Mon, January 6, 2020
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11:00am [11:00am] Aaron Charles Naber: Northwestern University:Mathematics Colloquium
Description:
Mathematics Colloquium. Speaker: Aaron Charles Naber. Affiliation: Northwestern University. Date and Time: Monday 06 January, 11:00 am - 12:00 noon. Venue: Ramanujan Hall, Department of Mathematics. Title: Analysis of Geometric Nonlinear Partial Differential Equations. Abstract: It is well known that solutions of a linear elliptic equation, for instance a harmonic function $\Delta u = 0$, are automatically smooth. Indeed, one has many ways to quantify this and understand precise estimates on solutions. In the context of nonlinear equations, this need not be the case and one may be forced to deal with a singular set $Sing(u)$. Though dimension estimates on singular sets have been understood since the 60's, it is only in the last few years that the structure of the singular sets is starting to come into focus. This talk will give an introduction to all of this, including a rough idea of the methods and results. We will study the case of nonlinear harmonic maps as it requires the least background, however these methods and extensions have been used lately in many areas (e.g. minimal surfaces, Yang-Mills, Einstein manifolds, nodal analysis and Q-valued harmonic maps, to name a few).v

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