Department of


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

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 24, 2017

4:00 pm in 131 English Building,Tuesday, January 24, 2017

Organizational Meeting

(UIUC Math)

Abstract: A brief meeting to schedule speakers for the semester.

Tuesday, January 31, 2017

4:00 pm in 131 English Building,Tuesday, January 31, 2017

Well-posedness for the "Good" Boussinesq on the Half Line

Erin Compaan   [email] (Erin Compaan)

Abstract: 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

Banach Lattices

Chris Gartland   [email] (UIUC Math)

Abstract: 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

John's ellipsoid theorem and applications

Matthew Romney   [email] (UIUC Math)

Abstract: 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

A variant of Gromov's H\"older equivalence problem for small step Carnot groups

Derek Jung   [email] (UIUC Math)

Abstract: 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

The Waist Inequality and Quantitative Topology

Hadrian Quan   [email] (UIUC Math)

Abstract: 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

4:00 pm in 131 English Building,Tuesday, April 18, 2017

Free rods under tension and compression: cascading and phantom spectral lines

Jooyeon Chung (UIUC Math)

Abstract: 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.

Tuesday, May 2, 2017

4:00 pm in 131 English Building,Tuesday, May 2, 2017

Partial synchronization in dynamical systems

Lan Wang (UIUC Math)

Abstract: In nature, synchronization phenomena are ubiquitous. In this talk, we will focus on a specific type of partial synchronization. Basically, partial synchronization occurs due to two reasons: the inhomogeneity of oscillators and the inhomogeneity of coupling strength. For the first reason, a famous representative model is the Kuramoto Model. A sufficient condition of partial synchronization will be given for this model. For the second reason, we consider a slightly different model and analyze its partial synchronized state. Since this state is so fascinating and unexpected, it is specially named as "Chimera state". In the end, some open questions will be discussed. This talk should be approachable to all math graduate students.