Martin A. Fisher School of Physics

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.

"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 non-trivial fusion rules in the associated global symmetry category. 

"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

• 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 energy-conserving Hamiltonian dynamical systems"

Zoom Link for All Talks

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

• Lecture II: Motivic Г-functions

• Lecture III: Relative Completions

• 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

• Lecture I: Algebraic curves and differential equations

• Lecture II: Generalizing hyperbolic surfaces

• Lecture III: Higgs bundles and mirror symmetry

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

• Lecture 2: Mock modular forms in mathematics and physics

• Lecture 3: Umbral Moonshine

• 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

• 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

• Science Blog article

• Lectures: Integrable Systems, Operator Determinants and Probabilistic Models

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

• Lecture II: Convergent Sequences of Networks

• Lecture I: Differential K-theory and Dirac operators

• Lecture II: Twisted K-theory and loop groups

• Lecture III: Dirac charge quantization in string theory

• 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

• Lecture: The Algebra of Random Surfaces

• 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