2010 Lecture Series

There will be several distinguished IGA Lecturers spread throughout the year, who will give lecture series on current topics of intense international interest in Geometry and its Applications.

Frank Kutzschebauch (University of Berne, Switzerland)

• Group Actions in Complex Analytic Geometry

1:10 pm to 3:00 pm, Friday 8 January 2010
10:10 am to 12:00 pm, Fridays 15, 22, and 29 January 2010,
in the Board Room (room 3.01) on level 3, 10 Pulteney Street.

Mohammed Abouzaid (Clay Research Fellow, MIT)

• Introduction to Mirror Symmetry and the Fukaya Category

Abstract:
I shall give an overview of recent progress in Homological mirror symmetry both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified.

A series of 10 hours of lectures, 14-22 July 2010
1:10 pm - 3:00 pm, July 15, 16, 19, 20, 21, 2010.
in Napier G04 in the Napier building on the main campus.

Titles for the individual lectures:

• An overview of Homological mirror symmetry
• Singular torus fibrations and geometric origin of mirror symmetry
• The Fukaya category of Lagrangians
• Homological mirror symmetry for the simplest abelian surface
• Landau-Ginzburg potentials as mirrors to Fano varieties
• Mirror symmetry for toric varieties
• Towards Mirror Symmetry for hypersurfaces of general type

Talks by David Baraglia (ANU)

• Moduli of special Lagrangian and coassociative submanifolds
• Moduli of special Lagrangian and coassociative submanifolds, part 2

Dan Freed (University of Texas at Austin)

• Dirac Operators in Geometry, Topology, Representation Theory, and Physics

Abstract:
Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations.

A series of 10 hours of lectures, 18-22 October, 2010.
10:00 am-12:00 am, October 18, 19, 20, 21, 22, 2010.
In Conference Room 7.15, Level 7, Innova 21 building on the main campus (see the map).

Titles of individual lectures:

• Introduction to twisted K-theory:
  After a review of standard K-theory I will discuss the twisted form and some properties. Then I will compute twisted K_G(G) in some cases.
• Loop groups and Dirac families:
  I will describe the finite and infinite-dimensional versions of the construction which yields my theorem with Hopkins and Teleman. This will include some generalities about loop groups and their representations.
• A TQFT from twisted K-theory:
  I will discuss TQFTs in general and give some examples, etc. I will show how to construct the ring structure on twisted K_G(G).
• Differential K-theory and the Atiyah-Singer theorem:
  An introductory lecture on differential cohomology theories in general and differential K-theory in particular. Then the differential index theorem with Lott.
• Anomalies and "categorified" index theorems:
  A general lecture on some physics, then some discussion of anomalies in supersymmetric quantum mechanics and on the worldsheet of string theory.