Mathematical Physics

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Curvature in Noncommutative Geometry

masoud khalkhali Western University
May 09, 2014

PIRSA:14050064
Mathematical Physics
The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics

Robbert Dijkgraaf Institute for Advanced Study (IAS)
March 05, 2014

PIRSA:14030083
Mathematical Physics
The Sherrington-Kirkpatrick model and its diluted version

Dmitry Panchenko Texas A&M University
February 20, 2014

PIRSA:14020151
Mathematical Physics
Non equilibrium thermodynamic of gravitational screens

Laurent Freidel Perimeter Institute for Theoretical Physics
February 19, 2014

PIRSA:14020144
General Relativity & Quantum Cosmology

Mathematical Physics
Fractional statistics in two-dimensions: Anyon there?

Smitha Vishveshwara University of Illinois Urbana-Champaign
November 06, 2013

PIRSA:13110062
Mathematical Physics
Slippery Waves: Brilliance Brings Blind Spots

Leo Kadanoff
September 25, 2013

PIRSA:13090051
Mathematical Physics
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical Physics
Resources

Tobias Fritz Universität Innsbruck
May 15, 2013

PIRSA:13050019
Mathematical Physics
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical Physics
Energy and the Environment - What Physicists Can Do

John Baez University of California, Riverside
April 17, 2013

PIRSA:13040030
Mathematical Physics
Mathematica - Lecture 4

Pedro Vieira Perimeter Institute for Theoretical Physics
December 14, 2012

PIRSA:12120022
Mathematical Physics
Mathematica - Lecture 3b

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120021
Mathematical Physics

Curvature in Noncommutative Geometry

masoud khalkhali Western University
May 09, 2014

PIRSA:14050064
Mathematical Physics
After the seminal work of Connes and Tretkoff on the Gauss-Bonnet theorem for the noncommutative 2-torus and its extension by Fathizadeh and myself, there have been significant developments in understanding the local differential geometry of these noncommutative spaces equipped with curved metrics. In this talk, I will review a series of joint works with Farzad Fathizadeh in which we compute the scalar curvature for curved noncommutative tori and prove the analogue of Weyl's law and Connes' trace theorem. Our final formula for the curvature matches precisely with the one computed independently by A. Connes and H. Moscovici. I will then report on our recent work on the computation of scalar curvature for noncommutative 4-tori (which involves intricacies due to violation of the Kähler condition). We show that metrics with constant curvature are extrema of the analogue of the Einstein–Hilbert action. A purely noncommutative feature in these works is the appearance of the modular automorphism from Tomita–Takesaki theory of KMS states in the final formulas for the curvature.
The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics

Robbert Dijkgraaf Institute for Advanced Study (IAS)
March 05, 2014

PIRSA:14030083
Mathematical Physics
Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. In this lecture I want to argue for the reverse effect: Nature is an important source of inspiration for mathematics, even of the purest kind. In recent years ideas from quantum field theory, elementary particles physics and string theory have completely transformed mathematics, leading to solutions of deep problems, suggesting new invariants in geometry and topology, and, perhaps most importantly, putting modern mathematical ideas in a `natural’ context.
The Sherrington-Kirkpatrick model and its diluted version

Dmitry Panchenko Texas A&M University
February 20, 2014

PIRSA:14020151
Mathematical Physics
I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main motivations in these models is to find a formula for the maximum of the process, or the free energy, in the limit when the size of the system is getting large. The answer depends on understanding the structure of the Gibbs measure in a certain sense, and this structure is expected to be described by the so called Parisi solution in the SK model and Mézard-Parisi solution in the diluted SK model. I will explain what these are and mention some results in this direction.
Non equilibrium thermodynamic of gravitational screens

Laurent Freidel Perimeter Institute for Theoretical Physics
February 19, 2014

PIRSA:14020144
General Relativity & Quantum Cosmology

Mathematical Physics
In this talk I will review the evidence for a mysterious and deep relationship between gravitational dynamics and thermodynamics. I will show how we can extend this connection to non equilibrium thermodynamics. Using the fact that the gravitational equations are fundamentally holographic, we express them in a way that shows a deep connection between gravity and the dynamics of viscous bubbles. We will explore some aspects of this surprising correspondence.
Fractional statistics in two-dimensions: Anyon there?

Smitha Vishveshwara University of Illinois Urbana-Champaign
November 06, 2013

PIRSA:13110062
Mathematical Physics
A fascinating aspect of the two dimensional world is the possible existence of anyons, particles which obey 'fractional' statistics different from fermionic and bosonic statistics. In this colloquium, following an introduction to fractional particles in the context of quantum Hall systems, some of the tantalizing experiments for detecting the fractional charge of these particles will be described. Probes of fractional statistics in these systems will be discussed, drawing from analogies with the bosonic behavior of light studied by Hanbury Brown and Twiss in the 1950's as well as in the more recent beam-splitter settings in quantum optics. Finally, the exciting prospect of detecting fractional statistics in the context of superconductors will be explored.
Slippery Waves: Brilliance Brings Blind Spots

Leo Kadanoff
September 25, 2013

PIRSA:13090051
Mathematical Physics
Superfluidity and superconductivity are two remarkable phenomena in which, at low temperatures, materials abruptly gain the ability to flow without friction. Microscopic quantum theories of these phases of matter were constructed in blockbuster papers of Lev Landau (1940) and John Bardeen, Leon Cooper, and J. Robert Schrieffer (1957). The actual explanation of the flow, however, is rooted in a Einstein paper of 1924 that introduces a condensate, a quantum configuration describing a finite fraction of the particles in the system. Superfluidity can then be understood in terms of the wave function for this configuration, which necessarily extends over a finite fraction of the system. Neither blockbuster paper mentions Einstein or the crucial idea of a condensate wave function. The reasons for this omission are mooted.
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical Physics
The last few years have seen a spate of operational or information-theoretic
derivations (or \reconstructions") of nite-dimensional quantum mechanics [1]. These rest of some strong assumptions. In particular, most assume the state of a composite system is entirely determined by the joint probabilities it assigns to the outcomes of measurements on the component systems. This condition, often called local tomography, is satis ed by neither real nor quaternionic quantum theory. If we are interested in the possibilities for theories more general than orthodox quantum mechanics, we might wish to relax this constraint.
In this talk I will discuss a weaker system of assumptions, involving correla-
tions between a probabilistic system and an isomorphic conjugate system, that leads to a representation of such systems in terms of euclidean Jordan algebras [2]. These have a well-known classi cation as direct sums of real, complex or quaternionic quantum systems, possibly the exceptional Jordan algebra, and spin factors. The last are a form of \bit", characterized by a family of two-valued observables, parametrized by antipodal vectors in a sphere of arbitrary dimension. Orthodox quantum mechanics can be singled out by imposing local tomography, plus the existence of a qubit as additional axioms [3]. However, there is a natural way to form non-signaling, but generally non-locally tomo-graphic, composites of systems based on special euclidean Jordan algebras (that is, excluding the exceptional one). This yields a probabilistic theory strictly, but not wildly, more general than orthodox nite-dimensional QM; one that elegantly uni es real, complex and quaternionic quantum theory, has a simple operational basis, and allows for a spectrum of bits more general than permitted in orthodox quantum theory. Parts of this talk reflect ongoing joint work with Howard Barnum, Matthew Graydon and Cozmin Ududec.
References:
[1] G. Chiribella, M. D'Ariano and P. Perinotti, Phys. Rev. A 84, (2011), 012311-
012350; B. Dakic and C. Brukner, in H. Halvorson (ed.), Deep Beauty, Cambridge,
2011; P. Goyal, Phys. Rev. A 78 (2008), 052120-052146; L. Hardy, arXiv:quant-
ph/0101012 (2001); L. Masanes and M. Mueller, New J. Phys. 13 (2011) ; J. Rau,
Annals of Physics 324 (2009) 2622{2637;
[2] A. Wilce, Conjugates, correlation and quantum mechanics, arXiv:1206.2897 (2012)
[3] H. Barnum and A. Wilce, Local tomography and the Jordan structure of quantum
theory, arXiv:1202.4513, (2012)
Resources

Tobias Fritz Universität Innsbruck
May 15, 2013

PIRSA:13050019
Mathematical Physics
One of the main challenges that we face both as individual persons and as a species concerns the distribution and use of resources, such as water, time, capital, computing power or negatively valued
resources like nuclear waste. Also within theoretical physics, one frequently deals with resources like free energy or quantum entanglement. I will describe a mathematical theory of resources which makes quantitative predictions about how many resources are required for producing a certain commodity and outline some applications to information theory.
Joint work with Bob Coecke and Rob Spekkens.
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical Physics
In two spatial dimensions, there is a good correspondence between TQFTs and topological phases of matter for spin systems. I will discuss this correspondence in one and three spatial dimensions for spin systems. If time permits, I will also discuss the situation for fermion systems.
Energy and the Environment - What Physicists Can Do

John Baez University of California, Riverside
April 17, 2013

PIRSA:13040030
Mathematical Physics
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. While politics and economics pose the biggest challenges, physicists are in a good position to help make this transition a bit easier. After a quick review of the problems, we discuss a few ways physicists can help.
Mathematica - Lecture 4

Pedro Vieira Perimeter Institute for Theoretical Physics
December 14, 2012

PIRSA:12120022
Mathematical Physics
Mathematica - Lecture 3b

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120021
Mathematical Physics

Title	Speaker(s)	Date	Talk Type	Info link
Curvature in Noncommutative Geometry	masoud khalkhali	2014-05-09	Scientific Series	View details
The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics	Robbert Dijkgraaf	2014-03-05	Scientific Series	View details
The Sherrington-Kirkpatrick model and its diluted version	Dmitry Panchenko	2014-02-20	Scientific Series	View details
Non equilibrium thermodynamic of gravitational screens	Laurent Freidel	2014-02-19	Scientific Series	View details
Fractional statistics in two-dimensions: Anyon there?	Smitha Vishveshwara	2013-11-06	Scientific Series	View details
Slippery Waves: Brilliance Brings Blind Spots	Leo Kadanoff	2013-09-25	Scientific Series	View details
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory		2013-05-30	Conference	View details
Resources	Tobias Fritz	2013-05-15	Scientific Series	View details
TQFTs and Topological Phases of Matter	Zhenghan Wang	2013-05-06	Conference	View details
Energy and the Environment - What Physicists Can Do	John Baez	2013-04-17	Scientific Series	View details
Mathematica - Lecture 4	Pedro Vieira	2012-12-14	Course	View details
Mathematica - Lecture 3b	Pedro Vieira	2012-12-10	Course	View details

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Format results

Curvature in Noncommutative Geometry

The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics

The Sherrington-Kirkpatrick model and its diluted version

Non equilibrium thermodynamic of gravitational screens

Fractional statistics in two-dimensions: Anyon there?

Slippery Waves: Brilliance Brings Blind Spots

Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory

Resources

TQFTs and Topological Phases of Matter

Energy and the Environment - What Physicists Can Do

Mathematica - Lecture 4

Mathematica - Lecture 3b

Curvature in Noncommutative Geometry

The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics

The Sherrington-Kirkpatrick model and its diluted version

Non equilibrium thermodynamic of gravitational screens

Fractional statistics in two-dimensions: Anyon there?

Slippery Waves: Brilliance Brings Blind Spots

Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory

Resources

TQFTs and Topological Phases of Matter

Energy and the Environment - What Physicists Can Do

Mathematica - Lecture 4

Mathematica - Lecture 3b