Bi-Co Mathematics Colloquium with Dr. Tanushree Shah
Abstract:
Mathematics and art, often seen as distinct realms, share a profound connection in their pursuit of structure, abstraction, and beauty. In the intricate world of differential topology, contact structures on 3-manifolds offer a rich tapestry of geometric elegance—one that can be reimagined through the lens of painting. In this artistic exploration, paintings become more than visual metaphors—they act as intuitive windows into the hidden structure of 3-manifolds. We begin with a friendly introduction to two flavours of contact structure: tight and overtwisted—the latter well understood, while the former remains more elusive. Using surgery and convex surface theory we push classification of tight structure to Seifert fibered manifolds. Finally, we ask: What new results can we hope for using 4 manifold techniques, and what remains beyond reach?
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