Southeast Geometry Conference Titles and Abstracts (Highlighted names are links to the speaker's home page.) C. Agut, On special classes of submanifolds in contact metric manifolds with a nullity condition Abstract: Considering the class of contact metric manifolds with a nullity condition, there will be presented few particular properties of special classes of submanifolds: invariant, anti-invariant, CR-submanifolds, CR-products. Will be given expressions for the curvature tensor field, for the bisectional curvature and special conditions regarding the dimension and codimension of submanifolds. V. Berestovskii, Dimensions of R-trees and self-similar fractal spaces of nonpositive curvature--click here for abstract J. Clelland, Sub-Finsler geometry in dimensions three and four Abstract: Motivated by examples from optimal control theory, we consider the notion of sub-Finsler geometry and show how it is a natural generalization of sub-Riemannian geometry.  In dimensions three and four, we can compute a complete set of local invariants and derive geodesic equations, whose solutions represent optimal paths for the corresponding control theory problem.  We will show examples and discuss some of the difficulties that arise in higher dimensions. This work is joint with Christopher Moseley and George Wilkens. G. Craig, Dehn Filling and Asymptotically Hyperbolic Einstein manifolds Abstract: We extend Anderson's higher-dimensional Dehn filling construction to a large class of infinite-volume hyperbolic manifolds. This gives an infinite family of topologically distinct asymptotically hyperbolic Einstein manifolds with the same conformal infinity. This construction is done through a gluing procedure, and involves finding a sequence of approximate solutions to the Einstein equations and then perturbing them to exact ones. M. Ionel, Special Lagrangians in the deformed and resolved conifolds Abstract: Special Lagrangian submanifolds represent an important class of minimal submanifolds that appear in branches of high energy physics: String Theory and M-theory. In this talk, I will first discuss a few important properties of the special Lagrangian submanifolds and give some examples in flat space. Then I will present our constructions of special Lagrangians in the deformed and resolved conifolds and discuss their asymptotic behavior. (work done jointly with Maung Min-Oo of McMaster University) J. McCuan, A variational formula for floating bodies and the criticality of planar capillary interfaces Abstract: The surface of a liquid in zero gravity in contact with fixed rigid bounding surfaces is said to be in equilibrium if it has constant mean curvature and meets the bounding surfaces in a materially dependent contact angle.  When a portion of the rigid bounding structure consists of a freely floating or partially floating object, these conditions are inadequate for criticality in the associated variational problem.  We formulate a notion of criticality applicable to the latter situation based on a suitable variational formula and give examples of its application.  We show, in particular, that any planar interface that is critical for the fixed boundary problem remains critical when portions of the boundary structure are allowed to float. J. Parsley, The geometry of the Taylor problem in plasma physics Abstract: In plasma physics, the Taylor problem is to find the steady-state flow of a plasma injected into a non-simply-connected containment vessel M in R^3.  More precisely, we seek, among all divergence-free vector fields which are tangent to the boundary of M, the one which has minimum energy subject to two constraints:  (1) its flux(es) across disks in the interior of M, and (2) its helicity.  The helicity of a vector field measures the extent to which its flowlines coil and wrap around each other.  We show that the vector field which solves the Taylor problem must be a curl eigenfield:  curl(V) = kV. The physicist J.B. Taylor derived the solution explicitly on a solid flat torus in 1986 and showed that it agreed with experimental results of plasma flowing in a tokamak (a torus of large aspect ratio).  We prove his results and extend them to all compact subdomains M of R^3 with piecewise smooth boundary. C. Plaut, Generalized Universal Covers of Metric Spaces Abstract: Metric spaces that are not locally nice occur in increasingly many situations in geometry, for example as limits of Riemannian manifolds with Ricci curvature bounded below and as boundaries at infinity of hyperbolic groups. I will present ongoing work on generalized universal covers of a large class of metric spaces, including all geodesic spaces. Associated with the generalized universal cover is a "deck group" that in general is different from, but related to, the classical fundamental group. I'll discuss the basic ideas and theorems, and describe the universal covers and deck groups of some well-known pathological spaces such as the Hawaiian Earring, the topologist's sine curve, and the countably infinite product of circles. F. Schwartz, Yamabe problem on noncompact manifolds with boundary Abstract: Let (M^n,g),  n>2, be a noncompact, complete, scalar flat manifold whose boundary is compact.  We show that on a large class of such M, any smooth function on the boundary is realized as the mean curvature of a complete, conformally related scalar flat metric.  The problem is equivalent to finding a positive solution to an elliptic equation with a non-linear boundary condition with critical Sobolev exponent. M. Stern,  Index theory from a de Rham perspective Abstract: We will show that the Atiyah Singer index theorem for the classical operators admits analytic proofs outside the framework of index theory. Analyzing these more cohomological arguments leads to the discovery of many new fixed point formulas of Lefschetz type associated to your favorite geometries. A. Wade, Dirac fibrations Abstract:  Symplectic fibrations naturally occur in various areas of mathematics and physics.  They hanve played an important role in Sternberg's construction of the phase space of a particle in a Yang-Mills field.  In this talk, we will discuss an extension of Sternberg's minimal coupling construction to the context of Dirac structures. G. Weinstein, Minimal Surfaces with a Free Elastic Boundary Note: All talks will be in room 207 of the Tate Center on Liberty Street. Coffee will be served in room 211 across the hall. Posters and preprints will be on display in the lobby throughout the conference, and a special "Q&A" session has been arranged for Saturday evening at 8pm. After-dinner refreshments will be served, and poster authors should be on hand to answer any questions. SEGC06 is supported by the National Science Foundation and by the Department of Mathematics at the College of Charleston. Links: SEGC Main Page / Math Department / College of Charleston