Intro

August 2011 – the first day of the West Coast Algebraic Topology Summer School at the University of Washington, Seattle.

Hi everyone,

First I want to thank the organizers for bringing us together.

My name is Yifei Zhu. I’m a grad student at the University of Minnesota entering my 5th year.

For what I’ve been doing about algebraic topology, I’ve been studying power operations in elliptic cohomology. These can be viewed as higher analogs of the Steenrod operations in ordinary cohomology and the Adams operations in K-theory.

I’ll try to avoid further technicalities and just say something about motivations.

Last week there was a doodle on the Google homepage celebrating the French mathematician Fermat’s 410^th birthday. When I first saw it in the morning when I opened my computer, I felt something really refreshing and exciting. There was the Google logo on a blackboard, not quite completely erased, covered by the inequality Xⁿ + Yⁿ ≠ Zⁿ, [n > 2], together with a mouse-over comment which was nothing but Fermat’s tantalizing remark making an excuse of not writing down his truly marvelous proof.

OK, I’m not claiming my research has anything to do with Fermat’s last theorem, with all the deep theories underlying its actual proof which is truly truly marvelous. But the math involved, especially the world of elliptic curves, is something I’ve been gradually appreciating more and more.

I remember reading an article on the Notices of the AMS by its editor Andy Magid reflecting on his forty years since receiving his PhD degree. He mentioned that a former colleague of his had an interesting image for learning and working in math: he liked to quip that his professional goal was to slow the increase in the distance between the math he did and the math he appreciated. His point, that as one continues working and learning, areas one thought would always be too difficult to understand can become accessible, if still too hard to be part of one’s research agenda.

That said, a good thing of studying operations in the so-called elliptic cohomology theories is that one can translate algebraic topology to quite explicit calculations with elliptic curves. There is a larger framework behind this, called chromatic theory, where algebraic topology, algebraic geometry and number theory interact. In order to understand this, I’ve also been spending time learning algebraic geometry, which is quite a tough thing for me.

Lastly, as instructed by the organizer I should talk about something I’d genuinely like to know about other participants: besides math, I LOVE classical music, my favorite composers being Bach and Mozart. Over the years I’ve almost given up trying to find someone talking about classical music, so never mind. Thank you!