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Colloquium: New Perspectives on Symmetry in Nature and the Arts

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Venkatraman Gopalan, Pennsylvania State University
19 February 2015 from 4:00 PM to 5:00 PM
117 Osmond Laboratory
Contact Name
Moses Chan
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Symmetry considerations are a cornerstone in the sciences and the arts.  In this talk, I will give one example from each, emphasizing some new insights. 

Molecules and crystals often exhibit strikings symmetry that helps us classify them into 32 point and 230 space group types. With the addition of time reversal, this expands to 90 magnetic point and 1651 magnetic space groups. Matter also changes configuration under external stimuli.  A general distortion (including translation, rotation, scaling, deformation) of a set of atoms to another set of positions can be described by a distortion field.  In this talk, I introduce a new antisymmetry operation that describes hidden symmetries in this distortion field.  The new distortion groups assigned to distortions can help in improving the speed and accuracy of numerical calculations, as well as in predicting the form of tensors that describe any property change under a distortion.

Kolam is an ancient south Indian artform that is very popular.  The 5 states of south India, namely Karnataka, Tamil Nadu, Andhra Pradesh, Telangana, and Kerela, have a combined population of 252 million. Women in nearly every household wash the threshold of their homes every morning, place a pattern of dots using rice powder, and then circumscribe these dots with a line that follows specific rules.  The mathematics behind Kolams has been investigated for many decades.  Yet, creating a new kolam is not easy, and only a few "talented" people create them, and others learn them from compilations. In this talk, I present a simple 5 step method by which anyone can create an infinite number of kolams from any arbitrary set of dots placed in 2-dimensions. I will also emphasize some topological concepts underpinning the method.

These works were performed in collaboration with Brian VanLeeuwen, graduate student in Materials Science and Engineering.