"Almost all of its appearances in mathematics, and almost all the formulas relating to it, have something of the fantastical in them, as if this function alone among all others possessed a sense of humor."
- Don Zagier, on the classical dilogarithm
One can only imagine what happens when you q-deform...


QDL

I study string theory and quantum field theory, and try to build new relations between mathematics and physics -- and between physics and physics, and math and math. My interests range from the study of BPS states, surface operators, and topological quantum field theory (on the physical side) to knot theory, hyperbolic geometry, and categorification (on the mathematical).

Much of my graduate work (unexpectedly) revolved around the above function: the *quantum* dilogarithm. It encodes the way that supersymmetric black holes can bind or split as their masses are varied. It's an open topological string partition function. It's the key ingredient in the construction of "quantum" invariants of knots. And it relates the spectra of particles in gauge theories with the topology of three-manifolds.



Some documents:
Some past conferences: