### 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.

### 2017-2018

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.

### 2016-2017

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

### 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: **E**igenvalues 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