# 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 10, 2013 4:10 pm (Tuesday)

## Absorbing Subalgebras: Where to Find Them, and How to Use Them

Alexandr Kazda, Vanderbilt University
Location: Stevenson 1310

While studying the complexity of the Constraint Satisfaction Problem, Libor Barto and Marcin Kozik discovered the idea of absorption. If B is an absorbing subalegebra of the algebra A, then many kinds of connectivity properties of A are also true for B. This is very useful for proofs by induction, and absorption has since played a role in several other universal algebraic situations. After giving a taste of how absorption works, we would like to talk about our current project (which is a joint work with Libor Barto): How to decide, given an algebra A with finitely many basic operations and some B subalgebra of A, if B absorbs A.
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.

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 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 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.

August 28, 2013 4:10 pm (Wednesday)

## Counting Non-Simple Closed Geodesics on a Pair of Pants

Jenya Sapir, Stanford University
Location: Stevenson 1310

We give coarse bounds on the number of (non-simple) closed geodesics on a pair of pants with upper bounds on both length and intersection number. We acheive our bounds by transforming the problem of counting geodesics into a combinatorial problem of counting words with certain conditions. If time permits, we will give an idea of how to extend these results to a general surface, and give an application.

August 28, 2013 3:10 pm (Wednesday)

## Error Bounds for Kernel-Based Numerical Differentiation

Oleg Davydov, Strathclyde University (Scotland)
Location: Stevenson 1307

The literature on meshless methods observed that kernel-based numerical differentiation formulae are highly accurate and robust. We present error bounds for such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds for kernel-based interpolation but are not applicable in this setting. Since differentiation formulas based on polynomials also have error bounds in terms of growth functions, we show that kernel-based formulas are comparable in accuracy to the best possible polynomial-based formulas. The talk is based on joint research with Robert Schaback.

August 23, 2013 4:10 pm (Friday)

## Coassembly Maps, Gauge Groups, and K-Theory

Cary Malkiewich, Stanford University
Location: Stevenson 1432

Calculus of functors is a powerful technique from homotopy theory, which studies computationally difficult constructions by means of "linear approximations." We will describe a new variant of this calculus, based on the embedding calculus of Weiss and Goodwillie. This theory provides us with a sequence of approximations to the stable gauge group of a principal bundle, in which the linear approximation is the Cohen-Jones string topology spectrum. We will finish with some future applications to algebraic K-theory, a subject which provides a powerful (but difficult to compute) invariant for rings, algebras, and groups.

July 28, 2013 9:00 am (Sunday)

## Topology, Algebra, and Categories in Logic 2013, July 24-27, 2013 (Summer School) and July 28 - August 1, 2013 (Conference)

Location: Stevenson 1 (Summer School) and Wilson Hall (Conference)

This summer school and conference, held in conjunction with the 28th Annual Shanks Lectures, will focus on three interconnecting mathematical themes central to the semantical study of logics and their applications: algebraic, categorical, and topological methods. For more information, see the conference web site: http://www.math.vanderbilt.edu/~tacl2013

July 27, 2013 9:00 am (Saturday)

## Topology, Algebra, and Categories in Logic 2013, July 24-27, 2013 (Summer School) and July 28 - August 1, 2013 (Conference)

Location: Stevenson 1 (Summer School) and Wilson Hall (Conference)

This summer school and conference, held in conjunction with the 28th Annual Shanks Lectures, will focus on three interconnecting mathematical themes central to the semantical study of logics and their applications: algebraic, categorical, and topological methods. For more information, see the conference web site: http://www.math.vanderbilt.edu/~tacl2013