# Math Calendar

 Categories: Choose a category... View all categories _______________________ Biomath Seminar Colloquium Computational Analysis Seminar Departmental Student Awards Faculty Meeting Graph Theory and Combinatorics Seminar Informal von Neumann Algebras Seminar Noncommutative Geometry and Operator Algebras Seminar Partial Differential Equations Seminar Subfactor Seminar Symplectic and Differential Geometry Seminar Topology and Group Theory Seminar Undergraduate Seminar Universal Algebra and Logic Seminar Vandy Math Club RSS

###### » Seminar Pages

September 17, 2013 4:10 pm (Tuesday)

## The Definable Principal Subcongruences Problem is Undecidable

Matthew Moore, Vanderbilt University
Location: Stevenson 1310

For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is undecidable. Using this, we present another proof that A. Tarski's finite basis problem is undecidable.

September 18, 2013 3:10 pm (Wednesday)

## Compressed Sensing with Equiangular Tight Frames

Matt Fickus, Air Force Institute of Technology
Location: Stevenson 1307

Compressed sensing (CS) is changing the way we think about measuring high-dimensional signals and images. In particular, CS promises to revolutionize hyperspectral imaging. Indeed, emerging camera prototypes are exploiting random masks in order to greatly reduce the exposure times needed to form hyperspectral images. Here, the randomness of the masks is due to the crucial role that random matrices play in CS. In short, in terms of CS's restricted isometry property (RIP), random matrices far outshine all known deterministic matrix constructions. To be clear, for most deterministic constructions, it is unknown whether this performance shortfall (known as the "square-root bottleneck") is simply a consequence of poor proof techniques or, more seriously, a flaw in the matrix design itself. In the remainder of this talk, we focus on this particular question in the special case of matrices formed from equiangular tight frames (ETFs). ETFs are overcomplete collections of unit vectors with minimal coherence, namely optimal packings of a given number of lines in a Euclidean space of a given dimension. We discuss the degree to which the recently-introduced Steiner and Kirkman ETFs satisfy the RIP. We further discuss how a popular family of ETFs, namely harmonic ETFs arising from McFarland difference sets, are particular examples of Kirkman ETFs. Overall, we find that many families of ETFs are shockingly bad when it comes to RIP, being provably incapable of exceeding the square-root bottleneck. Such ETFs are nevertheless useful in variety of other real-world applications, including waveform design for wireless communication and algebraic coding theory.

September 18, 2013 4:10 pm (Wednesday)

## Relatively Hyperbolic Groups with the Falsification by Fellow Traveler Property

Yago Antolin Pichel, Vanderbilt University
Location: Stevenson 1310

The falsification by fellow traveler property is a property of the Cayley graph of a group. It was introduced by Neumann and Shapiro, it has several implications. For example, it implies the regularity of the language of geodesics, the rationality of the growth series or having a quadratic Dehn function. I will explain how to find a generating set with the falsification by fellow traveler property for groups relatively hyperbolic to groups with a generating set with this property. This is a joint work with Laura Ciobanu.

September 20, 2013 3:10 pm (Friday)

## Optimal Regularity in the Thin Obstacle Problem with Lipschitz Variable Coefficients

Mariana Smit Vega Garcia, Purdue University
Location: Stevenson 1307

We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator $L = div(A(x)\nabla)$ with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when $L = \Delta$, the variational solution has the optimal interior regularity. We achieve this by proving some new monotonicity formulas for an appropriate generalization of Almgren's frequency functional. This is joint work with Nicola Garofalo.

September 20, 2013 4:10 pm (Friday)

## $W^*$-Superrigidity for Arbitrary Actions of Central Quotients of Braid Groups

Ionut Chifan, University of Iowa
Location: Stevenson 1432

For any $n > 4$ let $\tilde B_n = B_n/Z(B_n)$ be the quotient of the braid group $B_n$ through its center. We prove that any free ergodic probability measure preserving (pmp) action $\tilde B_n \ca (X, \mu)$ is virtually $W^*$-superrigid: whenever $L^\infty (X,\mu)\rtimes \tilde B_n =L^\infty (Y,\nu)\rtimes \Lambda$, for an arbitrary free ergodic pmp action $\Lambda \ca (Y, \nu)$ it follows that the actions $\tilde B_n \ca X,\Lambda \ca Y$ are virtually conjugate. Moreover, we prove that the same holds if $\tilde B_n$ is replaced with any finite index subgroup of the direct product $\tilde B_{n_1} \times \cdots \times \tilde B_{n_k}$, for some $n_1, \ldots , n_k > 4$. The proof uses a dichotomy theorem of Popa-Vaes for normalizers inside crossed products by free groups in combination with a $OE$-superrigidity theorem of Kida for actions of mapping class groups. This is based on joint work with A. Ioana and Y. Kida.