A Talk on ‘Brushstrokes of Geometry: Visualizing Contact Structures on 3-Manifolds Through Paintings’
About the Talk
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?
About the Speaker
Dr Tanushree Shah is a postdoctoral fellow at Chennai Mathematical Institute, India. Previously, she was a ESI research fellow in Vienna, Austria with Vera Vertesi. Before that, she was a visiting researcher at Alfred Renyi Institute in Budapest. She did her PhD from the University of Glasgow, working on contact topology under the guidance of Ana Lecuona, Andy Wand and Brendan Owens.
Her research interests are low dimensional topology especially contact and symplectic topology, knot theory, and Heegaard Floer homology. She is also an artist and is passionate about connections between mathematics and art.