### Videos

## Eisenbud Lectures in Mathematics and Physics

The Eisenbud Lectures are the result of a generous donation by Leonard and Ruth-Jean Eisenbud, intended for a yearly set of lectures by an eminent physicist or mathematician working close to the interface of the two subjects.### 2016-2017

Nigel Hitchin **(University of Oxford)**

**November 15, 2016 (Lecture I)
**Eisenbud Lecture Series in Mathematics and Physics

**Algebraic curves and differential equations**

Abstract: Euler’s equations for a spinning top are well-known to be solvable by elliptic functions. They form the first example of a much wider range of equations, in particular Nahm’s equations, which are solvable using algebraic curves of higher genus. Nahm’s equations appear in various parts of differential geometry and physics, related to hyperk ahler geometry and magnetic monopoles in particular. Loosely speaking, the equations are linearized on the Jacobian of the curve. However, there are many situations where that curve is singular or non-reduced and this viewpoint is no longer valid. The talk will discuss the geometry of what happens in some of these cases.

**November 16, 2016 (Lecture II)**

Eisenbud Lecture Series in Mathematics and Physics

**Generalizing hyperbolic surfaces**

Abstract: The theory of Higgs bundles on a compact Riemann surface provided a natural setting for hyperbolic surfaces within the context of an SU(2)-gauge theory with a complex Higgs field. Replacing the group SU(2) by the group of symplectic diffeomorphisms of the two-sphere provides, thanks to work of Biquard, an infinite-dimensional gen eralization of Teichm ̈uller space, but it is as yet unclear what type of geometry, generalizing hyperbolic metrics, on the surface this parametrizes. The lecture will investigate some of the questions and features involved.

**November 18 (Lecture III)
**Eisenbud Lecture Series in Mathematics and Physics

**Higgs bundles and mirror symmetry**

Abstract: The moduli space of Higgs bundles on a curve, together with its fibration structure as an integrable system, forms a natural example to examine the predictions of mirror symmetry in the approach of Strominger, Yau and Zaslow. The mirror for gauge group G is regarded as being the moduli space for the Langlands dual group LG. Of particular interest is the how this manifests itself in the duality of “branes” on each side. We consider in the talk cases arising from noncompact real forms of complex groups, and also Lagrangians arising from the existence of holomorphic spinor fields.

### 2015-2016

Jeffrey Harvey (University of Chicago)

Lecture 1: **A physicist under the spell of Ramanujan and moonshine**

Watch the video

Lecture 2: **Mock modular forms in mathematics and physics***
* Watch the video

Lecture 3:

**Umbral Moonshine**

*Watch the video*

### 2014-2015

Peter Sarnak (Institute for Advanced Study and Princeton University)

Lecture 1: **The topology of random real hypersurfaces and percolation** (video) PDF

Lecture 2: **Nodal domains for Maass (modular) forms** (video). PDF

Lecture 3: **Families of zeta functions: their symmetries and applications** (video) PDF

poster Science Blog Article

### 2014

Cumrun Vafa (Harvard University)

Lecture 1: **Strings and the Magic of Extra Dimensions**

Lecture 2: **Recent Progress in Topological Strings I**

Lecture 3: **Recent Progress in Topological Strings II**

poster Science Blog article

### 2012

Craig Tracy (Distinguished Professor of Mathematics, University of California at Davis)**
** Lectures

**: Integrable Systems, Operator Determinants and Probabilistic Models**

poster

**abstract**

### 2011

Jennifer Chayes (Microsoft Research of New England)

Lecture I: **Models and Behavior of the Internet, ****the World Wide Web**

Lecture II: **Convergent Sequences of Networks**

poster abstract

### 2010

Daniel Freed (University of Texas at Austin)

Lecture I: **Differential K-theory and Dirac operators**

Lecture II: **Twisted K-theory and loop groups**

Lecture III: **Dirac charge quantization in string theory**

poster

### 2009

Leo Kadanoff (University of Chicago)

Lecture I: **Making a Splash, Breaking a Neck: The Development of Complexity in Fluids**

Lecture II: **The Good the Bad and the Awful-- Scientific Simulation and Prediction**

Lecture III: **Eigenvalues and Eigenfunctions of Toeplitz Matrices**

### 2008

Andrei Okounkov (Princeton University)

Lecture: **The Algebra of Random Surfaces**

poster

### 2007

Robbert Dijkgraaf (University of Amsterdam)

Lecture I: **The Unreasonable Effectiveness of Physics in Modern Mathematics**

Lecture II: **The Quantum Geometry of Topological String Theory**

Lecture III: **Quantum Field Theory, D-Modules and Integrable Systems**

abstract