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.


James Sethna (Cornell University)

Lecture I: Monday, November 27, 2017, 4:00pm, Gerstenzang 121
"Sloppy Models, Differential Geometry, and How Science Works"
James P. Sethna, Katherine Quinn, Archishman Raju, Mark Transtrum, Ben Machta, Ricky Chachra, Ryan Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers
Abstract: Models of systems biology, climate change, ecosystems, and macroeconomics have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? We have found that predictions can be made despite huge uncertainties in the parameters – many parameter combinations are mostly unimportant to the collective behavior. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. We show that physics theories are also sloppy – that sloppiness may be the underlying reason why the world is comprehensible.

Lecture II: Tuesday, November 28, 2017, 4:00pm, Abelson 131
"Crackling Noise"
James P. Sethna
Abstract: A piece of paper or candy wrapper crackles when it is crumpled. A magnet crackles when you change its magnetization slowly. The earth crackles as the continents slowly drift apart, forming earthquakes. Crackling noise happens when a material, when put under a slowly increasing strain, slips through a series of short, sharp events with an enormous range of sizes. There are many thousands of tiny earthquakes each year, but only a few huge ones. The sizes and shapes of earthquakes show regular patterns that they share with magnets, plastically deformed metals, granular materials, and other systems. This suggests that there must be a shared scientific explanation. We shall hear about crackling noise and that it is a symptom of a surprising truth: the system has emergent scale invariance – it behaves the same on small, medium, and large lengths.

Lecture III: Wednesday, November 29, 2017, 10:00am, Abelson 333
"Normal Form for Renormalization Groups: The Framework for the Logs"
James P. Sethna, Archishman Raju, Colin Clement, Lorien Hayden, Jaron Kent-Dobias, Danilo Liarte, and Zeb Rocklin
Abstract: Ken Wilson’s renormalization group solved for the behavior of phase transitions by mapping statistical mechanics into a differential equation in the space of all Hamiltonians, as we examine them on different length scales. This mapping from complex physical systems to simple differential equations has allowed us to explain scale invariance that emerges in everything from crackling noise to the onset of chaos. The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. This classic prediction is often violated, with logarithms and exponentials that pop up in the most interesting cases. Mathematicians have developed normal form theory to describe the likely behaviors of differential equations. We use normal form theory to systematically group these seeming violations into universality families. We recover and explain the existing literature, predict the nonlinear generalization for universal homogeneous functions, and show that the procedure leads to a better handling of the singularity even for the classic 4-d Ising model.


Nigel Hitchin (University of Oxford)

Lecture I: Algebraic curves and differential equations
Lecture II: Generalizing hyperbolic surfaces<strong
Lecture III: Higgs bundles and mirror symmetry


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