Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

The Presence of Words in Visual Art from Surrealism to Conceptualism

Without a doubt, one of the biggest changes that affected XXth century art is the introduction of words into paintings and, in more recent years, in installations. For centuries, if words were part of a visual composition, they functioned as reference; strictly speaking, they were used as a guideline for a better perception of the subject represented. With the developments of the XXth century, words became a very important part of the visual composition, and sometimes embodied the composition itself. About this topic, American art critic and collector Russell Bowman wrote an interesting article called Words and images: A persistent paradox, in which he examines the American and the European art of the XXth century in almost its entirety, dividing it up in six “categories of intention”. The aforementioned categories are not based on the art history timeline, but on the role that language played for specific artists or movements. Taking inspiration from Bowman's article, this paper is structured in three chapters, respectively: words in juxtaposition and free association, words as means of exploration of language structures, and words as means for political and personal messages. The purpose of this paper is therefore to reflect on the role of language in contemporary art and on the way it has changed from artist to artist.