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"Where there is matter, there is geometry."
Johannes Kepler (1571-1630)
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IGA Lecture Series
There will be 6 or more 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.
More information.
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.