The Department of Mathematics is highlighting the great work accomplished by our Graduate Students
The first of many more to come is the art work by Graduate student, Matthew Weaver. Matthew created the art using pine to showcase a digital image of the Whitney Umbrella.
The theory of singularities is rich with interesting phenomena and strange anomalies. Shown here, the Whitney Umbrella is a self-intersecting surface in affine space and is the classical example of a pinch point singularity. Named after Hassler Whitney, this surface is often depicted with the negative z-axis serving as the “handle” of the umbrella.
Matthew goes on to say, as a "commutative algebraist, my research directs me to the study of the equations and algebraic structures associated to geometric varieties like the one shown here. However, one cannot help but appreciate the geometric nature of these objects. Details such as tangents, intersections, smoothness, etc. have their algebraic translations, but there is something intrinsically satisfying one only obtains from visualizing such an object or even using one’s imagination. For instance, my own research relates to the resolution of singularities using blowup algebras. If I were to resolve the singularities here along the z-axis, I would have to figure out how to “open up the umbrella”.
The Whitney Umbrella is located on the 8th Floor of the Mathematical Science Building next to office 822, be sure to stop by and admire it!