# Joshua Sabloff

## Associate Professor of Mathematics; Department Chair

## Biography

Though I flirted with physics and history as an undergraduate at Harvard, I became enamored with mathematics (and topology in particular) and graduated with an A.B. in mathematics in 1996. I then spent a year abroad in Cambridge, taking Part III of the Mathematical Tripos, on a Churchill Scholarship. I returned to this side of the Atlantic for graduate school at Stanford, where I earned my PhD in Mathematics in 2002 under the direction of Yasha Eliashberg. After a year as a postdoctoral lecturer at the University of Pennsylvania, I arrived at Haverford.

## Education

A.B., Harvard University

MMath, Cambridge University

Ph.D., Stanford University

## Research

I am primarily interested in knot theory (yes, the things you use to tie your shoes), mostly in the context of contact and symplectic topology (which, as far as I know, cannot be used to tie your shoes). To a mathematician, a knot is like the knots you use to tie your shoes, with two differences: first, a mathematical knot has no ends, that is, it is a knotted up circle. Second, a mathematical knot has no thickness. Two knots are defined to be equivalent if one can be deformed into the other without cutting the string. A natural question --- at least for a mathematician --- is if there exists a general and effective method for determining if two knots are, or are not, equivalent? In knot theory, as in other branches of mathematics, it is much easier to find methods for telling knots apart. The key idea is that of an invariant. An invariant is an object you assign to a knot that does not change when the knot is deformed. That object can be as simple as an integer or a polynomial, though they can get much more complicated. If two knots have different invariants, then it is impossible to deform one into the other.