Special Colloquium Series On Analysis

In this series of talks, I explore pieces of analysis that I find interesting for one reason or another, at a level that a motivated, advanced undergraduate can keep up with. The intended audience ranges from those undergraduates to graduate students and even faculty who find the titles and abstracts interesting. I am hoping that physics and engineering students -- actually anybody who uses analysis -- will find these lectures interesting and inspiring. The frequency of these talks will vary. I intend to give them Tuesday's from 4-5 and will begin in Neill Hall 5W.

Lecture 1

  • When and Where: October 26, 4:10 - 5:00, Neill Hall 5W (basement of Neill Hall)

  • Title: Uniform Boundedness Principle and Weak Convergence: how 

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    can look like (almost) any function, yet 
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    as 
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  • Abstract: In this talk I will explore some issues that came up when I was designing a recent exam and ended up reminding myself of some functional analysis. In keeping with the aim of this series of talks, the level will be such that advanced undergraduates will be able to follow the talk, assuming they are willing to pedal a bit to keep up. Weak convergence will be introduced and then a curious property about this kind of convergence will be examined. The uniform boundedness principle will enter when we try to get too crazy, effectively reigning in a complete loss of our bearings. For those who have never heard of weak convergence, it suffices to say that it is ubiquitous in analysis and that, if you are a first year graduate student, you will see it in 502 next semester. If you are an advanced undergraduate, it is not too early to start learning some functional analysis, as it can be very illuminating in mathematics, physics and engineering.

Upcoming talks

  • Hilbert Spaces: why infinite dimensional spaces are almost no different than three-space ... and the big beasts that live in the space between 'almost no' and 'no'.

  • Derivatives in Hilbert Spaces: Why you have known how to derive Euler-Lagrange equations (whatever they are!) ever since you understood the equation y = ax+b.

  • Steiner-Minkowski and Tubular Neighborhoods: convex sets, sets with positive reach and curvature (measures)

  • Measure Theory for the Geometrically Inclined: Lebesgue, Radon and Hausdorff measures and all that.