Talks 2019

Scholar in Residence: Drake Olejniczak, The uniform spectrum of a graph, July 22, 2019

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Analysis Seminar: Martino Fassina, University of Illinois, Non-solvability of differential operators in the flat category, Jan. 28, 2019.

ABSTRACT: In 1957 a ground-breaking three-page paper in the Annals marked the birth of CR geometry. There, Hans Lewy gave the first example of a locally non-solvable first-order linear partial differential equation. In this talk I will present a Lewy-type phenomenon for flat functions, that is, smooth functions whose derivatives are all equal to zero at a point. I will describe some of the consequences of the result, with special attention to complex analysis. The talk is based on joint work with Yifei Pan.

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COLLOQUIUM - Spring 2019

• Eric Baer, Carnegie Mellon University, The Isoperimetric Inequality and Some Results on Symmetry in Geometric Problems from the Calculus of Variations. April 3.

  • Many mathematical models in the physical sciences involve understanding how nature balances the cost of enclosing a volume of material with the amount of material to be enclosed. One fundamental tool used to understand this balance is the isoperimetric inequality, a classical result showing that for sets of fixed volume, perimeter (or surface area) is minimized when the set is a ball. We will see how the tools of mathematical analysis (calculus) and the calculus of variations interact to establish inequalities of this type, and what they tell can tell us about models of real-world phenomena.

• Alyssa Genschaw, University of Missouri - Columbia, An Introduction to Caloric Measure. April 2.

  • We first give an introduction to harmonic measure. Harmonic measure can be described from two different points of view: a probabilistic interpretation or a solution to a boundary value problem. We then define caloric measure and discuss some similarities and differences to harmonic measure.

• Alan Legg, Purdue University Fort Wayne, Some Useful Ideas from Complex Analysis. April 1.

  • The field of complex analysis finds wide application both within mathematics and in science generally. I'll give an overview of some ways in which ideas from complex analysis can help simplify and resolve questions. A special emphasis will be given to the idea of conformal mapping, where complicated shapes in a problem can be replaced by nicer ones while preserving the integrity of the problem.

• Peter Dragnev, The Mastodon Theorem - 20 Years in the Making, Feb. 6. PDF Abstract

ANALYSIS SEMINAR - Spring 2019

• Adam Coffman, Isolated CR singularities of n-manifolds in Cⁿ, March 20.

• Yifei Pan, A Unique continuation result on total differential of high order and Hardy type inequality, Feb. 18.