Bridges 2024 Exhibition of Mathematical Art, Craft, and Design

Amrita Acharyya

Artists

Amrita Acharyya

Senior Lecturer in Mathematics

University of Toledo

Toledo, Ohio, USA

amrita.acharyya1@gmail.com

Statement

Whereas painting is my personal hobby, I try to connect it with mathematics for pleasure. I express mathematical structures like Hass diagrams of subgroups and posets, Cayley graphs of groups, and shapes created by various curves through colorful pictures that provide visual representations of the underlying mathematical notions. Colors and various shapes can help create a visual understanding and deeper appreciation of many challenging mathematical ideas, and can even bring immense joy to the inner artist of anyone able to synchronize math and art simultaneously. Toward these ends I use acrylic paints, ball and gel pens, pencils, canvas, acrylic and watercolor sketchbooks.

Artworks

Image for entry 'Cayley graph of Baumslag–Solitar group BS(1,3)'

Cayley graph of Baumslag–Solitar group BS(1,3)

40.0 x 40.0 cm

Water color sketch book, acrylic colors, colored ball pens, painting brushes

2023

The painting is based on the Cayley graph of two-generators $a, b$ and one relator groups that play an important role in combinatorial group theory and geometric group theory as (counter)examples and test-cases. It is given by the group presentation $BS(m,n)=\langle a,b:ba^{m}b^{-1}=a^{n}\rangle$ for any integer $m,n$. For example, $BS(1, -1)$ is the fundamental group of the Klein bottle. We describe $BS(1,3)$. The cottages represents the vertices of the Cayley graph of the group and the horizontal connectors between two consecutive cottages represents $a$, whereas the vertical stair connectors corresponds to $b$. The groups were defined by Gilbert Baumslag and Donald Solitar in 1962 to provide examples of non-Hopfian groups.