Intellectual merit. Over the last 40 years, there have been tremendous advances in complex analysis, broadly understood. It would be perhaps impossible to have a single conference taking a look back at everything that has been done, to review current developments, and to peek into the future of the entire field. However, a look at complex analysis with a particular view towards the mathematics of David Drasin and Linda Sons covers many of the core areas and offers a reasonable foundation for taking stock of a substantial number of developments. The topics of the proposed Conference on Complex Analysis, to be held at the University of Illinois at Urbana-Champaign in May, 2010, will be value distribution, classical and p-harmonic potential theory, normal families, complex differential equations, and symmetrization methods.
Broader impact. The Conference will bring together many of the significant contributors to the development of complex analysis in the last forty years. It will thus provide perspective, both for the senior and junior participants, on the advances in recent times in the areas of focus of the Conference. With many younger mathematicians attending, both as speakers in the parallel sessions and as participants in informal discussions, the Conference should add to the vitality of the subject in the coming years. In fact, three of the main speakers received doctoral degrees less than five years ago. The organizers have been mindful that one effective way to contribute to the health of complex analysis in the future is to encourage greater participation among groups who in the past have not had representation in large numbers in the field. Accordingly, one of the two mathematicians whose work constitutes a theme of the Conference is a woman and women participants will deliver plenary talks as well as parallel session talks.
was held at the University of Illinois at Urbana-Champaign in May 2010. Complex analysis is a branch of mathematics concerned with properties of functions involving square roots of negative numbers. It has many practical applications in science and engineering, including fluid flow, electrostatic potential, and steady state temperature distributions. On the theoretical side, it provides the natural context in which to understand power series, a topic typically first introduced to students in a second calculus course. Complex analysis is a subject studied by most undergraduate mathematics majors, and is an essential component of the education of any mathematics graduate student. The Conference on Complex Analysis, featuring speakers from nine different countries, provided an opportunity for workers in the field to discuss recently proved theorems and future directions in the discipline. There were eight plenary addresses by senior researchers in the field, thirty-nine additional invited lectures, and many informal interactions among conference participants. It is expected that the dissemination of recent results, as well as informal discussion of ideas in the germination phase, will lead to significant future results. Speakers and registrants at the conference were a diverse group, with substantial participation by young researchers, women, and members of populations traditionally underrepresented in mathematics.
