### Research areas :

### String theory, representation theory, combinatorics

My recent work has largely been in gauge-string duality, in particular the AdS/CFT correspondence, which relates 4-dimensional quantum field theory (QFT) to 10-dimensional string theory. I have developed a mathematical framework based on symmetric groups, Brauer algebras, representation theory, combinatorics, in understanding the map between states in the QFT and states of strings, branes and geometries in the 10 dimensions. A recent theme emerging from these investigations is the role of two-dimensional topological field theories (TFT2) as a structure which captures both the combinatorics and spacetime dependences of correlators in four-dimensional theories. I have also developed simple mathematical models of gauge-string duality in low dimensions, e.g deriving the counting of strings wrapping the two-dimensional sphere from matrix models, which can be viewed as zero dimensional QFT. Some of the mathematical techniques have also been applied to find new counting results for Feynman diagrams in QFT, including the simplest ones : scalar field theory and quantum electrodynamics (QED, which describes photons and electrons).

A complete list of my papers can be accessed at Inspire-HEP-database or Google scholar (Following standard practice in theoretical particle physics, author lists are all alphabetical)

Selected papers organised by theme (although some lie at interfaces of these themes** **

**CFT4 as TFT2**

1. CFT4 as SO(4,2)-invariant TFT2

3. Free quantum fields in 4D and Calabi Yau spaces

#### AdS/CFT, giant graviton branes, correlators of gauge invariant operators

Half-BPS case (related to one-matrix combinatorics)

Eighth-BPS case (related to multi-matrix combinatorics)

- Diagonal multi-matrix correlators and BPS operators in N=4 SYM.
- From counting to construction of BPS states in N=4 SYM.
- Branes, anti-branes and brauer algebras in gauge-gravity duality.

#### Non-BPS and Integrability

#### Fuzzy geometry

- On spherical harmonics for fuzzy spheres in diverse dimensions.
- The Fuzzy S2 structure of M2-M5 systems in ABJM membrane theories.
- Noncommutative gravity from the AdS / CFT correspondence.
- Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons.

#### Mathematical models of gauge-string duality

- Large N 2-D Yang-Mills theory and topological string theory
- From Matrix Models and Quantum Fields to Hurwitz Space and the absolute Galois Group.
- Strings from Feynman Graph counting : without large N.

#### Supersymmetric Gauge theories

#### Matrix Model of M-theory

### Some research presentations

- Permutation centralizer algebras, polynomial invariants and supersymmetric states (talk at conference on representation theory and physics, Leeds, July 2016)
- BPS states, permutations and information (talk at YITP Kyoto programme on string theory, condensed matter physics and quantum information, June 2016)
- Quantum Field thories (QFTs), quivers and word combinatorics (talk at theory group, computer science, EECS, QMUL, Oct. 21, 2015)
- CFT4 (4D conformal QFT) as TFT2( 2D topological field theory) (talk at school of Maths, QMUL, Mar 2, 2015)
- Quiver gauge theory and TFT2s (2d topological field theories) (talk at Quantum integrability workshop, Surrey, 08/2014)
- Quantum states to brane geometries via fuzzy moduli space (talk at Oxford Maths Institute, 02/12)
- Permutations, strings and Feynman Graphs ( talk at City Maths Dept, 11/2011)
- Strings, Permutations and Quantum Fields (talk at Corfu2011 workshop on non-commutatve field theory and gravity)
- Symmetric groups and local operators in gauge theory (talk at Lisbon 2011)
- From numbers to strings and branes (talk at Galileo Galilei Institute 2011)
- Feynman Diagrams and Absolute Galois group (talk at B(A)MC 2010)
- Matrix Models, Hurwitz spaces Galois Group (talk in Southampton Pure Maths group)
- Fuzzy geometry of membranes in M-theory (talk at Imperial)

### A short review article :

- Schur-Weyl duality and Gauge-string duality (Talk given at "Ten years of AdS/CFT in Argentina,2008)

### Teaching

Currently teaching :

Undergraduate Projects supervised :

- From classical strings to photons and gravtions
- Plasma Physics and Nuclear Fusion
- Dark Matter, dark energy and cosmology
- Entanglement and decoherence in quantum physics

Modules taught in the past :

- Electromagnetic theory (4th year MSci course)
- Quantum Mechanics and Symmetry (3rd year)
- Electromagnetism for pre-medical (at Brown)

### Outreach

Some popular talks :

- Symmetries and Surprises in String Theory (Talk for Psi Star QMUL, December 2013)
- What is String Theory ? (talk at Bryanston School, April 2012)
- Strings and hidden geometries (talk at Inauguration of School of Phys and Astro 2012)
- String Theory and Hidden dimensions of spacetime (talk for Waltham Forest Physics masterclass)
- From force and matter to strings( talk at Highgate school, 2003)
- Strings in the quantum world ( talk at Oxford, 2009 )
- Duality and the nature of quantum space-time : ( talk at Oxford,Jan 2009 )
- Space and Time, Light and Gravity in String Theory ( talk at PPARC 2006)

### Grants

Current and recent grants :

- Science and Technology Facilities Council, (£632,432). Brandhuber, Berman, Ramgoolam, Russo, Spence, Thomas, Travaglini, Wecht. Consolidated grant String theory, gauge theory and duality (2011-2015)
- Science and Technology Facilities Council, (£1,431,413). Spence Berman, Brandhuber, Ramgoolam, Russo, Thomas, Travaglini. Rolling grant String theory, gauge theory and duality (2008-2013)
- Particle Physics and Astronomy Research Council: Spence , Berman, Brandhuber, Ramgoolam, Thomas. Rolling grant String theory, gauge theory and gravity (2006-2010), (£249,800.)
- STFC (PPARC) Advanced Fellowship, 2003-2008 ( £220,000 )
- Scientist in charge for Marie Cure Outgoing Fellowship ( MOIF-CT-2006-038381) held by Diego Rodriguez Gomez at QMUL and Princeton.
- Royal Society International exchange grants with South Africa and Cyprus.

### PhDs/Postdocs

PhD students supervised :

- Costis Papageorgakis
- Tom Brown
- David Turton
- Jurgis Pasukonis
- David Garner
- Paolo Mattioli (current)

Recent post-doctoral collaborators at QMUL :

- Diego Rodriguez Gomez
- Vishnu Jejjala
- Yusuke Kimura
- Paul Heslop
- Congkao Wen

### Scientific interests

- Energy issues : I initiated and developed the module "Physics of Energy" at QMUL (PHY250)
- Fusion Energy : This is a fascinating area involving theoretical problems in plasma physics and materials sciences.
- Popular science.

### Some other Interests :

- Science fiction : e.g authors Alistair Reynolds, Stephen Baxter
- Mauritius
- The Village : Isidore-Rose (where I was born)
- Physics at the University of Mauritius
- RCPL : my high school.

- Poetry : There was a time where I had some interest in writing poetry (rigorously free-style when it came to rhyming considerations). Some of it is still at my old web-page at Brown.
- Running, football ....

The complete and up-to-date list of my publications is available at the Inspire-Hep database and at Google Scholar

A description of some my research organized according to some general themes is under the Research tab.