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.

For the IGA Lecturers in 2013, click here.

For the IGA Lecturers in 2012, click here.

For the IGA Lecturers in 2011, click here.

Frank Kutzschebauch (University of Berne, Switzerland)

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.

More information.

Mohammed Abouzaid (Clay Research Fellow, MIT)

** 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: **

Talks by David Baraglia (ANU)

Dan Freed (University of Texas at Austin)

**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:**

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.

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.

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).

An introductory lecture on differential cohomology theories in general and differential K-theory in particular. Then the differential index theorem with Lott.

A general lecture on some physics, then some discussion of anomalies in supersymmetric quantum mechanics and on the worldsheet of string theory.

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