Monthly Archives: July 2012

In my last lecture today I explained how to compute the ECH capacities of , where is a convex domain in the first quadrant of the plane, and is its inverse image under the moment map (at least assuming that … Continue reading →

Someone at the Munich workshop suggested that it would be helpful to have a comparison of ECH versus SFT (Symplectic Field Theory, due to Eliashberg-Givental-Hofer). I think this would make a nice conclusion to an introduction to ECH,  but there … Continue reading →

Sorry I haven’t had a chance to post any more notes in the last three days. Anyway here is what I talked about in Munich: In the second lecture, I discussed the ECH index inequality and the definition of ECH, … Continue reading →

Having defined ECH (modulo some details which I have not yet explained), we would now like to define maps on ECH induced by suitable kinds of symplectic cobordisms. It turns out that there is a serious technical difficulty with this, … Continue reading →

Today I gave the first of five lectures at the SFT VI workshop in Munich. Thanks to the excellent minicourses over the weekend, I could assume some background about holomorphic curves and Seiberg-Witten theory (and I’ll be able to assume … Continue reading →

Today was the end of the Budapest minicourse. Basically it covered installments 1-10 of the lecture notes (with a lot of details omitted), plus the application to symplectic embeddings which was outlined in installment 0. The Munich course is supposed … Continue reading →

In the fourth and penultimate lecture of the Budapest minicourse, I stated the formulas of ECH index theory and defined all the ingredients that go into them. The contents of the lecture roughly correspond to installments 5 and 6 of … Continue reading →

In the third lecture of the Budapest minicourse today, I reviewed the definition of Taubes’s Gromov invariant and discussed the mapping torus example.  The material in the lecture corresponds to installments 2 and 3 of the notes here, except that … Continue reading →

Today I gave the first two lectures in the minicourse on ECH in Budapest. Instead of telling the story from the beginning, as I have been doing on this blog, I thought it would be better to first state an … Continue reading →