to print your information so other alumni can reach you. Information can be mailed to: Polymath Editor, Mathematics Department, California Polytechnic State University, San Luis Obispo, CA 93407-0403 or e-mail updates can be sent to: math@calpoly.edu.
Credits
Polymath is published by the Mathematics Department. Inquiries, suggestions and comments are welcome. Jonathan Shapiro is the Faculty Editor, Production Editor, and Graphic Designer. Jonathan Shapiro, with photo contributions from Stan Yoshinobu, is also the Photographer. The web version of the newsletter is produced by Cami Reece.