A metric space is multiended if it admits a bounded subset whose complement has at least two unbounded connected components. For instance, the line is multiended but higher-dimensional Euclidean spaces are not. In the late sixties, Stallings has given a remarkable characterization of those finitely generated groups whose Cayley graph is multiended; the only such torsion-free groups are free products of two nontrivial groups! A key part of the proof is the construction of a action on a tree; in the seventies, the study of general group actions on trees was achieved by Bass and Serre. In the meantime, the study of multiended Schreier graphs was started by Abels and Houghton, and a remarkable connection with nonpositively curved cube complexes was discovered by Sageev twenty years later. While outstanding applications of cube complexes have been made since then, I will try to focus on the question of understanding which finitely generated groups admit a multiended Schreier graph. Tea at 3:30 pm in SC 1425.

A character on a group is a positive definite function which takes the identity to 1 and is constant on conjugacy classes. Characters on a finite group gives an essential tool for understanding the representation theory of the group and motivated by this Thoma in 1964 initiated the study of characters on infinite groups. In 1966 Kirillov classified all characters on GL_n(k), and SL_n(k) for k a field and n \geq 2, excluding the case of SL_2(k). A number of other classification results have since been obtained for other groups by Ovcinnikov, Vershik, Kerov, and more recently by Bekka, Dudko, and Medynets, however the classification for SL_2(k) has not been completed. In my talk I will present the classification for SL_2(k) and SL_2 of some other rings and give some applications of these results. This is based on joint work with Andreas Thom.

nos-o-co-mi-al  (adjective)  - originating or occurring in a hospital
“get down R0, know your place, do not torment the human race”
primum non nocere – first, do no harm
Nosocomial epidemics are an increasing threat to society. The microbes that cause these epidemics are increasingly resistant to antibiotics. In the US they cause more than 100,000 deaths each year and that number is increasing. R0 (pronounced R-naught) is a quantity derived from mathematical models that predict the course of an epidemic. It is obtained from various parameters that determine the transmission dynamics of the infection. If R0 < 1, then the epidemic will abate. If R0 > 1, then the epidemic will worsen. The Hippocratic oath is the promise of physicians to not make the condition of a patient worse. It is the fundamental precept of medicine. I will tell you how all these are connected. I will also tell you how to avoid being infected by a nosocomial infection. Nosocomial infections occur in specific locations in the US, and only in these locations. You will never suffer a nosocomial infection if you do not go to one of these locations. I will tell you where these locations are. 

The main aim of talk is twofold. Firstly, to present an elementary method based on Farkas' lemma for rationals on how to embed any finite partial subalgebra of a linearly ordered MV-algebra into $\mathbb Q\cap [0,1]$ and then to establish a new elementary proof of the completeness of the Lukasiewicz axioms. Secondly, to present a direct proof of Di Nola's Representation Theorem for MV-algebras and to extend his results to the restriction of the standard MV-algebra on rational numbers.

We show that the explicit ALE Ricci-flat Kahler metrics constructed by Eguchi-Hanson, Gibbons-Hawking, Hitchin and Kronheimer, and their free quotients are Tian-Yau metrics. The proof relies on a construction of appropriate compactifications of Q-Gorenstein smoothings of quotient singularities as log del Pezzo surfaces. Time permitting, a geometric description of the compactifications will be provided. This is a joint work with I. Suvaina.

A quadrangulation is a 2-cell embedded graph where every face is a quadrangle. An even triangulation is a 2-cell embedded graph where every face is a triangle and every vertex degree is even. A triangulation on the sphere is 3-chromatic if and only if it is an even triangulation. In this talk, we show that any quadrangulation can be extended to an even triangulation by adding diagonal edges to all quadrangle faces. We also determine the number of distinct even triangulations. This is joint work with Atsuhiro Nakamoto and Kenta Ozeki.

Abstract is available at: http://sitemason.vanderbilt.edu/files/eVpAGc/TangVanderbilt.pdf

In past work, we define a notion of l^{p}-Dimension for uniformly bounded Banach space representations of a sofic group. This dimension is equal to the von Neuamn dimensnion, when H is a unitary representation of G contained in a multiple of the left-regular representation. We also computed this dimension for central natural representations of a sofic group, including direct sums of the translation action on l^{p}(G), and the multiplication action on L^{p}(L(G)). In this work, we shall explain how to define this notion of l^{p}-Dimension for representations of a sofic equivalence relation. When this equivalence relation satisfies a certain "finite presentation" assumption, we define an analogue of l^{2}-Betti numbers (or really l^{2}-Betti number +1) in the l^{p}-case. We can then connect some natural questions about this dimension with the cost versus l^{2}-Betti number conjecture.

We discuss a directionally sensitive time-frequency decomposition and representation of functions. The coefficients of this representation allow one to measure the "amount'' of frequency the function (signal, image) contains in a certain time interval, and also in a certain direction. This has been previously achieved using a version of wavelets called ridge lets, but in this work we discuss an approach based on time-frequency or Gabor elements. Applications to image processing are discussed. Tea at 3:30 pm in SC 1425.