Parameterized Morse Theory in Low-Dimensional and Symplectic Topology (14w5119)

Arriving in Banff, Alberta Sunday, March 23 and departing Friday March 28, 2014


(University of Georgia)

(University of Massachusetts)


The Banff International Research Station will host the "Parameterized Morse Theory in Low-Dimensional and Symplectic Topology" workshop from March 23rd to March 28th, 2014.

Mathematicians with diverse intellectual perspectives are gathering at the Banff International Research Station to explore and expand upon the common set of tools they are all using in their different fields, taking steps against the trend of compartmentalization so common in much of science today. This common set of tools is known as parameterized Morse theory, and the areas in which this is being applied range from the study of possible 3-dimensional spaces (like our universe) and 4-dimensional spaces (like our universe extended forwards and backwards in time), to the study of the dynamic evolution of mechanical systems, to the study of the most general ways to abstractly construct spaces of any dimension out of simple building blocks.

Morse theory is a tool which, if applied to the surface of the earth, would mark all the mountain peaks, all the deepest points in oceans and lakes, and all the saddles between mountains and between basins, and would then identify all the watersheds so we could see how water flows across the surface and whether rain falling in Banff flows to the Atlantic, the Pacific, the Arctic, or to an internal drainage basin. Parameterized Morse theory would then look at how all this information changes over time as tectonic plates rise and fall; what changes would make the rain in Banff flow to the Gulf of Mexico? The mathematicians working together in Banff will be thinking about higher-dimensional versions of exactly these kinds of questions, applied to many different generalizations of this simple idea of water flowing across the surface of the earth.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).