2011 Strings Journal Club Seminars

A learning seminar on topics related to the geometric aspects of string theory. Several mathematical subjects, including topology, representation theory, and operator algebras are also discussed.

The notes of a few talks are available below.

Time: Tuesdays, 2:00 pm - 4:00 pm
Location: Innova 21 Building, Room 5.56

This seminar is organised by Pedram Hekmati and Snigdhayan Mahanta.

2011 Seminars

• January 6
  Speaker: P. Hekmati
  Title: Group-valued moment map and quasi-Hamiltonian quantisation
  
  Abstract: This will be an introduction to group-valued moment maps and pre-quantization of quasi-Hamiltonian group actions, as developed by Alekseev-Malken-Meinrenken. I will also discuss the bijective correspondence between quasi-Hamiltonian G-spaces and Hamiltonian LG-spaces with proper moment map.

• March 10
  Speaker: P. Hekmati
  Title: Gerbal representations
  
  Abstract: I will discuss the notion of gerbal group representations following Frenkel-Zhu and provide some concrete examples.

• March 17
  Speaker: S. Mahanta
  Title: Bivariant K-theory for m-algebras (after Cuntz)
  
  Abstract: An m-algebra is an inverse limit of Banach algebras. Many geometric examples can be studied using m-algebras. The construction of the bivariant K-theory groups for m-algebras will be described. Some formal properties will also be discussed, including a universal characterization.

• March 24
  Speaker: P. Hekmati
  Title: Topics in Morse Theory
  
  Abstract: Morse theory studies the relation between the critical points of functions on a space and the shape of the space. This talk will cover the basic concepts and treat a few selected examples in more detail.

• March 31
  Speaker: S. Mahanta
  Title: Bivariant Chern-Connes character (after Cuntz)
  
  Abstract: Building upon the contents of the previous talk we are going to construct the bivariant Chern-Connes character. To this end we shall introduce the bivariant periodic cyclic homology for m-algebras. The bivariant Chern-Connes character is a binatural transformation from bivariant K-theory to bivariant periodic cyclic homology. After outlining its construction we are going to focus on the univariant Chern-Connes character from (univariant) K-theory to (univariant) periodic cyclic homology, which is a generalization of the Chern character in topology.

• April 14 (Special time: 2-3 pm)
  Speaker: V. Mathai
  Title: T-duality - topology change in spacetime
  
  Abstract: I will explain a geometric approach to T-duality, which is a fundamental symmetry of String Theory. In the presence of a background "H-flux", I will show that T-duality implies that a String Theory on topologically different spacetimes can be equivalent! A background in differential forms and some undergraduate topology will be useful for understanding the talk.

• April 21 No Seminar
  Student Vs. Staff Football Match

• April 28
  Speaker: A. Fernández Tojo
  Title: Birkhoff factorisation of loop groups
  
  Abstract: We will give an analytic proof of the Birkhoff decomposition of loop groups and explain how it provides a complete classification of holomorphic vector bundles on the Riemann sphere.

• May 5 (Special time: 12-2 pm)
  Speaker: D. Roberts
  Title: Introduction to 2-groups
  
  Abstract: Whereas a group is a set with a multiplication and an inverse satisfying some properties, a 2-group is a category with a (weak) multiplication and a (weak) inverse satisfying some coherence conditions. Under another name, 2-groups arose in Whitehead and MacLane's classification of low-dimensional homotopy types in the late 1940's, and are now being put to use in contemporary mathematical physics and category theory, with the "string 2-group" engendering many new constructions. This talk will present an introduction to 2-groups, and point towards the latest uses to which 2-groups have been put. A familiarity with categories as far as knowing about natural transformations will be helpful.

• May 12
  Speaker: P. Hekmati
  Title: Octonions: a panorama
  
  Abstract: “The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.” —John Baez.
  
  This talk will let the crazy old uncle out of the attic.

• June 2
  Speaker: Jacob Lurie's lectures at the University of Texas at Austin in 2009
  Title: TQFT and the Cobordism Hypothesis

• June 9
  Speaker: Jacob Lurie's lectures at the University of Texas at Austin in 2009
  Title: TQFT and the Cobordism Hypothesis

• June 16
  Speaker: Jacob Lurie's lectures at the University of Texas at Austin in 2009
  Title: TQFT and the Cobordism Hypothesis

• June 23
  Speaker: Jacob Lurie's lectures at the University of Texas at Austin in 2009
  Title: TQFT and the Cobordism Hypothesis

• July 21
  Speaker: Nigel Higson's Grasp lectures at the University of Texas at Austin in 2010
  Title: K-homology and index theory
  
  Abstract: Lecture 1

• July 26
  Speaker: Nigel Higson's Grasp lectures at the University of Texas at Austin in 2010
  Title: K-homology and index theory
  
  Abstract: Lecture 2

• August 2
  Speaker: Nigel Higson's Grasp lectures at the University of Texas at Austin in 2010
  Title: K-homology and index theory
  
  Abstract: Lecture 3

• August 9
  Speaker: Nigel Higson's Grasp lectures at the University of Texas at Austin in 2010
  Title: K-homology and index theory
  
  Abstract: Lecture 4

• August 16
  Speaker: Siye Wu
  Title: The geometry and physics of Nahm and Bogomolny equations

• August 23
  Speaker: V. Mathai
  Title: Topics related to the Meinrenken's lectures I

• August 30
  Speaker: P. Hekmati
  Title: Topics related to the Meinrenken's lectures II

• September 5-9
  IGA/AMSI Workshop: Group-valued moment maps with applications to mathematics and physics

• December 9
  Speaker: P. Hekmati
  Title: Chern-Simons gauge theory and knot invariants
  
  Abstract: This talk will be a survey of Witten's 1989 classic "Quantum field theory and the Jones polynomial". I will also say a few words on Khovanov homology which provides a modern "categorified" description of knot invariants.