<a href="https://youtu.be/_5o_bSv_yxs">Video</a> of the lecture.<br>
<a href="https://www.youtube.com/watch?v=ktmr_uNjLws">Waiting room video</a>: interview with Edward Frenkel.<br><br>

The lecture was based on Section 1.1 and 1.2 of <a href="https://ebookcentral.proquest.com/lib/nuig/reader.action?docID=3084286"><I>Basic Topology</I> by M.A. Armstrong</a>.<br><br>

I explained that 
<blockquote><I>topology is the study of those properties of a space that remain unchanged throughout any continuous deformation of the space.</I></blockquote>
The usual map of the London Underground is a continuous deformation of an accurate geographic map; the usual deformed map retains topologocal properties sufficient for passengers to plan their journey.
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I then defined the Euler characteristic (=V-E+F) of a spherical surface such as the surface of Mars or the surface of a soccer ball, and informally proved that this number is a topological property of the surface. 
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I used the Euler characteristic to count the number of pentagons in a soccer ball, the number of pentagons in <b>any</b> fullerene molecule, and the number of pentagons in <b>any</b> Buckminster Fuller dome (assuming that the basement of the dome completes the sphere).
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Here are some <a href="uploads/topintro.pdf">slides</a> used during the lecture.
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If you are interested in applications of topology to finance and data science take a look at the <a href="https://www.ayasdi.com/">Ayasdi</a>
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