The Fields Institute will be hosting a series of workshops aimed at students interested in research level mathematics. For each workshop, the Fields Undergraduate Network has invited four researchers to speak about interesting branches of analysis. At the end of the day, the four researchers will participate in a 1-hour panel discussion on current questions of interest in analysis touching on progress as well as historical developments and overviews.

Establishment of the Fields Undergraduate Network (FUN) will foster activity both at the Fields Institute and at each of the universities affiliated with Fields. It will serve to simultaneously develop students’ conceptions of research in mathematics as well as to bring students and researchers together. We would like to highlight the interactions between different fields of analysis by having our discussion led by researchers working on a variety of different problems in the same field.

10:00 a.m. - Introduction: Richard Cerezo and FUN Lecture "Title and Abstract: TBA"

10:15 a.m. - Deping Ye, Fields Institute Invitation to Geometry of Convexity and Quantum States in High Dimension

11:15 a.m. - Spyros Alexakis, University of Toronto, "Minimal surfaces in hyperbolic 3-space and renormalized area"

1:00 p.m. - Boris Khesin, University of Toronto "Nondegenerate curves and the Kortweg-de Vries equation"

A plane curve is called nondegenerate if it has no inflection points. How many classes of closed nondegenerate curves exist on a sphere? We are going to see how this geometric problem, solved in 1970, reappeared along with its generalizations in the context of the Korteweg-de Vries (KdV) equation. We will also discuss how the KdV equation can be viewed as the geodesic flow on an infinite-dimensional group.

2:15 p.m. - Maung Min-Oo, McMaster University, "The Sign of Curvature"

In this talk I will first introduce the notion of curvature, the most fundamental invariant in Geometry. I will describe the three main types of curvatures that Riemannian geometers use: sectional, Ricci and scalar. The main theme of the talk is then to explore the significance of the sign of curvature. The message is that imposing conditions on the curvature has global topological implications. I will begin with a selected survey of some classical results. I will then give a rough indication of the basic ideas and techniques used to establish these results. I will end my talk with a few open problems that I find interesting.

3:00 p.m. - Discussion

- · Saturday, Sep. 25, 2010: Research in Analysis Workshop (Ed Barbeau, Eli Glasner, Vladimir Pestov, Eric Sawyer)
- · Saturday, Oct. 23, 2010: Research in Geometry Workshop (Spyros Alexakis, Boris Khesin, Maung Minoo)
- · Saturday, Mar. 05, 2011: Number Theory and Cryptography (Hugh Williams (Calgary), Leo Goldmakher (Toronto), Henry Kim (Toronto))