Seminar Calendar
for Graduate Student Analysis Seminar events the year of Friday, April 21, 2017.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2017             April 2017              May 2017
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Tuesday, January 24, 2017

4:00 pm   in 131 English Building,  Tuesday, January 24, 2017
 Del Edit Copy
Submitted by compaan2.
 (UIUC Math)Organizational MeetingAbstract: A brief meeting to schedule speakers for the semester.

Tuesday, January 31, 2017

4:00 pm   in 131 English Building,  Tuesday, January 31, 2017
 Del Edit Copy
Submitted by compaan2.
 Erin Compaan   [email] (Erin Compaan)Well-posedness for the "Good" Boussinesq on the Half LineAbstract: I'll present some recent results on well-posedness for the "good" Boussinesq equation on the half line at low regularities. The method is one introduced by Erdogan and Tzirakis, which involves extending the problem to the full line and solving it there with Bourgain space methods. A forcing term ensures that the boundary condition is enforced. I'll introduce the method and talk about the estimates required to close the argument. This is joint work with N. Tzirakis.

Tuesday, February 14, 2017

4:00 pm   in 131 English Building,  Tuesday, February 14, 2017
 Del Edit Copy
Submitted by compaan2.
 Chris Gartland   [email] (UIUC Math)Banach LatticesAbstract: Many classical spaces such as $C(K)$ and $L^p(\mu)$ carry not only a normed linear structure, but also a lattice structure which behaves well with respect to the norm and vector space operations. The abstraction of this structure gives rise to objects known as Banach lattices, and classical theorems from point-set topology and measure theory can be proved in this purely abstract setting. We'll define the category of Banach lattices and concentrate on the specific subcategories of M-spaces and abstract $L^p$-spaces. We'll outline the Kakutani representation theorems for the spaces, in the former case establishing a duality between the category of M-spaces and the category of compact Hausdorff spaces. Nutter Butters will be provided.

Tuesday, February 28, 2017

4:00 pm   in 131 English,  Tuesday, February 28, 2017
 Del Edit Copy
Submitted by compaan2.
 Matthew Romney   [email] (UIUC Math)John's ellipsoid theorem and applicationsAbstract: We will discuss and prove a beautiful piece of classical mathematics, a theorem of Fritz John (1948) which characterizes the ellipsoid of maximal volume contained in a convex body in Euclidean space. Among many other applications, it has proven useful in my area of research, quasiconformal mappings.

Tuesday, March 7, 2017

4:00 pm   in 131 English Building,  Tuesday, March 7, 2017
 Del Edit Copy
Submitted by compaan2.
 Derek Jung   [email] (UIUC Math)A variant of Gromov's H\"older equivalence problem for small step Carnot groupsAbstract: This is the second part of a talk I gave last semester in the Graduate Geometry/Topology Seminar. A Carnot group is a Lie group that may be identified with its Lie algebra via the exponential map. This allows one to view a Carnot group as both a sub-Riemannian manifold and a geodesic metric space. It is then natural to ask the following general question: When are two Carnot groups equivalent? In this spirit, Gromov studied the problem of considering for which $k$ and $\alpha$ there exists a locally $\alpha$-H\"older homeomorphism $f:\mathbb{R}^k\to G$. Very little is known about this problem, even for the Heisenberg groups. By tweaking the class of H\"older maps, I will discuss a variant of Gromov's problem for Carnot groups of step at most three. This talk is based on a recently submitted paper. Some knowledge of differential geometry and Lie groups will be helpful.

Tuesday, April 4, 2017

4:00 pm   in 131 English Building,  Tuesday, April 4, 2017
 Del Edit Copy
Submitted by compaan2.
 Hadrian Quan   [email] (UIUC Math)The Waist Inequality and Quantitative TopologyAbstract: If F is a continuous map from the unit n-Sphere to $\mathbb{R}^q$, then one of its fibers has (n-q)-measure at least that of an (n-q)-dimensional equator. This estimate joins other results like the Isoperimetric Inequality for being simple to state and much harder to prove than at first glance. We’ll discuss the history of this result and some of its relations to topology, geometry, and combinatorics. Time permitting, we shall also sketch a proof of Gromov’s with non-optimal constant.

Tuesday, April 18, 2017

 Jooyeon Chung (UIUC Math)Free rods under tension and compression: cascading and phantom spectral linesAbstract: In this talk, I will consider the spectrum of the one-dimensional vibrating free rod equation $u'''' − \tau u'' = \mu u$ under tension ($\tau > 0$) or compression ($\tau < 0$). The eigenvalues $\mu$ as functions of the tension/compression parameter $\tau$ are shown to exhibit three distinct types of behavior. In particular, eigenvalue branches in the lower half-plane exhibit a cascading pattern of barely-avoided crossings. I will graphically illustrate properties of the eigenvalue curves such as monotonicity, crossings, asymptotic growth, cascading and phantom spectral lines.