A few years ago a musician friend asked me “there’s this new tool topologists have called Persistent Homology. I’d like to see what it can do when you apply it to data from music. 947 more words

## Tags » Metric Geometry

#### The travelling salesman problem

This is one of those items I should have written about long ago: I first heard about it over a lunch chat with professor Guth; then I was in not one, but two different talks on it, both by Peter Jones; and now, finally, after it appeared in this algorithms lecture by Sanjeev Arora I happen to be in, I decided to actually write the post. 1,226 more words

#### Stable isoperimetric inequality

Eric Carlen from Rutgers gave a colloquium last week in which he bought up some curious questions and facts regarding the ‘stability’ of standard geometric inequalities such as the isoperimetric and Brunn-Minkowski inequality. 744 more words

#### Ultrametrics and the nonlinear Dvoretzky problem

Hi guys~ The school year here at Princeton is finally (gradually) starting. So I’m back to this blog :-P

In this past week before anything has started, … 987 more words

#### A remark on a mini-course by Kleiner in Sullivan's 70th birthday

I spent the last week on Long Island for Dennis Sullivan’s birthday conference. The conference is hosted in the brand new Simons center where great food is served everyday in the cafe (I think life-wise it’s a wonderful choice for doing a post-doc). 735 more words

#### Stabilization of Heegaard splittings

In the last lecture of a course on Heegaard splittings, professor Gabai sketched an example due to Hass-Thompson-Thurston of two genus Heegaard splittings of a -manifold that requires at least stabilization to make them equivalent. 984 more words

#### A report of my Princeton generals exam

Well, some people might be wondering why I haven’t updated my blog since two weeks ago…Here’s the answer: I have been preparing for this generals exam — perhaps the last exam in my life. 1,146 more words