Lecture I: The topology of random real hypersurfaces and percolation (video)


Lecture II:  Nodal domains for Maass (modular) forms (video)


Lecture III: Families of zeta functions: their symmetries and applications (video)


Eisenbud Lectures in Mathematics and Physics

sarnakThe 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.

2014 - 2015 Recipient:

Peter Sarnak, Institute for Advanced Study and Princeton University
Lectures: Tuesday, December 2; Wednesday December 3 and Thursday December 4, 2014 at 4pm in Abelson 131.

Randomness in number theory and geometry 

The behavior of many arithmetic and geometric objects, from the zeros of zeta functions to the the topologies of random real algebraic, varieties are apparently dictated by models from statistical physics. We will review some of these and highlight the basic conjectures and some of what is known towards them.


Lecture I: Tuesday, December 2, 2014
Abelson 131, 4:00pm 
Reception in ground-floor atrium, Shapiro Science Center at 5pm
The topology of random real hypersurfaces and percolation

Abstract: The topologies of the connected components of the zero sets of random real projective hypersurfaces of high degree follow a universal law of distribution. We explain this (and a more general phenomenon for random band limited functions), its source and some possible connections to percolation. 

Lecture II: Wednesday, December 3, 2014
Abelson 131, 4:00pm
Nodal domains for Maass (modular) forms

Abstract: The eigenstates of the quantization of a classically chaotic hamiltonian are expected to behave like random monochromatic waves .We discuss this in the context of the eigenfunctions on the modular surface-ie "Maass Forms ", and especially what can be proved about their nodal domains.

Lecture III: Thursday, December 4, 2014
Abelson 131, 4:00pm
Families of zeta functions, their symmetries and applications

Abstract: The local statistical laws for the distribution of the zeros of the Riemann Zeta function and more generally of families of zeta functions ,follow  one of 4 of the 10 universal random matrix ensembles. We review some this phenomenon ,especially in connection with applications.


Previous lecturers:

  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 at the University of California at Davis.
Lectures: Integrable Systems,  Operator Determinants and Probabilistic Models
poster  abstract

Jennifer Chayes, Microsoft Research of New England
Lecure 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"

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
“The Algebra of Random Surfaces"

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.