Eisenbud Lectures in Mathematics and Physics

hitchenThe 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.

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 However, there are many situations where that curve is singular or non-reduced and this viewpoint is no longer valid.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.


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


Peter Sarnak (Institute for Advanced Study and Princeton University)

Lecture 1: The topology of random real hypersurfaces and percolation (videoPDF
Lecture 2: Nodal domains for Maass (modular) forms (video). PDF
Lecture 3: Families of zeta functions: their symmetries and applications (videoPDF
poster  Science Blog Article


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


Craig Tracy (Distinguished Professor of Mathematics, University of California at Davis)
Lectures: Integrable Systems, Operator Determinants and Probabilistic Models
poster  abstract


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


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


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


Andrei Okounkov (Princeton University)
Lecture: The Algebra of Random Surfaces


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