## Workshop on Geometric Complexity Theory: Wrap Session and Discussion

This session has a talk by Jerzy Weyman on „Quiver Theory” followed by a talk by Ketan Mulmuley giving a brief sketch of the systematic GCT program to cross the GCT chasm (the subject of the two tutorials on the first two days of the workshop) along with a discussion on the broader issues in the context GCT (including the more philosophical issues concerning the basic strategy of GCT and also concerning possible alternatives to GCT or alternative approaches to GCT).

English

**Workshop on Geometric Complexity Theory: Dealing with Orbit Closures in Representations with Finitely Many Orbits**

In this talk I explain the techniques needed to deal with the orbit closures in representations with finitely many orbits. These representations were classified by Kac in 1980. The goals are to decide the normality and Cohen-Macaulay property of the orbit closure, the Hilbert function of the coordinate ring, the defining equations and even in some cases the free resolution of the polynomial ring.

English

**Polish Mathematical Society Mini-Conference: Generic free resolutions and root systems**

In this talk I give an explicit construction of the generic ring R_{gen} for finite free resolutions of length 3. The corresponding problem for resolutions of length 2 was solved in 1970’ies by Hochster and Huneke. The key role is played by the defect Lie algebra introduced in my old work on the subject. The defect Lie algebra turns out to be a parabolic Lie algebra in a Kac-Moody Lie algebra associated to the graph T_{p,q,r} corresponding to the format of the resolution. The ring R_{gen} is Noetherian if and only if the graph T_{p.q.r} is a Dynkin graph.

Polish

**ASARC Seminar: Introdcution to Boij-Soderberg theory: Part I**

The first part of the Australia South Asia Research Centre Seminar talk took place on 11th of December, 2009. The main subjects: finite resolution, pure resolutions, simple structure, simplices of maximal dimension and the greedy algorithm.

English

## ASARC Seminar: Introdcution to Boij-Soderberg theory: Part II

The second part of the Australia South Asia Research Centre Seminar talk took place on 14th of December, 2009. The main subjects: Ferrars diagram, partition preserving cross, conjugate partition, lineary reductive and arbitrary shifts with an example.

English

**ASARC Seminar: Introdcution to Boij-Soderberg theory: Part III**

The third part of the Australia South Asia Research Centre Seminar talk took place on 14th of December, 2009. The main subjects: cone of co-homology tables, existance of supernatural bundles, first approximation pairing and open problems.

English

## ASARC Seminar: Boij-Soderberg conjectures on Betti tables of graded modules

This talk was also a part of the Australia South Asia Research Centre Seminar, which took place on 10th of December, 2009. The main subjects: Hilbert’s energy crm, the Hilbert serious, the normalized Betty table and construction of the pure resolutions.

English