Mekler Lecture

Alan Mekler
1947 - 1992



The Dr. Alan Mekler Memorial Endowment was established at Simon Fraser University by colleagues, friends and family in memory of Dr. Mekler. Dr. Mekler was a member of the Mathematics and Statistics Department from 1980 until his death from cancer in 1992. During his life, he was known to us as a juggler, birder, mathematician and lover of life. A valuable colleague, he was recognized internationally for his work in the applications of set theory and/or model theory to algebraic systems. He had an appreciation for and an understanding of much diverse mathematics.

The first priority of the Alan Mekler Memorial Endowment is to sponsor an annual lecture in pure mathematics. The inaugural lecture in the series was delivered on July 22, 1994, by Professor Paul Eklof of the University of California, Irvine. The lecture addressed Alan Mekler's life and work.

This Year's Lecture and Alan's CV.

Previous Mekler Lecturers

1. Paul Eklof (1994/95)

University of California, Irvine, July 22, 1994

Title: "Alan Mekler: his life and work"

Paul Eklof was born in Brooklyn in 1942. He received his Ph.D. from Cornell in 1968. He was a Gibbs Instructor at Yale from 1968 to 1970, and an assistant professor at Stanford from 1970-73. Since 1973 he has been on the faculty at the University of California at Irvine, attaining the rank of professor in 1978. Paul Eklof has published extensively. His research has focused on model theory, the theory of modules, and applications of model theory and set theory to algebra.

While at Stanford, Paul Eklof was Alan Mekler's Ph.D. supervisor. He had a long collaboration with Alan, one of the fruits of which was the monograph: "Almost Free Modules: Set-theoretic methods" published by North-Holland in 1990, two years before Alan's death.


2. Hugh Woodin (1995/96)

University of California, Berkeley, March 28, 1996

Dr. Hugh Woodin, born in Tucson in 1955, was an NSF Graduate Fellow from 1977-80, a Sloan Fellow in 1983, a Presedential Young Investigator in 1985 and the recipient of the Karp Prize in 1989. He was Assistant Professor at Cal Tech from 1980 to 83, and Professor from 1983-89. During this time, in 1984, he received his Ph.D. from Berkeley. In 1989 he joined the faculty at the University of California, Berkeley, where he has become world-renowned for his research in set theory.

Title: "Do sets suffice?"

Abstract: Has the proliferation of indeependence results reduced the foundational role of set theory to simply that of formalism? Is the apparent intractability of such fundamental problems as the Continuum Hypothesis evidence for the inadequacy of set theory?


3. Keith Devlin (1996/97)

Saint Mary's College of California, Moraga, California, October 17, 1996

Keith Devlin is Dean of the School of Science at Saint Mary's College of California in Moraga, California. His research is focused on the development and use of mathematical techniques to study language, communication, and information.

Many of you may know Dr. Devlin from his articles on Computers and Mathematics in the Notices of the AMS. He is also the editor of FOCUS, the news magazine of the Mathematical Association of America. His book "Logic and Information", published by Cambridge University Press in 1991, provides a comprehensive introduction to situation theory and situation semantics.

Title: "Goodbye Descartes?"

Abstract: Attempts to develop a mathematics of thought and language began with Aristotle and Zeno in ancient Greece and progressed through the work of Leibniz and then Boole to the mathematical logic and the mathematical linguistics of the twentieth century. After a rapid tour of this two thousand year development, I'll ask the question, "What will the twenty-first century bring by way of new developments in this area?"


4. Reinhard Diestel (1997/98)

University of Chemnitz, Germany, February 18, 1998

Reinhard Diestel received a PhD from the University of Cambridge, following research (1983-86) as a scholar of Trinity College under Béla Bollobás. He was a fellow of St. John's College, Cambridge, from 1986 to 1990. Research appointments and scholarships have taken him to Bielefeld (Germany), Oxford and the US. Since 1994 he has been Professor of Mathematics at the University of Chemnitz, Germany.

Reinhard Diestel's main area of research is graph theory, especially infinite graph theory. He has published numerous papers and a research monograph, Graph Decompositions (Oxford 1990).

Title: "Dominating arithmetic functions, and the growth of infinite graphs."

Abstract: The growth of an infinite graph can be measured in various ways. Two of these, one due to Halin and the other to Thomassen, have turned out after many years to be almost equivalent. Given the superficial disparity of the two notions, this result points to an underlying deeper notion that may still not have been fully understood. Moreover, in the form of Halin's concept this notion sheds a surprising new light on the old set-theoretic problem of determining the bounding and domination numbers of arithmetic functions."


5. Béla Bollobás (1998/99)

University of Memphis and Cambridge, May 12th, 1999

Béla Bollobás holds the Chair of Excellence in Combinatorics at the University of Memphis, and is a Fellow of Trinity College, Cambridge. He did his undergraduate work in Budapest and Cambridge, and his doctorates are also from those universities. In 1969, he left Hungary for England, and for over 25 years taught at Cambridge, where he supervised close to thirty research students.

Dr Bollobás works mostly in extremal and probabilistic combinatorics, and is especially interested in random graphs, random partial orders, percolation, and isoperimetric inequalities. His mathematical taste was greatly influenced by the late Professor Paul Erdös, with whom he collaborated for over 35 years. He has published about 250 research papers and several books, including Extremal Graph Theory~(1978), Graph Theory (1979), Random Graphs (1984), Combinatorics (1986) and Linear Analysis (1990). His most recent book, Modern Graph Theory, was published a few months ago by Springer Verlag. He is the founder and Editor-in-Chief of the international journal Combinatorics, Probability and Computing, and he serves on on the editorial boards of six other journals.

Title: "Projections of Bodies and Hereditary Properties of Graphs"

Abstract: A property P of graphs is hereditary if every induced subgraph of a graph in P is also in P. For a property P, we write Pn for the set of graphs in P with vertex set {1,... ,n}. Also, the P-chromatic number of a graph is the minimal number of classes in a vertex partition wherein each class spans a subgraph with property P.

Much of extremal and probabilistic graph theory is concerned with the study of Pn for various hereditary properties. In this talk we shall address global questions of the following kind. What can we say about the growth of the function |Pn | for a hereditary property? What is the connection between |Pn | and the maximal size of a graph in P? What can we say about the P-chromatic number of a random graph? One of the tools used to attack these questions is an isoperimetric inequality concerning projections of bodies in Rn obtained with Thomason. In the talk we shall present this isoperimetric inequality, together with a number of recent results concerning hereditary properties, obtained jointly with Thomason, and Balogh and Weinreich.

Dr. Bollobás will be speaking in the Discrete Mathematics seminar, 10:30, Thursday, May 13th - K9509

Title: Projections of Bodies and Hereditary Properties of Graphs


6. Persi Diaconis (1999/2000)

Stanford University, February 15, 2000

After running away from home to do magic at the age of 14, Persi Diaconis read Feller's Probability on his own before entering City College of New York at age 24. Completing his B.S. two years later (1971) he went on to Harvard for his MS (1972) and PhD (1974). He joined the Department of Statistics at Stanford in 1974. He has been Professor of Mathematics at Harvard and Cornell and is now Professor of Mathematics and of Statistics at Stanford. Winner of a MacArthur Foundation Fellowship, he has worked in many areas of probability and statistics; a random selection of examples includes asymptotic theory of Bayes estimates, finite de Finetti theorems, Markov Chain Monte Carlo, rates of convergence in the ergodic theorem for Markov chains, the statistics of vision, the mathematics of card shuffling, spectral analysis for ranked data, random matrix theory and applications of group theory in statistics. Volume 1 of Statistical Science, pages 319-334, has an entertaining interview with Professor Diaconis.

Title: "An introduction to random matrix theory"

Abstract: Typical unitary matrices show remarkable patterns in their eigenvalue distribution. This same pattern occurs in particle scattering data, the zeroes of the zeta function, and telephone encryption. I will explain the pattern and some of its applications.


7. Yuri Gurevich (2000/2001)

Microsoft Research, Redmond, WA, March 8, 2001

Yuri Gurevich ( heads the Foundations of Software Engineering group at Microsoft Research in Redmond, WA. He is Professor Emeritus of Electrical Engineering and Computer Science at the University of Michigan. He started his career as an algebraist. Then he became a logician. Finally he moved to computer science, where his main projects have been Abstract State Machines, Average Case Computational Complexity, and Finite Model Theory. Dr. Gurevich has been honored as a Dr. Honoris Causa of the University of Limburg, Belgium (1998), as a Fellow of the Association for Computing Machinery (1996), as well as a Fellow of the John Simon Guggenheim Memorial Foundation (1995).

Title: "What is an Algorithm?"

Abstract: One may think that the title problem was solved long ago by Church and Turing. It wasn't; there is more to an algorithm than the function it computes. (Besides, what function does an operating system compute? The term algorithm is understood broadly here.) The interest to the problem is not only theoretical. Applications include modeling, specification, verification, design and testing of software and hardware systems. The first part of the talk will be devoted to the sequential abstract state machine (ASM) thesis: every sequential algorithm is behaviorally equivalent to a sequential ASM.

The thesis was proved recently (ACM Transactions on Computational Logic 1, no. 1, July 2000) from first principles. The remainder of the talk will be devoted to extensions of the thesis to general computations and to the current applications of ASMs in Microsoft and elsewhere.


8. Martin Groetschel (2001/2002)

Konrad-Zuse-Zentrum, Berlin, February 14, 2002 (3.30pm in B9201)

Martin Groetschel is a professor in the department of mathematics at the Technical University of Berlin and is Vice-President of the Konrad-Zuse Centre for Scientific Computing. His current research is focused on problems of optimization which arise in the management of public transportation, and in telecommunications. He is the author of more than 100 mathematical papers, and has also published extensively in the area of electronic information and communication as they relate to libraries. Amonst the books he has edited or authored, probably the best known is "The Handbook of Combinatorics" which he edited with R. Graham and L. Lovasz. He is the recipient of many honours, amongst them the 1982 Fulkerson Prize, the 1984 IBM Prize, the 1990 Karl Heinz Beckurts Prize, and the 1991 George B. Dantzig Prize. In 1999 he was elected as a foreign associate of the National Academy of Engineering, USA.

Title: "Mathematical Opportunities in Telecommunication"

Abstract: This talk will begin with a survey of mathematical challenges that arise in telecommunication. Mathematics is involved, e. g., in the design and manufacturing of chips, devices and network components, the choice of locations, the planning of the network topology, and the dimensioning of the equipment involved. Adequate cryptography, the need of fast data processing, demand routing and failure handling require efficient and reliable mathematical algorithms on the operational side.

The presentation will focus on the problem of designing low-cost telecommunication networks that provide sufficient capacity to serve a given demand, are based on a chosen technology mix, satisfy various technical side constraints, and survive certain failure situations. This problem is difficult in theory and practice. It will be indicated how algorithms integrating polyhedral combinatorics, linear and integer programming, and various heuristic ideas can help solve real-world instances within reasonable quality guarantees in acceptable running times.

This talk is based on work of the telecommunications research group at ZIB, the examples discussed and the computational results reported are from joint projects with several telecommunication companies.

(Dr. Groetschel will also give a more specialized Discrete Math Seminar in the morning.)


9. Jeff Weeks (2002/2003)

Canton, New York, December 4, 2002 (2.30pm on Burnaby Mountain AQ3005, followed by a reception in K9509)

Jeff Weeks is a freelance mathematician living in Canton, NY. He has an A.B. from Dartmouth College and a Ph.D. from Princeton University, both in mathematics. His main interests are geometry, topology, cosmology and education. After several years of teaching undergraduate mathematics, he resigned to care for his newborn son. When his son began school, Jeff began doing mathematical research and software development for the University of Minnesota's Geometry Center, designing and implementing software for creating and studying possible shapes for 3 dimensional space. Currently a MacArthur Fellow, he splits his time between research and education. His present research centers on a collaboration with cosmologists, with whom he plans to test the shape of the universe using satellite data to become available in 2002-2010. His educational activities have lead to a multimedia unit for middle schools on geometry and space. The unit uses classroom activities, computer games, and video to let students explore universes that are finite but have no boundaries. Jeff is the author of the book The Shape of Space (Marcel Dekker, 1985; second edition 2002), the unit Exploring the Shape of Space (Key Curriculum Press, 2001), and numerous research and expository articles.

Title: "The Curvature of Space"

Abstract: The talk will begin with an elementary introduction to curved space, using physical models and interactive 3D graphics to build intuition and demonstrate some surprising visual effects. We'll then see how physicists' understanding of a curved, expanding universe evolved over the 20th century, leading to measurements of the microwave background radiation which are now revealing the curvature of the observable universe. But even as these measurements answer old questions about the curvature of space, they raise new questions about the matter and energy it contains.

(Intended Audience: For mathematics faculty, graduate students, and undergraduate math and physics majors. Note: The other half of the story, namely the topology of space, will be the subject of the evening lecture.)

Public lecture on Burnaby Mountain (6.00pm in AQ3005)

Title: "The Shape of Space"

Abstract: When we look out on a clear night, the universe seems infinite. Yet this infinity might be an illusion. During the first half of this presentation, computer games will introduce the concept of a "multiconnected universe". Interactive 3D graphics will then take the viewer on a tour of several possible shapes for space. Finally, we'll see how data from a small NASA satellite could soon reveal the true shape of our universe. The only prerequisites for this talk are curiosity and imagination.

(Intended Audience: For middle school and high school students, people interested in astronomy, and all members of the SFU community.)


10. Helaman and Claire Ferguson (2003/2004)

November 18, 2003 (3.30PM on Burnaby Mountain AQ3149, followed by a reception in K9509)

Helaman Ferguson is both a sculptor whose work is located in institutions and collections worldwide and an internationally known mathematician whose algorithm has been listed as one of the top ten in the twentieth century. He enjoys a CRADA between his sculpture studio and NIST which is in the third generation of cable-based metrology systems. Claire Ferguson has written extensively on Helaman's work, including the Gold Ink and Ozzie Award winning book "Helaman Ferguson: Mathematics in Stone and Bronze". She is a graduate of Smith College where she was an Ada Comstock Scholar. Together they have parented seven children.

Title: "Mathematics in Stone and Bronze"

Abstract: Helaman Ferguson's mathematical sculptures in stone and bronze celebrate ancient and modern mathematical discoveries, melding the universal languages of sculpture and mathematics. Using slides and video, Helaman and Claire trace Helaman's creations from initial concept, mathematical design, computer graphics, diamond cutting and final form. Their lectures have fascinated audiences worldwide, bringing together multiple disciplines and stimulating dialogue among them. (Back to top)

Page maintained by Jon Borwein. Last revised September 12, 2003.