Eisenbud Lectures in Mathematics and Physics
20232024
Prof. Heckman received his A.B. from Princeton in 2004 and his PhD from Harvard in 2009. After postdocs at the IAS and Harvard, Heckman was a professor at UNC Chapel Hill. Since 2017 he has been a professor of physics at the University of Pennsylvania, where he holds a secondary appointment in math. Heckman's work involves a blend of techniques from physics and math centered on string theory and quantum field theory, which he uses to address questions in particle physics, cosmology, and quantum gravity, as well as topics in algebraic geometry, algebraic topology and information theory.
Lecture I: Tuesday April 9, 11:30 amLocation: Gzang 123
Refreshments before the talk
Reception after the talk
"Geometric Approach to Quantum Fields "
Abstract: Quantum field theory (QFT) is the universal language used by physicists to describe a wide variety of phenomena in Nature. Quite remarkably, this framework has also found many applications within pure mathematics. But what is quantum field theory and how is it characterized? In this talk, I highlight recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory. This includes the discovery of entirely new kinds of QFTs in a wide range of spacetime dimensions, leading to a remarkable interplay between physics and geometry.
Lecture II: Tuesday April 9, 4:00 pm
Location: Abelson 333
Refreshments before the talk
"Top Down Approach to Global Categorical Symmetries"
Abstract: Symmetries play an important role in many areas of physics and mathematics. One recent discovery is that in quantum field theory (QFT), there are deep topological and categorical structures connected with global symmetries. Here we show how “top down” (i.e., stringy) constructions of QFTs provide a general template for constructing and studying these newfound structures. Using this perspective, we also extract the corresponding topological operators associated with such symmetries. This provides a systematic method for reading off further properties such as nontrivial fusion rules in the associated global symmetry category.
Lecture III: Wednesday April 10, 4:00 pm
Location: Abelson 333
Refreshments before the talk
"Topological Approach to Symmetries in Quantum Gravity "
Abstract: One of the outstanding challenges in physics is to unify quantum theory with gravity. Based on various thought experiments, several pieces of lore have developed, including the statement that there are no global symmetries in quantum gravity. In this talk we discuss two applications of topology in addressing symmetries in quantum gravity. First, we use the top down approach to realizing global categorical symmetries to show how topological operators become dynamical once coupled to gravity. Second, we show how cobordism theory provides a novel tool in predicting specific physical objects in quantum gravity.
Zoom Link for All Talks
20222023
 Lecture I: Tuesday, March 28th at 4pm in Abelson 131
"The accelerating universe and rigid Einstein manifolds"  Lecture II: Wednesday, March 29th at 11am in Abelson 333
"The accelerating universe and integrable deformations of quantum field theories"  Lecture III: Thursday, March 30th at 10am in Abelson 333
"Optimization and sampling from energyconserving Hamiltonian dynamical systems"
Zoom Link for All Talks
20192020
20182019

Lecture I: Multiple Zeta Values and Mixed Tate Motives over ℤ

Lecture II: Motivic Гfunctions

Lecture III: Relative Completions
20172018

Lecture I: Sloppy Models, Differential Geometry, and How Science Works

Lecture II: Crackling Noise

Lecture III: Normal Form for Renormalization Groups: The Framework for the Logs
20162017

Lecture I: Algebraic curves and differential equations

Lecture II: Generalizing hyperbolic surfaces

Lecture III: Higgs bundles and mirror symmetry
20152016

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

Lecture 2: Mock modular forms in mathematics and physics

Lecture 3: Umbral Moonshine
20142015

Lecture 1: The topology of random real hypersurfaces and percolation

Lecture 2: Nodal domains for Maass (modular) forms

Lecture 3: Families of zeta functions: their symmetries and applications
2014

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
2012

Lectures: Integrable Systems, Operator Determinants and Probabilistic Models
2011

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

Lecture II: Convergent Sequences of Networks
2010
2009

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

Lecture: The Algebra of Random Surfaces
2007

Lecture I: The Unreasonable Effectiveness of Physics in Modern Mathematics

Lecture II: The Quantum Geometry of Topological String Theory

Lecture III: Quantum Field Theory, DModules and Integrable Systems