Department of Mathematics
http://as.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityWed, 29 Oct 2014 21:10:45 +0000enhourly1http://wordpress.org/?v=3.1.4Highly Transitive Actions and Acylindrical Hyperbolicity
http://as.vanderbilt.edu/math/2014/10/highly-transitive-actions-and-acylindrical-hyperbolicity/
http://as.vanderbilt.edu/math/2014/10/highly-transitive-actions-and-acylindrical-hyperbolicity/#commentsWed, 29 Oct 2014 21:10:45 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1416I will discuss my work in progress with Michael Hull. We prove that every countable acylindrically hyperbolic group admits a highly transitive action with finite kernel. This theorem uniformly generalizes many previously known results and allows us to answer a question of Garion and Glassner on the existence of highly transitive actions of mapping class groups. It also implies that, in certain geometric and algebraic settings, transitivity degree of a faithful permutation representation of an infinite groups can only take two values, namely 1 and infinity. Further, for any countable group G admitting a highly transitive faithful action, we prove the following dichotomy: Either G contains a normal subgroup isomorphic to the infinite alternating group or G resembles a free product in a certain precise sense. We discuss applications of this theorem to the study of universal theory and mixed identities of acylindrically hyperbolic groups.
]]>http://as.vanderbilt.edu/math/2014/10/highly-transitive-actions-and-acylindrical-hyperbolicity/feed/0Graduate Student Tea
http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-6/
http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-6/#commentsWed, 29 Oct 2014 19:30:37 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1436http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-6/feed/0Much Ado About Knotting
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-7/
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-7/#commentsTue, 28 Oct 2014 23:00:11 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=1227“What is your favourite kind of math?”
“Knot theory.”
“Yeah, me either”.
]]>http://as.vanderbilt.edu/math/2014/10/talk-title-tba-7/feed/0Large Dimension and Standard Examples
http://as.vanderbilt.edu/math/2014/10/large-dimension-and-standard-examples/
http://as.vanderbilt.edu/math/2014/10/large-dimension-and-standard-examples/#commentsMon, 27 Oct 2014 20:10:11 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1433Let chi(G) denote the chromatic number of graph G, and let omega(G) denote the maximum clique size of G. It is known there are triangle-free graphs (graphs with omega(G) <= 2) with large chromatic number. In fact there are triangle-free graphs on n vertices with chromatic number Omega(sqrt(n/log n)). However, when a graph on n vertices has chromatic number close to n, it must have a large clique. For instance, if c is a positive integer, n > 2c and G is a graph on n vertices with chi(G) >= n – c, then omega(G) >= n – 2c. This talk is concerned with analogous results for finite partially ordered sets. This is a joint work with Csaba Biró, University of Louisville, Attila Pór, Western Kentucky University, and William T. Trotter, Georgia Institute of Technology.
]]>http://as.vanderbilt.edu/math/2014/10/large-dimension-and-standard-examples/feed/0Operator Algebras When Every Set is Lebesgue Measurable
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-19/
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-19/#commentsFri, 24 Oct 2014 21:10:28 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=1327The assumption that every set of real numbers is Lebesgue measurable is particularly convenient in functional analysis. I will describe the theory of operator algebras in one model of set theory satisfying this assumption. I will then discuss the V*-algebras, which are $*$-algebras of bounded operators closed in a continuum analog of the ultraweak topology. Every unital separable C*-algebra has an enveloping V*-algebra, which may be identified with the space of strongly affine functions on the state space.
]]>http://as.vanderbilt.edu/math/2014/10/talk-title-tba-19/feed/0Graduate Student Tea
http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-5/
http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-5/#commentsWed, 22 Oct 2014 19:30:56 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1405http://as.vanderbilt.edu/math/2014/10/graduate-student-tea-5/feed/0Big Problems
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-6/
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-6/#commentsTue, 21 Oct 2014 21:10:51 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=1225Have you ever wondered what math research is? This talk will present some of the major unsolved problems that have guided mathematics research throughout history. Some of them have been solved, some of them are very close to being solved, and some of them are still wide open. The talk will require no advanced mathematics and all audiences are welcome.
]]>http://as.vanderbilt.edu/math/2014/10/talk-title-tba-6/feed/0Contractible Edges and Some Applications
http://as.vanderbilt.edu/math/2014/10/contractible-edges-and-some-applications/
http://as.vanderbilt.edu/math/2014/10/contractible-edges-and-some-applications/#commentsMon, 20 Oct 2014 20:10:50 +0000rongiolhttp://as.vanderbilt.edu/math/?p=1403A *k-contractible edge* is an edge in a k-connected graph which when contracted leaves the resulting graph k-connected. We will present an introduction to the theory of 3- and 4-contractible edges, including some interesting known results and applications to the characterization of 4-connected planar K_2,5-minor-free graphs.
]]>http://as.vanderbilt.edu/math/2014/10/contractible-edges-and-some-applications/feed/0Nonlocal Phenomena in Partial Differential Equations
http://as.vanderbilt.edu/math/2014/10/nonlocal-phenomena-in-partial-differential-equations/
http://as.vanderbilt.edu/math/2014/10/nonlocal-phenomena-in-partial-differential-equations/#commentsFri, 17 Oct 2014 21:10:50 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=1221Four examples of nonlocal phenomena in partial differential equations will be presented: (1) partial differential equations with time delay (non-local in time – the future depends not only on the present time, but on a history before the present time; (2) age structured population models (nonlocal in the boundary condition – offspring are born at age 0 from a mother with age in a specified age range); (3) cell-cell adhesion models (nonlocal in the transport term – cells have a spatial sensing radius, on the order of several cell diameters, that modulates their adhesion to other cells within their sensing radius); (4) interference phenomena in quantum mechanics (nonlocal in the probability density of spatial position – the detection of a quantum particle is determined only probabilistically).
]]>http://as.vanderbilt.edu/math/2014/10/nonlocal-phenomena-in-partial-differential-equations/feed/0Some Right-Angled Artin Groups Whose Automorphism Groups Do Not Have Property (T)
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-5/
http://as.vanderbilt.edu/math/2014/10/talk-title-tba-5/#commentsWed, 15 Oct 2014 21:10:05 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=1218Grunewald and Lubotzky described a family of representations of finite index subgroups of the automorphism group of a non-abelian free group, Aut(Fn). In particular, they showed that the image of these representations are arithmetic groups, and furthermore one particular subfamily of these representations have image SL(n-1,Z). A consequence of this is that Aut(F3) does not have Kazhdan’s Property (T). I will describe how these representations can be generalised to automorphism groups of right-angled Artin groups and hence describe a condition sufficient to imply when they do not have Property (T).
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