On May 4-7, 2000 a conference, ``Recent Trends in Geometry and Symmetry" in honor of Emeritus Professor Donald W. Crowe was held in Madison. As the conference announcement said, Donald W. Crowe has spent over 40 years popularizing, researching and teaching the many facets of geometry, especially aspects of geometry related to symmetry. The purpose of this conference was to honor his efforts by providing a forum to discuss new trends and developments in the study of geometry and symmetry.

Donald W. Crowe
The four invited speakers were: H. S. M. Coxeter (Univ. of Toronto) speaking on ``Isohedra With Rhombic Or Rectangular Faces'' [about this talk, Marty Isaacs was heard to say: Ït was like going to hear a talk by Gauss."]; Chandler Davis (Univ. of Toronto) on ``Wavelet Systems Which Respect Symmetry Groups''; Greg Frederickson (Purdue Univ.) on ``Geometric Dissections That Swing And Twist''; and Sue Whitesides (PhD 1975, R. H. Bruck) (McGill Univ.) on ``Geometry in Motion: a Survey of Linkage Movement Problems'' [Sue's results on unfolding polygonal paths in the plane were written about in Ivars Peterson's September 23, 2000 column in Science News]. The banquet speaker, who made less serious but surely mathematical comments, was Solomon Garfunkel (PhD 1967, H. J. Keisler) from COMAP.

There were twenty-one contributed papers, including those given by former UW-Madison students Darrah Chavey (PhD 1984, D. W. Crowe), Gary Ebert (PhD 1975, R.H. Bruck), Leroy Dickey (PhD 1970, D. W. Crowe), Joe Malkevitch (PhD 1968, D. W. Crowe). In addition, there were sessions devoted to proposing and discussing problems, and exhibits of books and geometrical models and constructions. There were approximately 50 participants from all over.

The conference was organized by Amir Assadi (UW), Steve Bauman (UW), Joseph Malkevitch (York College (CUNY)), Dorothy Washburn (Maryland Institute, College of Art), and Bob Wilson (UW). Funding support came from the UW Mathematics Department and from NSF. Cambridge University Press donated a large number of geometry-related books for use at the conference and placement in the Stephen Cole Kleene Mathematics Library at UW-Madison.

More details including a gallery of pictures of Don Crowe and family and friends, as well as the conference program, are available at the conference web site, http://outreach.math.wisc.edu/conference.htm.

Contributed by Robert Wilson

Conference in Honor of Louis Solomon

The Mathematics Department hosted a 6 day meeting, ``Combinatorics of Lie Type,'' June 16-22, 2000, in honor of the career, mathematics, retirement, and birthday of our colleague, Louis Solomon. Over 130 participants traveled from Argentina, Australia, Canada, England, Denmark, France, Germany, India, Israel, Italy, Japan, Korea, Mexico, Wales and from all over the United States to attend the conference, which was organized by Georgia Benkart, Peter Orlik, and Arun Ram. The lecture topics represented Lou's mathematical tastes: reflection groups, aperiodic order, arrangements of hyperplanes, fundamental groups of configuration spaces, the representation theory of finite groups of Lie type, Lie algebras of characteristic p, Iwahori-Hecke algebras, and quantum affine algebras, growth of group and Lie algebras, symmetric functions, Kazhdan-Lusztig polynomials, reductive monoids, coverings and moduli of curves, and invariants in modules for groups of Lie type.

Two innovations introduced at the meeting were the ``preprint buffet'' and the mentoring system. Participants brought their preprints for display on ``buffet'' tables in the ninth floor lounge and submitted files of them to our web page. Attendees browsed the preprints during the breaks. Yvonne Nagel helped set up a computer and printer nearby to enable participants to print out copies of preprints they desired. This was especially valuable to young mathematicians, as it provided them the opportunity to have their work noticed. A second innovation paired the young mathematicians attending the conference with a senior mathematician who served as an informal mentor.

The new Frank Lloyd Wright Convention Center on Lake Monona was the setting for the conference banquet held the last evening of the meeting. As one participant wrote later, ``The mathematics, participants, atmosphere, and organization were all great. I was also very much moved by the reminiscences at the banquet. Their intensity and sincerity made the conference more than great, they made it memorable. Thank you for making me a part of this great event," (and thanks to Lou for providing the occasion).

Contributed by Georgia Benkart

Conference in Honor of J. Marshall Osborn

J. M. Osborn
In May, Marshall Osborn retired after 43 years on the mathematics faculty at Wisconsin. He had served as both chair and associate chair of the department. In honor of the occasion and to celebrate Marshall's 70th birthday, a conference, ``Lie Algebras and Related Topics,'' was held at the new Pyle Center (formerly the Alumni Center) September 8-10, 2000. Participants were treated to great lectures on Lie algebras, representation theory, and Jordan algebras as well as to a great view of Lake Mendota.

The conference included a ``Marshall Osborn Trivia Contest,'' which posed questions about Marshall's life and career. Richard Block, professor of mathematics at the University of California, Riverside, who has known Marshall since their days as graduate students at the University of Chicago, was the winner of the contest. Georgia Benkart organized the meeting and Efim Zelmanov, Fields Medalist and former UW professor, was the master of ceremonies at the banquet, which was held in the Alumni Lounge overlooking Lake Mendota. Besides teaching mathematics, Marshall has taught many mathematicians to drive - as both Richard Block and Efim Zelmanov attested in their testimonials to Marshall. The meeting in September provided an opportunity to celebrate Marshall's success in all these endeavors.

Contributed by Georgia Benkart

2000 MWMT Held in Madison

The Annual Midwest Model Theory Meeting (MWMT) meeting was held in Madison on the weekend of November 11-12, 2000. The meeting was organized by Patrick Speissegger.

The American Midwest is now one of the world's major centers for research in the branch of Mathematical Logic known as Model Theory. The three schools most prominently involved are the University of Illinois at Urbana-Champaign, the University of Illinois at Chicago, and the University of Notre Dame, with prominent researchers also at the University of Wisconsin-Madison and the Ohio State University. The meeting featured talks by: Matthias Aschenbrenner (University of Illinois, Urbana-Champaign) on ``Ideal Membership in Polynomial Rings over the Integers '', Martin Grohe (University of Illinois, Chicago) on ``Graph Isomorphism Testing through Definability'', Jean-Philippe Rolin (Universite de Bourgogne, Dijon, France) on ``Quasianalytic Denjoy-Carleman Classes '', Shawn Hedman (University of Maryland, College Park) on ``Finite Variable Axiomatizability and Local Modularity '', Byunghan Kim (MIT, Boston) on ``Stable local forking'', Rahim Moosa (University of Illinois, Urbana-Champaign) on ``Saturated Compact Complex Spaces'', Andrei Morozov (Russian Academy of Sciences, Novosibirsk, and Novosibirsk State University) on ``On groups of computable automorphisms of computable structures'', Artur Piekosz (Cracow University of Technology) on ``Semilinear and semialgebraic loci of o-minimal sets''.

To promote attendance at the conference by graduate students, some travel grants for graduate students were made available. This year's meeting was supported by the Van Vleck funds through the Department of Mathematics at the University of Wisconsin-Madison.

Madison Conference on Nonlinear Analysis 2000

(in honor of Paul H. Rabinowitz)

Paul H. Rabinowitz
On May 28-30, 2000 the Department of Mathematics sponsored a conference on nonlinear analysis, recognizing the 60th birthday of Paul Rabinowitz. The themes of the conference were (1) Variational Methods, and (2) Bifurcation and Degree Theory. A description of these two themes, taken from the conference announcement is:

(1) The idea to use variational principles to prove existence or multiplicity results for solutions to PDEs (elliptic problems, minimal surfaces, Yamabe problem) or ODEs (periodic orbits in Hamiltonian Systems) goes back at least to Poincaré and has been successfully exploited throughout this century. Two classical methods are (i) the direct approach in the calculus of variations, in which existence of minimizers of functionals is proved by suitable compactness arguments, to obtain, e.g. existence results for minimal surfaces; and (ii) Morse and Ljusternik-Schnirelman theory, in which topology and analysis are combined to deduce existence of periodic orbits in mechanical systems. The last few decades have seen a rapid growth in the number of problems which have been attacked, as well as the emergence of new variational methods which have been brought to bear upon them, e.g.

·: Minimax arguments have been used for the construction of closed orbits in Hamiltonian systems with starshaped energy surfaces
·: Floer introduced a new approach to Morse theory which allowed him to prove the Arnol'd conjecture in many cases; the complete conjecture was proved by several groups of people. Further developments involve the variational study of closed characteristics on contact manifolds.
·: Variational methods have been used in varying degrees of abstractness and generality to construct so-called chaotic solutions or ``multibump solutions" in Hamiltonian systems, and in Lagrangian systems (monotone twist maps of an annulus being the simplest example.)

(2) The Brouwer and Leray-Schauder degrees have classically been used for existence proofs for PDEs, and to keep track of solutions to PDEs through bifurcations (e.g. in the Crandall-Rabinowitz bifurcation theorem). More recent developments concern the extension of the definition of the Brouwer degree to maps which are not continuous but close to continuous, and the use of the Leray-Schauder degree in singular perturbation problems.

The conference was organized by Sigurd Angenent and Marshall Slemrod. It featured invited lectures by H. Brezis (Rutgers University and Universit'e Paris VI), A. Bahri (Rider University), H. Hofer (New York University), M. G. Crandall (UC-Santa Barbara), J. N. Mather (Princeton University), S. Bolotin (Moscow State University), V. Coti-Zelati (University of Naples), P. E. Souganidis (UW-Madison), D. Sattinger (Utah State University), D. G. Aronson (University of Minnesota), and A. Ambrosetti (University of Trieste). There were also contributed talks sessions each day.

A reception was held in the 9th floor lounge of Van Vleck Hall on Saturday, May 27. On Sunday evening, May 28, there was a conference dinner in the 9th floor lounge. Many people talked about Paul's spectacular mathematical accomplishments, and Paul as a warm and caring human being.

Orbifold String Theory Workshop in Madison

A Workshop on Mathematical Aspects of Orbifold Theory will be held in Madison on May 4-8, 2001. The organizers are Alejandro Adem and Yongbin Ruan of our Department, and Jack Morava of Johns Hopkins University. Expected participants include P. Abramovich (Boston University), P. Aspinwall (Duke University), V. Batyrev (Tübingen University), W. Chen (SUNY-Stony Brook), H. Compean (CINVESTAV, Mexico), B. Greene Columbia University), M. Gross (Warwick University), J. Harvey (University of Chicago), E. Ionel (UW-Madison), G. Mason (UC-Santa Cruz), I. Moerdijk (Utrecht University), M. Reid (Warwick University), B. Toen (University of Nice), C. Vafa (Harvard University), W. Wang (North Carolina State University), and E. Zaslow (Northwestern University).

Information about the meeting can be found at the URL: http://www.math.wisc.edu/ conklin/ost/

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