Seminar Calendar
for events the week of Thursday, June 30, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, June 28, 2016

REU Seminar
12:00 pm   in 345 Altgeld Hall,  Tuesday, June 28, 2016
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Submitted by santana.
Derek Jung (University of Illinois at Urbana-Champaign)
Density of "nice" functions in Sobolev spaces
Abstract: A Sobolev space consists of integrable functions $f:X\to Y$ with integrable derivative, where $X$ and $Y$ are "sufficiently'' Euclidean manifolds. One can naturally define metrics on these spaces, leading one to ask the following question: Are "nice'' functions dense in a Sobolev space? Here, "nice'' depends on $X$ and $Y$ and may refer to smooth, Lipschitz, etc. In this talk, I will introduce Sobolev spaces between manifolds and discuss my current research of investigating the density of Lipschitz functions in Sobolev spaces of functions from balls to a class of sub-Riemannian manifolds, Jet spaces.

Thursday, June 30, 2016

REU Seminar
12:00 pm   in 345 Altgeld Hall,  Thursday, June 30, 2016
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Submitted by santana.
Bruce Reznick (University of Illinois at Urbana-Champaign)
What does '>' really mean?
Abstract: One of the favorite serious games of mathematicians is to take a familiar idea in a familiar situation, extract its essence, and try to apply it in a more general environment. This talk will be about moving the idea of ">" from the real numbers to any field. You can't always do it, but when you can, you discover the importance of writing objects as sums of squares. It can also happen that a field has more than one equally valid definition of ">" and an element x can be positive in one and negative in another.