Department of Mathematics
http://as.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityWed, 28 Jan 2015 19:30:37 +0000enhourly1http://wordpress.org/?v=3.1.4Graduate Student Tea
http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-12/
http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-12/#commentsWed, 28 Jan 2015 19:30:37 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1691http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-12/feed/0Circuit graphs and relative connectivity
http://as.vanderbilt.edu/math/2015/01/circuit-graphs-and-relative-connectivity/
http://as.vanderbilt.edu/math/2015/01/circuit-graphs-and-relative-connectivity/#commentsMon, 26 Jan 2015 20:10:48 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1693Induction arguments on k-connected graphs can be difficult because subgraphs of a k-connected graph are not necessarily k-connected. In 1966 David Barnette found a way to get around this for 3-connected planar graphs, by defining something called a “circuit graph”. We review some of the results obtained using circuit graphs, including the fact that a 3-connected planar graph has a spanning tree of maximum degree at most 3, and a spanning closed walk visiting each vertex at most twice. Then we show how the notion of circuit graph can be extended in a very general way, to graphs that are “k-connected relative to S”, where S is a set of vertices. We establish some basic properties of this idea. This is joint work with Dan Biebighauser of Concordia College in Moorhead, Minnesota.
]]>http://as.vanderbilt.edu/math/2015/01/circuit-graphs-and-relative-connectivity/feed/0Representations and Universal Norm for the Tube Algebra of Rigid C*-tensor categories
http://as.vanderbilt.edu/math/2015/01/representations-and-universal-norm-for-the-tube-algebra-of-rigid-c-tensor-categories/
http://as.vanderbilt.edu/math/2015/01/representations-and-universal-norm-for-the-tube-algebra-of-rigid-c-tensor-categories/#commentsFri, 23 Jan 2015 21:10:34 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1650In the finite depth case, the tube algebra of a rigid C*-tensor category is finite dimensional, and its representation category is known to be equivalent to the Drinfeld center of the category. In the infinite depth case, the tube algebra is infinite dimensional, but the category of Hilbert space representations of the tube algebra retains the structure of a braided weakly rigid monoidal category. In analogy with discrete groups, we show that one can define a universal norm on the tube algebra and that Hilbert space representations of the tube algebra are given by representations of the C* closure of the tube algebra with respect to this norm. Recently, Popa and Vaes defined a universal norm on the fusion algebra of a rigid C*-tensor category, allowing them to define various approximation properties (Amenability, Property T, Haageruup) for rigid C*-tensor categories which they show agree with previously existing definitions from the subfactor case. The fusion algebra is naturally identified as a sub-algebra of the tube algebra, and we will show that the restriction of our norm to this subalgebra agrees with the universal norm defined by Popa and Vaes. This is joint work with Shamindra Ghosh.
]]>http://as.vanderbilt.edu/math/2015/01/representations-and-universal-norm-for-the-tube-algebra-of-rigid-c-tensor-categories/feed/0Exponential frames on unbounded sets
http://as.vanderbilt.edu/math/2015/01/talk-title-tba-3/
http://as.vanderbilt.edu/math/2015/01/talk-title-tba-3/#commentsFri, 23 Jan 2015 20:10:32 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1607In contrast to orthonormal and Riesz bases, exponential frames (i.e., ‘over complete bases’) are in many cases easy to come by. In particular, it is not difficult to show that every bounded set of positive measure admits an exponential frame. When unbounded sets (of finite measure) are considered, the problem becomes more delicate. In this talk I will discuss a joint work with A. Olevskii and A. Ulanovskii, where we prove that every such set admits an exponential frame. To obtain this result we apply one of the outcomes of Marcus, Spielman and Srivastava’s recent solution of the Kadison-Singer conjecture. This talk is part of the Shanks Workshop on “Uncertainty Principles in Time Frequency Analysis”
]]>http://as.vanderbilt.edu/math/2015/01/talk-title-tba-3/feed/0Graduate Student Tea
http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-11/
http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-11/#commentsWed, 21 Jan 2015 19:30:52 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1648http://as.vanderbilt.edu/math/2015/01/graduate-student-tea-11/feed/0Equations in groups
http://as.vanderbilt.edu/math/2015/01/equations-in-groups/
http://as.vanderbilt.edu/math/2015/01/equations-in-groups/#commentsFri, 16 Jan 2015 21:10:05 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1643Two natural questions in algorithmic group theory are: is it decidable whether an equation whose coefficients are elements of a given group has at least one solution in that group? And if an equation has solutions, how can we best describe them? The talk will start with a survey on this topic, and will conclude with a language theoretic characterization of the solutions of equations in free groups (joint with M. Elder and V. Diekert) and results concerning the asymptotic behavior of satisfiable homogeneous equations in surface groups (with Y. Antoln and N. Viles).
]]>http://as.vanderbilt.edu/math/2015/01/equations-in-groups/feed/0Special Colloquium
http://as.vanderbilt.edu/math/2015/01/special-colloquium-3/
http://as.vanderbilt.edu/math/2015/01/special-colloquium-3/#commentsWed, 14 Jan 2015 21:10:04 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1593http://as.vanderbilt.edu/math/2015/01/special-colloquium-3/feed/0Topology Preliminary Exam
http://as.vanderbilt.edu/math/2015/01/topology-preliminary-exam/
http://as.vanderbilt.edu/math/2015/01/topology-preliminary-exam/#commentsWed, 14 Jan 2015 19:00:49 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1628http://as.vanderbilt.edu/math/2015/01/topology-preliminary-exam/feed/0Special Colloquium
http://as.vanderbilt.edu/math/2015/01/special-colloquium-2/
http://as.vanderbilt.edu/math/2015/01/special-colloquium-2/#commentsTue, 13 Jan 2015 21:10:14 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1591http://as.vanderbilt.edu/math/2015/01/special-colloquium-2/feed/0Special Colloquium
http://as.vanderbilt.edu/math/2015/01/splittings-suspension-flows-and-polynomials-for-free-by-cyclic-groups/
http://as.vanderbilt.edu/math/2015/01/splittings-suspension-flows-and-polynomials-for-free-by-cyclic-groups/#commentsThu, 08 Jan 2015 21:10:35 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1587http://as.vanderbilt.edu/math/2015/01/splittings-suspension-flows-and-polynomials-for-free-by-cyclic-groups/feed/0