International Research in Real Analysis and Dynamical Systems

Sites and Basic Information
The host institutions were carefully chosen for a variety of interrelated reasons. First, the scale of research in real analysis at each institution is relatively large and comprises a full range of researchers from professors through lecturers and graduate students to undergraduates. Each host program has contributed literally hundreds of research papers to the literature in a wide range of journals from specialized journals such as Real Analysis Exchange or Ergodic Theory and Dynamical Systems to more general journals such as the Journal of the London Mathematical Society and the Proceedings of the American Mathematical Society and the Transactions of the American Mathematical Society. The research program at each institution is solid but not so high-powered or demanding of experience and background that an undergraduate student would be unable to contribute to it in the short span of 10 weeks. This is important as it means NSF international scholars are more likely to find a niche where they can contribute in a meaningful way and not simply remain spectators. At each host institution, a scholar will be assigned a specific mentor who will help select an appropriate research project and oversee the work. Co-PI Humke is a research collaborator with one of the senior research mathematicians at each location and is personally acquainted with several real analysts at each location.

Second, the research sites were selected because they will provide the pedagogical benefits of a Òresearch apprenticeshipÓ within a more collective and hierarchical academic culture in which the ÒmasterÓ establishes the atmosphere of the ÒstudioÓ and presides over the ÒjourneymenÓ who coach the Òapprentices.Ó This provides a pedagogical context very different from the Òlaissez-faire individualismÓ of the American college or university. While the NSF international scholar will meet frequently with his/her mentor to follow a course of research and study, the real value of the scholarship will be the studentÕs apprenticeship in the collective research life of the university.

The Mathematical Institute at Silesian University at Opava, Czech Republic The Department of Mathematical Analysis of the Mathematical Institute will host the St. Olaf NSF international scholars in the Czech Republic. Led by the Director of the Institute, Professor Jaroslav Sm’tal, the research group at Opava has a strong program publishing in various aspects of dynamics, but focusing on one-dimensional dynamical systems. Specifically, Sm’tal and his group have been leaders in recent work concerning the notion of distributional chaos initiated by Bert Schweizer (University of Massachusetts). Another recent aspect of the work at Opava has involved the relation between functional equations and discrete dynamical systems; this work has resulted in a series of papers between mathematicians from several groups but most prominently the functional equations group at Graz. Of the younger people at Opava, Petra Sindelarova and Marta Stefankova have been quite active in the past two or three years. Each would be an ideal mentor for a NSF international scholar. Other active younger people include Marek Lampart, Gabriela Dvornikova, and Zdenek Kocan. Such younger scholars will provide intra-generational role models with whom the scholars are more likely to form lasting connections.

Information concerning the NSF international scholars will be shared and discussed in some detail with Professor Sm’tal about a month before the on-site program begins. Shortly after the scholar arrives in Opava, Professor Sm’tal will discuss various research options with the scholars and then assign mentors according to the interests, expectations and ability of the scholar. He will continue to monitor progress with the assigned mentor. Via email, Professor Sm’tal will keep the co-PIs at St. Olaf apprised of student progress and any problems (mathematical or otherwise) which may surface.

The parent university, Silesian University, is the youngest university in the Czech Republic, founded in 1991. It has a student body of over 3,500 students. The university is situated in Opava, the historical center of the Czech part of Silesia, a region in the northeast of the Czech Republic. Silesian University has developed rapidly as a modern internationally focused institution. It is a university with a wide range of programs of study and significant contacts and exchanges with universities in Europe and overseas. It organizes conferences at an international level and undertakes extensive and intensive publication activities. Opava is a city with rich cultural history and home of the oldest and third-largest museum in the Czech Republic - the Silesian Regional Museum. Other cultural establishments include the Silesian Theatre and the Opera House, the Regional Archives and a number of libraries.

The University is the seat of the editorial office of Differential Geometry and its Applications Ð a renown international journal Ð published by Elsevier Science Publishers / North Holland. The Mathematical Institute library, freely available to the NSF international scholars, includes more than 50 international mathematical journals. Students will also have access to computer labs on campus, each equipped with both PCs and Macintosh. All computer labs are connected to the Internet.

The Mathematical Institute at Lodz University, Poland The Department of Real Analysis in the Faculty of Mathematics will serve as host for the NSF international scholars in Poland. The group of real analysts at Lodz is led by Professor W_adys_aw Wilczynski, who has been the intellectual leader of this group for many years. Now, however, there are several other professors among the active researchers and they have contributed a great deal in their own right. These include Professors Miroslaw Filipczak and Elzbieta Wagner-Bojakowska and Associate Professors (dr. hab.) Marek Balcerzak and Ryszard Pawlak. In addition, there are about 15 other research mathematicians ranging in experience from associate professor to beginning researcher. This particular school focuses on attacking problems in real analysis and measure theory using the topological methods made famous by the Polish school. Specifically they have identified density topologies closely connected to measures, e.g. Lebesgue measure and the usual Hausdorff measures on the real line. A favorite topic to which this school has returned time and again is the classical duality between theorems involving sets of measure zero and those involving sets of the first Baire category. These are fundamental topics linking the geometry and topology of functions with the notions of measure and several of the ongoing areas of interest would be accessible to bright and enterprising undergraduates. Important, too, is the supportive and intellectually open research atmosphere that was crafted and is now carefully nurtured by Professor Wilczyiski and the other leaders of this school.

As with the Institute at Opava, information concerning the NSF international scholars in Lodz will be shared and discussed in some detail with Professor Wilczynski about a month before the on-site program begins. Shortly after the scholar arrives in Opava, Professor Wilczynski will discuss various research options with him or her and then assign mentors according to the interests, expectations and ability of the scholar. He will continue to monitor progress with the assigned mentor. Via email, Professor Wilczynski will keep the co-PIs at St. Olaf apprised of student progress and any problems (mathematical or otherwise) which may surface.

The Faculty of Mathematics at Lodz University was founded on June 1, 1996 as a result of a partitioning of the Faculty of Mathematics, Physics and Chemistry into two separate divisions. The Faculty of Mathematics employs 121 teaching and research staff including 14 Professors, 14 Associate Professors, 51 Assistant Professors, and 42 instructors with M.Sc. degrees. Six hundred and forty students are enrolled in day courses and 840 more attend evening and extramural courses.

Facilities for the Faculty of Mathematics are located in the city center next to an antique park. These include the faculty library with more than 36,000 volumes accessible. This is a fully equipped research library and it is also well equipped with preprints, scientific journals and on-line resources. There are nine computer labs containing almost 200 computers. All students have unlimited access to the network, including the Internet.

Both institutions are well prepared to provide intellectual atmospheres that will be accessible to and stimulating for St. Olaf undergraduates.

Questions? Click here: reuapp@stolaf.edu