Van Winter Memorial Lecture in Mathematical Physics: What is Quantum Field Theory?
Speaker: Nathan Seiberg, Charles Simonyi Professor, Institute for Advanced Study, Princeton
Abstract: We will review the status of Quantum Field Theory (QFT) as the language of physics. We will stress that despite enormous success and a lot of progress, we still do not have a completely satisfactory presentation of the theory. In particular, QFT is not yet mathematically rigorous. This will lead us to discuss the symmetries of QFT as associated with topological operators. This modern view has generalized our ideas of symmetries and has led to many new results.
The Van Winter Memorial Lecture in Mathematical Physics honors the memory of Clasine van Winter, who was a faculty member in the Department of Mathematics and the Department of Physics and Astronomy from 1968 until her retirement in 1999. The annual lecture is jointly sponsored by the Department of Mathematics and the Department of Physics and Astronomy.
Abstract: In many applications, e.g. photonic and quantum systems, one is interested in controlled localization of wave energy.
Edge States are a type of localization along a line-defect or interface between media. We study edge states in honeycomb structures (such as graphene and its photonic analogues) and discuss their novel properties. In particular, we examine the formation of Topologically Protected Edge States, which persist and are stable against strong local distortions of the edge, and are therefore potential vehicles for robust energy-transfer in the presence of defects and random imperfections.
We further discuss rigorous results and conjectures for families of continuum PDE models (Schroedinger and Maxwell) admitting edge states which are topologically protected, edge states which are not protected, and states which remain localized near an edge for a very long time, but likely decay eventually.
Abstract: Quantum mechanics is important for determining the geometry of spacetime. We will review the role of quantum fluctuations that determine the large scale structure of the universe. In some model universes we can give an alternative description of the physics in terms of a theory of particles that lives on its boundary. This implies that the geometry is an emergent property. Furthermore, entanglement plays a crucial role in the emergence of geometry. Large amounts of entanglement are conjectured to give rise to geometric connections, or wormholes, between distant and non-interacting systems.
Refreshments at 3:15 in CP179.
About the speaker: Juan Maldacena is the leading string theorist of his generation. His 1998 discovery of the AdS/CFT correspondence set off a revolution in string theory, and has found applications in many areas of physics and mathematics. Maldacena's work since then has included groundbreaking work in particle physics, cosmology, and quantum gravity. He was awarded a MacArthur Fellowship in 1999, the 2007 APS Dannie Heineman Prize, the 2008 Dirac Medal, the 2012 Fundamental Physics Prize, and is a member of the National Academy of Sciences.
About the van Winter Memorial Lecture in Mathematical Physics
The van Winter Memorial Lecture honors the memory of Clasine van Winter, who held a professorship in the Department of Mathematics and the Department of Physics and Astronomy from 1968 to her retirement in 1999. Professor Van Winter specialized in the study of multiparticle quantum systems; her contributions include the Weinberg-van Winter equations for a multiparticle quantum system, derived independently by Professor van Winter and Professor Steven Weinberg, and the so-called HVZ Theorem which characterizes the essential spectrum of multiparticle quantum systems. She died in October of 2000.
The Ginzburg - Landau theory was first developed to explain magnetic and other properties of superconductors, but had a profound influence on physics well beyond its original area. The theory provided the first demonstration of the Higgs mechanism and it became a fundamental part of the standard model in elementary particle physics. The theory is based on a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics. Geometrically, these are equations for a section of the principal bundle and a connection on this bundle. (The latest variant of these equations is the Seiberg – Witten equations.) In addition to their great importance in physics, they contain beautiful mathematics (see e.g. a review of E. Witten in Bulletin AMS, 2007; some of the mathematics was discovered independently by A. Turing in his explanation of patterns of animal coats). In this talk I will review recent results involving key solutions of these equations - the magnetic vortices and vortex lattices, their existence, stability and dynamics, and how they relate to the modified theta functions appearing in number theory. http://math.as.uky.edu/van-winter
Refreshments will be served at 3:30 p.m. in 179 Chemistry-Physics Building
