SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Agrobacterium tumefasciens-mediated transformation of the aquatic fungus Blastocladiella emersonii

Agrobacterium tumefaciens is widely used for plant DNA transformation and more recently, has also been used to transform yeast, filamentous fungi and even human cells. Using this technique, we developed the first transformation protocol for the saprobic aquatic fungus Blastocladiella emersonii, a Blastocladiomycete localized at the base of fungal phylogenetic tree, which has been shown as a promising and interesting model of study of cellular function and differentiation. We constructed binary T-DNA vectors containing hygromycin phosphotransferase (hph) or enhanced green fluorescent protein (egfp) genes, under the control of Aspergillus nidulans trpC promoter and terminator sequences. 24 h of co-cultivation in induction medium (IM) agar plates, followed by transfer to PYG-agar plates containing cefotaxim to kill Agrobacterium tumefsciens and hygromycin to select transformants, resulted in growth and sporulation of resistant transformants. Genomic DNA from the pool o resistant zoospores were shown to contain T-DNA insertion as evidenced by PCR amplification of hph gene. Using a similar protocol we could also evidence the expression of enhanced green fluorescent protein (EGFP) in zoospores derived from transformed cells. This protocol can also open new perspectives for other non-transformable closely related fungi, like the Chytridiomycete class. (C) 2011 Elsevier Inc. All rights reserved.