The Mathematical Implications of Gauge-String Dualities
5-9 March 2012
Conference Room 7.15, Level 7, Ingkarni Wardli (Innova 21) Building
(see on the map
Professor Rajesh Gopakumar obtained his Ph.D. from Princeton University in 1997 under the supervision of Nobel Laureate Professor David Gross. He was subsequently a research associate at Harvard University and he joined the prestigious Harish-Chandra Research Institute (HRI) in Allahabad, India as full-time researcher in 2001. He also held a visiting membership at the Institute for Advanced Study, Princeton during the period 2001-2004. Professor Gopakumar was awarded the 2004 B. M. Birla Science Prize in Physics and the ICTP Prize in 2006. He also received the highly esteemed Shanti Swarup Bhatnagar Award in 2009. He is a member of the Global Young Academy, the Indian National Science Academy, and the Indian Academy of Sciences. Professor Gopakumar is renowned for his outstanding contributions to the field of topological string theory, especially for his work with Cumrun Vafa on Gopakumar-Vafa duality and Gopakumar-Vafa invariants. His current research aims to understand gauge-string dualities better through simple examples with the eventual aim of a first principles derivation of this connection.
Titles of individual lectures
What are Gauge-String Dualities?
In this introduction, I will give a broad overview of the topic of Gauge-String duality (a.k.a. AdS/CFT correspondence)
which is one of the most engaging topics of current research in theoretical physics.
I will try to convey some of the physical motivation, context and importance as well as the mathematical significance of the subject. In particular, the famous Kontsevich derivation of the intersection numbers on the moduli space of Riemann surfaces, turns out to be a special case of such a duality.
From Knots to Counting Curves
To further illustrate the power of these ideas I will describe an unexpected connection between the theory of knots and three manifold invariants (as reformulated by Witten in terms of Chern-Simons quantum field theory) and enumerative invariants of (a class of) Calabi-Yau 3-folds.
From Gauge Theories to String Theories
I proceed to describe a general picture of how gauge theories (in the so-called large N limit) can reorganize themselves into string theories. Underlying this is a cell decomposition of the moduli space of punctured Riemann surfaces and its Strebel parametrisation.
What is the Simplest Gauge-String Duality?
I will argue that one of the most explicit illustrations of how the above reorganization is realized is in a conjectured relation between a Gaussian matrix integral and topological strings on $CP^1$.
Belyi maps and arithmetic Riemann surfaces seem to play a very special role in this case.
Dualities for 2d CFTs
In the final lecture I describe a new direction in which special solvable 2d conformal field theories (with so-called extended $W_N$ symmetry) are dual to theories involving gravity together with a whole tower of higher spin gauge fields in three dimensional hyperbolic space ($AdS_3$).
Professor Gopakumar will also give a colloquium talk on Friday 9 March at 3pm. The title of the talk is String Theory and the Quest for Quantum Spacetime.
Peter Bouwknegt (Australian National University)
Omar Foda (University of Melbourne)
Sergei Kuzenko (University of Western Australia)
Siye Wu (University of Hong Kong)
Titles and Abstracts
Schedule and Slides
There will be no registration fees: all are welcome. However,
if you are interested in attending, kindly send an e-mail to Snigdhayan Mahanta
by 31 January 2012, with the following information:
Position and Affiliation
Please also indicate in your e-mail whether you would like to attend the workshop dinner (Tuesday evening, 6 March), which will be $5 per person.
This event is co-sponsored by the Australian Mathematical Sciences Institute (AMSI). AMSI allocates a travel allowance to each of its member universities (for a list of members, click here). Students or Early Career Researchers from AMSI member universities without access to a suitable research grant or other source of funding may apply to their Head of Mathematical Sciences for subsidy of travel and accommodation out of the departmental travel allowance. No other funding is available.
Participants, other than the invited speakers, are asked to make their own travel and accommodation arrangements. For a list of budget hotels in Adelaide, please click here.
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Local Information for Visitors
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Spinning section of a quintic Calabi-Yau three-fold, courtesy of J. Bryant and based on concepts from A.J. Hanson.
Collision between two subatomic particles, producing other particles including a graviton that escapes from our macroscopically 4-D universe (or "brane") into the extra dimensions of space-time. Courtesy of Fermilab.
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