# 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 2, 2013 3:10 pm (Monday)

## Structure and Hamiltonicity of 3-Connected Graphs with Excluded Minors

Mark Ellingham, Vanderbilt University
Location: Stevenson 1432

Tutte showed in 1956 that all 4-connected planar graphs are hamiltonian. But examples of 3-connected planar graphs (triangulations, even) that are not hamiltonian have been known since at least the 1930s. So we may ask what additional conditions can be imposed on 3-connected planar graphs to make them hamiltonian. We show that K_{2,5}-minor-free 3-connected planar graphs are hamiltonian. Using similar techniques we investigated the hamiltonicity, and in fact the general structure of 3-connected K_{2,4}-minor-free graphs, leading to a complete characterization of all K_{2,4}-minor-free graphs. Recently we found a way to shorten our proof using some results of Guoli Ding and Cheng Liu. We discuss these results as well as some new directions. For example, computations by Gordon Royle suggest that although there are infinitely many nonhamiltonian 3-connected K_{2,6}_minor-free planar graphs, it may be possible to characterize them. The results of Ding and Liu may lead to characterizations of H-minor-free graphs for other small 2-connected graphs H. This is joint work with Emily Marshall, Kenta Ozeki and Shoichi Tsuchiya.

September 4, 2013 4:10 pm (Wednesday)

## On Pairs of Finitely Generated Subgroups in Free Groups

Alexander Olshanskii, Vanderbilt University
Location: Stevenson 1310

We prove that for arbitrary two finitely generated subgroups A and B having infinite index in a free group F, there is a subgroup H of finite index in B such that the subgroup < A,H > generated by A and H has infinite index in F. The main corollary of this theorem says that a free group of free rank r > 1 admits a faithful highly transitive action, whereas the restriction of this action to any finitely generated subgroup of infinite index in F has no infinite orbits.

September 5, 2013 4:10 pm (Thursday)

## Departmental Welcome Event

Location: Stevenson 5211

Please join us for the annual welcome meeting, which will be an opportunity for us to be introduced to new faculty and students. The event will be followed by a reception in the graduate student area. All faculty, students, and staff are invited and encouraged to attend.

September 6, 2013 4:10 pm (Friday)

## Subfactors with Prescribed Fundamental Groups

Arnaud Brothier, Vanderbilt University
Location: Stevenson 1432

In a joint work with Stefaan Vaes we study fundamental groups for subfactors. We consider a large class of subgroups $\mathcal S$ of $\mathbb R_+^\times$ that contains all countable subgroups and some uncountable groups with any Hausdorff dimension between 0 and 1. Using Popa's deformation/rigidity theory, we construct a hyperfinite subfactor of index 6 with its fundamental group equal to $G$, for any group $G$ in $\mathcal S$. Those subfactors are indexed by ergodic probability measure preserving transformation. This proves in particular that there are unclassifiably many subfactors at index 6 with the same standard invariant. Furthermore, using those technics we provide an explicit uncountable family of non outer conjugate actions on the hyperfinite II$_1$ factors for any non amenable group.