Abstract:
Tiling is a way of arranging plane shapes so that they completely cover an area without overlapping. They are very common in our everyday life - we see them on floors, on walkways and also in brick works. Tilings can also be seen in nature. They have also appeared in various artworks since ancient times. The most common tilings use regular polygonal shapes; occasionally we also see tiles with curved edges.
In the first part of the talk we will discuss regular and semi-regular Euclidean tilings which use regular polygonal tiles. While regular tilings use congruent copies of one single tile, the semi-regular tilings (also known as Archimedian tilings) use more than one type of tiles. All these tilings are known for thousands of years. They can be found in ancient Roman structures dating back to the First century. The notion of tiling can be generalised on round spheres in Euclidean spaces. They are intimately related to regular convex polyhedrons, known as Platonic solids. In the second half of the talk, we shall describe their classification using Euler number which is a topological invariant. We will also relate Platonic solids with certain finite subgroups of the Orthogonal group O(3).
About the Speaker:
Mahuya Datta did her undergraduate studies at Presidency College, Calcutta and then got her Master's degree from University of Calcutta. Thereafter, she joined Indian Statistical Institute, Kolkata and worked with Prof. Amiya Mukherjee for her PhD thesis. She did her post-doctoral study at the International Centre for Theoretical Physics, Trieste. She joined Calcutta University as a faculty in 1996 and then moved to Indian Statistical Institute in 2003. Since then she has been working there.
Her broad research interest is Differential Geometry and most of her research work can be classified under the theory of h-principle which deals with partial differential relations in Differential Geometry and Topology.
