Author Archives: Behnam Esmayli

About Behnam Esmayli

I started PhD in Mathematics at Pitt in Fall 2015. I have come to grow a passion for metric spaces -- a set and a distance function that satisfies the triangle inequality -- simple and beautiful! These spaces when equipped with other structures, such as a measure, becomes extremely fun to play with!


As math graduate students, we often get teaching assignments from our departments, some of us tutor independently for financial reasons, and some volunteer to teach at local schools or libraries. Teaching is an inseparable part of our job/life. But that is where … Continue reading

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Matrix Multiplication, the human way!

Having to do copious calculations by hand when preparing for an exam, I came to realize that there was an alternative way of interpreting a matrix multiplication. This new insight would allow me to instantly guess the following product without … Continue reading

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What is a Manifold? (6/6)

In posts 1-3 we were able to reduce all of the geometry of a curve in 3-space to an interval along with two or three real-valued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading

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What is a Manifold? (5/6)

In our last post, we invented a new geometry by re-scaling the inner product of the usual Euclidean plane. This modification did not change any of the angles in our geometry, in the sense that if two curves intersected in a particular Euclidean … Continue reading

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What is a Manifold? (4/6)

After our luxurious treatment of 1-d manifolds, we turn to 2-d manifolds. My story of surfaces starts in a beautifully weird morning when I got up to realize that life in the usual Euclidean plane had changed dramatically. Vectors had shortened, areas … Continue reading

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