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- Peter Bürgisser, Michael Clausen, Amin Shokrollahi
- Grundlehren der mathematischen Wissenschaften
- 1997

This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and… (More)

- Peter Bürgisser
- 2000

1 Introduction.- 2 Valiant's Algebraic Model of NP-Completeness.- 3 Some Complete Families of Polynomials.- 4 Cook's versus Valiant's Hypothesis.- 5 The Structure of Valiant's Complexity Classes.- 6… (More)

- Eric Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen
- SIAM J. Comput.
- 2008

We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis: (a) the Blum-Shub-Smale model of computation over the reals; and (b) a problem… (More)

- Peter Bürgisser, Felipe Cucker
- J. Complexity
- 2006

We define counting classes #PR and #PC in the Blum-Shub-Smale setting of computations over the real or complex numbers, respectively. The problems of counting the number of solutions of systems of… (More)

- Peter Bürgisser
- Theor. Comput. Sci.
- 2000

We first investigate the dependency of our complexity concepts on the field k. We prove that for algebraically closed fields k, the truth of Valiant’s hypothesis VP ≠ VNP depends at most on the… (More)

Introduction In the last few years the quantitative modelling of credit risk has received a lot of attention within the financial industry. Several models have been released to the public, notably… (More)

- Peter Bürgisser, Christian Ikenmeyer
- STOC
- 2010

Mulmuley and Sohoni [GCT1, SICOMP 2001; GCT2, SICOMP 2008] proposed to view the permanent versus determinant problem as a specific orbit closure problem and to attack it by methods from geometric… (More)

- Peter Bürgisser
- STACS
- 1998

In [25, 27] Valiant developed an algebraic analogue of the theory of NP-completeness for computations with polynomials over a field. We further develop this theory in the spirit of structural… (More)

- Peter Bürgisser, J. M. Landsberg, Laurent Manivel, Jerzy Weyman
- SIAM J. Comput.
- 2009

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the Geometric Complexity Theory program to prove a variant of Valiant's algebraic… (More)

- Eric Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen
- 21st Annual IEEE Conference on Computational…
- 2005

We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the… (More)