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Bobby Ramsey
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| email address: | bramsey@math.iupui.edu | ||||
| office phone: | (317) 274 - 1272 | ||||
| office hours: |
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| Syllabus | Schedule | Homework |
| Syllabus | Schedule |
| Syllabus | Schedule |
| Relatively Hyperbolic Groups, Rapid Decay Algebras, and a Generalization of the Bass Conjecture |
| With Crichton Ogle and Ronghui Ji. It will appear in 'Journal of Noncommutative Geometry', EMS publications. We propose a stronger version of the $\ell^1$ Bass conjecture and verify it for a wide class of groups. For the extension to relatively hyperbolic groups, we verify that if each of the peripheral subgroups satisfy a polynomially bounded conjugacy problem, then so does the group itself. |
| The Isocohomological Property, Higher Dehn Functions, and Relatively Hyperbolic Groups |
| With Ronghui Ji. Advances in Mathematics. Volume 222, Issue 1, 10 September 2009, Pages 255-280 . We study the weak isocohomological property for finitely generated discrete groups. In the case the group has a classifying space the type of a simplicial complex with finitely many simplices in each dimension, ( called a type HF_\infty group), the property is related to the higher Dehn functions of this complex. In extending to the case of relatively hyperbolic groups we show that a group which is hyperbolic relative to combable groups is itself combable. In the case the subgroups are not combable, but merely HF_\infty, we construct a classifying space for the group, and bound the Dehn functions in terms of those of the subgroups. |
| A Generalization of the Lyndon-Hochschild-Serre Spectral Sequence for Polynomial Cohomology |
| My Ph.D. Dissertation under the guidance of Ronghui Ji. I studied the weak isocohomological property and its behavior under a certain class of extensions defined by Noskov. A reworked version has been submitted to JFA. |
| Cyclic Cohomology for Discrete Groups and its Applications |
| A survey article written with Ronghui Ji. It appeared in 'Advances in Mathematics and its Applications', Univ. Sci. Tech. of China Publications. |
| Bounded Cohomology and Amenable Groups |
| An elementary proof of a theorem attributed to Hirsch and Thurston. The theorem says that for a discrete amenable group, the bounded cohomology vanishes in all positive degrees. |
| October 2009, Wabash Modern Analysis Conference |
| Complexes of groups, the Isocohomological property, and Rapid Decay. |
| Slides from the talk. |
| April 2009, Vanderbilt Topology and Group Theory Seminar |
| The polynomially bounded conjugacy problem for relatively hyperbolic groups. |
| Slides from the talk. |
| March 2009, Vanderbilt Noncommutative Geometry Seminar |
| The isocohomological property, higher Dehn functions, and relatively hyperbolic groups. |
| Slides from the talk. |
| February 2009, IUPUI Colloquium |
| The isocohomological property, higher Dehn functions, and relatively hyperbolic groups. |
| Slides from the talk. |
| September 2008, Wabash Modern Analysis Conference |
| The isocohomological property, higher Dehn functions, and relatively hyperbolic groups. |
| November 2006, IUPUI Nonlinear PDE and Integrable Systems Seminar |
| Geometric group theory, combability, and Dehn’s problems. |
| September 2005, Wabash Modern Analysis Conference |
| Quasiconvex length functions and the Rapid Decay property. |