# Speakers

**Jeff Cheeger**

*New York University***Richard Kadison**

*University of Pennsylvania*| Homepage**John Lott**

*University of California, Berkeley*| Homepage**Cumrun Vafa**

*Harvard University*| Homepage**Edward Witten**

*Institute for Advanced Study*| Homepage

**Morss Hall**

142 Memorial Drive

Cambridge, MA 02139

MIT Campus Map

# Schedule

Time | Speaker | Talk | |
---|---|---|---|

9:00AM-9:45AM | Coffee | ||

9:45AM-10:00AM | Opening Remarks | ||

10:00AM-11:00AM | Ed Witten |
The Dirac Equation in Index Theory And Condensed Matter Physics | Abstract |

The importance of the Dirac operator in index theory results largely from the relation of the "symbol'' of the Dirac operator to K-theory. In this lecture, I will explain some of the applications in physics of the topological facts that make the Dirac operator important for K-theory and index theory. | |||

11:00AM-12:00PM | Cumrun Vafa |
tt* Geometry | Abstract |

In quantum theories ground states of the theory, often counted by index theorems, form a bundle over the moduli space of the theory. For supersymmetric theories the natural connection on this bundle turns out to be a (reduction of) hyper-holomorphic connection on hyperKahler manifolds. This geometry is known as tt* geometry. We discuss how this structure provides a unifying theme for topological theories including Gromov-Witten theory and Chern-Simons theory. | |||

12:00PM-1:30PM | Lunch | ||

1:30PM-2:30PM | John Lott |
3D Ricci Flow Since Perelman | Abstract |

I'll talk about the advances and open questions in three-dimensional Ricci flow. Topics include the finiteness of the number of surgeries, the long-time behavior and flowing through singularities. | |||

2:30PM-3:30PM | Richard Kadison |
Early Work of Is Singer and Some Later Developments | Abstract |

We'll discuss some early joint work Is and I did involving our interest in Operator Algebras and Quantum Mechanics, Dirac's program (a few words) and the problem(s) it generated, along with some recent developments in that connection. As time allows, we'll look at the seminal influence Is had on the large interest in derivations and commutators in the theory of operator algebras, especially as they relate to generators of one-parameter symmetry and time-evolution groups in quantum mechanics. I'll try to keep all of this as simple and informal as I can. | |||

3:30PM-4:00PM | Break | ||

4:00PM-5:00PM | Jeff Cheeger |
Quantitative Degeneracy of Lipschitz Maps From the Heisenberg Group to $L_1$ | Abstract |

We will discuss joint work with Bruce Kleiner and Assaf Naor. Let $f : B_1(p) \rightarrow L_1$ denote a 1-Lipschitz map from a unit ball in the Heisenberg group $\mathbb{H}$, with its Carnot-Carathéodory metric $d^{\mathbb{H}}$, to the Banach space $L_1$. We show that $f$ must fail to be bi-Lipschitz in a precise quantitative sense. In particular, this leads to a counter example to the Goemans-Linial conjecture from theoretical computer science. | |||

5:30PM-6:30PM | Reception* | ||

6:30PM | Banquet* |

* Both the reception and banquet will be held in Building 6C Atrium: http://whereis.mit.edu/?go=6C