Geometry of the SL(3,ℂ)-character variety of torus knots.

Let G be the fundamental group of the complement of the torus knot of type (m, n). It has a presentation G = . We find a geometric description of the character variety X(G) of characters of representations of G into SL(3,ℂ), GL(3,ℂ) and PGL(3,ℂ).

E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

The English language used by the Chinese: A new variety of English?

The topic was chosen because of a simple fact that there are more Chinese studying English in China than U.S. Americans who speak English. The aim of this paper is to demonstrate the unique linguistic features that make the Chinese use English in a particular style. First, it shows the development of the English language used by the Chinese: Chinese Pidgin English, Chinglish, Chinese English and China English. Second, it takes a deeper look into certain linguistic features regarding the English language used by the Chinese: lexical features morphosyntactic features and pragmatic features