AIMS-GHANA & RESEARCH ON QUANTUM GRAVITY Prince K. Osei - - PowerPoint PPT Presentation

AIMS-GHANA & RESEARCH ON QUANTUM GRAVITY

Prince K. Osei

AIMS-Ghana & University of Ghana Next Einstein Initiative and Rural Prenatal Care in Ghana

October 20, 2014

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 1 / 43

Outline

1

Research on Quantum Gravity Motivation Research Focus Others...

2

AIMS-Ghana Neil’s vision = Our goal Academics Research Outreach

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 1 / 43

The universe as described by GR

Taken from hubblesite.org

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 2 / 43

Einstein’s General relativity

Phenomena at large scales are governed by gravitational interactions Gravitation is inherent in the dynamic Riemannian geometry

• f spacetime

Gravity is a property of spacetime

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Formulation of GR

Gravity = curvature of spacetime = ⇒ curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present.

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Evidence of GR

Taken from Wikipedia

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 5 / 43

General relativity

Led to

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 6 / 43

General relativity

Led to cosmology relativistic astrophysics GPS Leading us towards gravitational wave astronomy

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 6 / 43

General relativity

Predicts

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 7 / 43

General relativity

Predicts black holes gravitational waves expanding universe etc...

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 7 / 43

Quantum mechanics

A theory for the microscopic world Shows that Phenomena at small scales are dominated by strong and electroweak interactions

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 8 / 43

Quantum mechanics

A theory for the microscopic world Shows that Phenomena at small scales are dominated by strong and electroweak interactions

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 8 / 43

Quantum mechanics

Gave rise to

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 9 / 43

Quantum mechanics

Gave rise to particle physics atomic physics nuclear physics semiconductors computers

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 9 / 43

Formulation of QM

Quantum mechanics uses an external time variable or a fixed, non-dynamical background spacetime requires that any dynamical field be quantized, i.e. at small scales it manifests itself in discrete quanta governed by the laws of probability.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 10 / 43

Formulation of QM

Quantum mechanics uses an external time variable or a fixed, non-dynamical background spacetime requires that any dynamical field be quantized, i.e. at small scales it manifests itself in discrete quanta governed by the laws of probability. Formulation incompatible with general relativity!

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 10 / 43

Quantum gravity

quantum gravity = quantum theory of spacetime

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 11 / 43

Quantum gravity

quantum gravity = quantum theory of spacetime

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 11 / 43

Quantum gravity

QUESTION:

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 12 / 43

Quantum gravity

QUESTION: what then is the quanta of spacetime? how then does one describe a quantum spacetime?

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 12 / 43

Quantum gravity

Technical challenges:

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 13 / 43

Quantum gravity

Technical challenges: Einstein’s general relativity is mathematically complicated Einstein’s equations of motion which governs the theory of gravity are a set of highly non-linear differential equations which cannot be solve exactly. Even is a relatively simple case, one would require numerical techniques.

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Approaches to quantum gravity

perturbative quantum gravity canonica quantization & path integrals loop quantum gravity string theory

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 14 / 43

Approaches to quantum gravity

perturbative quantum gravity canonica quantization & path integrals loop quantum gravity string theory noncommutative geometry Spin Foam

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Research Focus

Noncommutative structures in quantum gravity Spin Foam Models Others...

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Noncommutative structures

Proposal

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Noncommutative structures

Proposal quantum gravity will require or predict a new mathematical framework for differential geometry.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 16 / 43

Noncommutative structures

Proposal quantum gravity will require or predict a new mathematical framework for differential geometry. A candidate for such a framework is provided by noncommutative geometry

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 16 / 43

Noncommutative structures

Our focus a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical quantum gravity corrections. the mathematical constraints of NCG may give us constraints on the structure of quantum gravity itself

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 17 / 43

Noncommutative structures

Our focus a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical quantum gravity corrections. the mathematical constraints of NCG may give us constraints on the structure of quantum gravity itself in particular the role of quantum groups or Hopf algebras as the most accessible tool of NCG.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 17 / 43

Some Results

P . K. Osei and B. J. Schroers, On Semiduals of local isometry groups in 3d gravity, J. Math. Phys. 53, (2012) 073510, arxiv: 1109.4086v3 [gr-qc]. P . K. Osei and B. J. Schroers, Classical r-matrices via semidualisation, J. Math. Phys. 54 (2013) 101702. P . K. Osei and B. J. Schroers, Classical r-matrices 3d gravity, in preparation.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 18 / 43

Implications of Results

This should lead to a coherent and precise scenerio of quantum gravity

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 19 / 43

Spin Foam Models

Aimed at providing a non-perturbative and background independent quantisation of gravity via an auxiliary discretization.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 20 / 43

Spin Foam Models

Our focus Study analogue spin foam and spin net models with q−deformed quantum groups understand the relation between them.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 21 / 43

Spin Foam Models

Our focus Study analogue spin foam and spin net models with q−deformed quantum groups understand the relation between them.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 21 / 43

Others

Quantitative Risk Analysis

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Others

Quantitative Risk Analysis Credit and Operational risk

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Quantitative market research for incremental Innovation

Using data to generate ideas for incremental product and service improvement Observation user Sales channel inputs Me too / me better Traditional quantitative marketing research

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 23 / 43

Outline

1

Research on Quantum Gravity Motivation Research Focus Others...

2

AIMS-Ghana Neil’s vision = Our goal Academics Research Outreach

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 24 / 43

Why AIMS?

Next Einstein Africa Neil’s vision = Our goal

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 25 / 43

The result

Graduates who: are independent thinking

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 26 / 43

The result

Graduates who: are independent thinking are technically strong are savvy

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 26 / 43

The result

Graduates who: are independent thinking are technically strong are savvy (entrepreneurial, at home, in academea/business/policy)

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 26 / 43

The result

Graduates who: have transferrable skills (software, English, groupwork, report) have African values.

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 27 / 43

How?

The AIMS model of pedagogy

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 28 / 43

How?

The AIMS model of pedagogy Skills, review, essay. (Balanced themes). Tutorial approach. (Problem based. Resident tutors.) Lectures of international MSc standard. (80% international.)

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 28 / 43

How?

The AIMS model of pedagogy

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 29 / 43

How?

The AIMS model of pedagogy Registration at 3 local universities. Local & International supervision. Academic quality (weekly reviews, continuing assessment). Network. Placement in Africa MPhil/PhD programmes (50% bursaries).

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 29 / 43

Research symbiosis

Tutors are research active. Workshops. Weekly journal seminars. Evening and visiting seminars. Public lectures. Research visitors (short courses).

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 30 / 43

AIMS-GHANA

About 140km from Accra

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AIMS-GHANA

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Academic Partners

local University of Ghana University of Cape Coast Kwame Nkrumah University of Science and Technology

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 33 / 43

Academic Partners

International Durham University, UK, Karlstad University, Sweden, Nanyang University, Singapore TU Chemnitz (Germany) Scottish Universities through the John Maxwell ICMS

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Governance

Board of Trustees Academic advisory board

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 35 / 43

Current Students

40 students from 16 African countries made up of: 12 females and 28 males 14 Ghanaians and 26 Non-Ghanaians 4 Tutors

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Graduation

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 37 / 43

Research

2 Joint research Chair for AIMS-Gh/AIMS-SA & Canadian University partner Mathematical Biology - Immunology

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 38 / 43

Research

BMBF Research Chair at AIMS-Ghana/University of Ghana Mathematical Modelling with differential equations Climate Modelling Water & Sanitation

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Research

Other research projects Rural Prenatal Care in Ghana ....

Prince K. Osei (AIMS-Ghana & UG) AIMS-Ghana & Research on Quantum Gravity October 20, 2014 40 / 43

Research

Workshops Annual workshop on differential equations Annual workshop on Mathematical Modelling

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Outreach

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