Some Computational Problems in Linear Algebra as Hard as Matrix Multiplication. - Peter Bürgisser; Marek Karpinski; Thomas Lickteig (Comput. Complex., 1991)

Test complexity of generic polynomials. - Peter Bürgisser; Thomas Lickteig; Michael Shub (J. Complex., 1992)

On Randomized Semi-algebraic Test Complexity. - Peter Bürgisser; Marek Karpinski; Thomas Lickteig (J. Complex., 1993)

Algebraic complexity theory. - Peter Bürgisser; Michael Clausen; Mohammad Amin Shokrollahi (Springer, 1997)

On the Parallel Complexity of the Polynomial Ideal Membership Problem. - Peter Bürgisser (J. Complex., 1998)

On the Structure of Valiant's Complexity Classes. - Peter Bürgisser (Discret. Math. Theor. Comput. Sci., 1999)

Completeness and Reduction in Algebraic Complexity Theory. - Peter Bürgisser (Springer, 2000)

The Computational Complexity to Evaluate Representations of General Linear Groups. - Peter Bürgisser (SIAM J. Comput., 2000)

The Computational Complexity of Immanants. - Peter Bürgisser (SIAM J. Comput., 2000)

Cook's versus Valiant's hypothesis. - Peter Bürgisser (Theor. Comput. Sci., 2000)

Lower Bounds and Real Algebraic Geometry. - Peter Bürgisser (Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2001)

On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity. - Peter Bürgisser (MFCS, 2001)

Counting Complexity Classes over the Reals I: The Additive Case. - Peter Bürgisser; Felipe Cucker (ISAAC, 2003)

Counting Complexity Classes for Numeric Computations I: Semilinear Sets. - Peter Bürgisser; Felipe Cucker (SIAM J. Comput., 2003)

The Complexity of Factors of Multivariate Polynomials. - Peter Bürgisser (Found. Comput. Math., 2004)

Lower bounds on the bounded coefficient complexity of bilinear maps. - Peter Bürgisser; Martin Lotz (J. ACM, 2004)

Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets. - Peter Bürgisser; Felipe Cucker; Martin Lotz (Found. Comput. Math., 2005)

The complexity of semilinear problems in succinct representation. - Peter Bürgisser; Felipe Cucker; Paulin Jacobé de Naurois (Comput. Complex., 2006)

On defining integers in the counting hierarchy and proving lower bounds in algebraic complexity. - Peter Bürgisser (Electron. Colloquium Comput. Complex., 2006)

Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets. - Peter Bürgisser; Felipe Cucker (J. Complex., 2006)

Differential forms in computational algebraic geometry. - Peter Bürgisser; Peter Scheiblechner (ISSAC, 2007)

On Defining Integers in the Counting Hierarchy and Proving Arithmetic Circuit Lower Bounds. - Peter Bürgisser (STACS, 2007)

The Complexity of Computing the Hilbert Polynomial of Smooth Equidimensional Complex Projective Varieties. - Peter Bürgisser; Martin Lotz (Found. Comput. Math., 2007)

Guest Editor's Preface. - Peter Bürgisser; Andrei Gabrielov; Teresa Krick; Gregorio Malajovich (J. Complex., 2008)

The probability that a slightly perturbed numerical analysis problem is difficult. - Peter Bürgisser; Felipe Cucker; Martin Lotz (Math. Comput., 2008)

On Defining Integers And Proving Arithmetic Circuit Lower Bounds. - Peter Bürgisser (Comput. Complex., 2009)

An overview of mathematical issues arising in the Geometric complexity theory approach to VP v.s. VNP - Peter Bürgisser; J. M. Landsberg; Laurent Manivel; Jerzy Weyman (CoRR, 2009)

Exotic Quantifiers, Complexity Classes, and Complete Problems. - Peter Bürgisser; Felipe Cucker (Found. Comput. Math., 2009)

On the complexity of counting components of algebraic varieties. - Peter Bürgisser; Peter Scheiblechner (J. Symb. Comput., 2009)

On the Complexity of Numerical Analysis. - Eric Allender; Peter Bürgisser; Johan Kjeldgaard-Pedersen; Peter Bro Miltersen (SIAM J. Comput., 2009)

10481 Abstracts Collection - Computational Counting. - Peter Bürgisser; Leslie Ann Goldberg; Mark Jerrum (Computational Counting, 2010)

10481 Executive Summary - Computational Counting. - Peter Bürgisser; Leslie Ann Goldberg; Mark Jerrum (Computational Counting, 2010)

Solving polynomial equations in smoothed polynomial time and a near solution to smale's 17th problem. - Peter Bürgisser; Felipe Cucker (STOC, 2010)

Counting Irreducible Components of Complex Algebraic Varieties. - Peter Bürgisser; Peter Scheiblechner (Comput. Complex., 2010)

Smoothed Analysis of Moore-Penrose Inversion. - Peter Bürgisser; Felipe Cucker (SIAM J. Matrix Anal. Appl., 2010)

Probabilistic analysis of condition numbers. - Peter Bürgisser (ISSAC, 2011)

Geometric complexity theory and tensor rank. - Peter Bürgisser; Christian Ikenmeyer (STOC, 2011)

An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to VP≠VNP. - Peter Bürgisser; J. M. Landsberg; Laurent Manivel; Jerzy Weyman (SIAM J. Comput., 2011)

Prospects for Geometric Complexity Theory. - Peter Bürgisser (CCC, 2012)

Robust smoothed analysis of a condition number for linear programming. - Peter Bürgisser; Dennis Amelunxen (Math. Program., 2012)

A Coordinate-Free Condition Number for Convex Programming. - Dennis Amelunxen; Peter Bürgisser (SIAM J. Optim., 2012)

Condition - The Geometry of Numerical Algorithms. - Peter Bürgisser; Felipe Cucker (Springer, 2013)

Explicit lower bounds via geometric complexity theory. - Peter Bürgisser; Christian Ikenmeyer (STOC, 2013)

Computational Counting (Dagstuhl Seminar 13031). - Peter Bürgisser; Leslie Ann Goldberg; Mark Jerrum; Pascal Koiran (Dagstuhl Reports, 2013)

Deciding Positivity of Littlewood-Richardson Coefficients. - Peter Bürgisser; Christian Ikenmeyer (SIAM J. Discret. Math., 2013)

Computing the Chow Variety of Quadratic Space Curves. - Peter Bürgisser; Kathlén Kohn; Pierre Lairez; Bernd Sturmfels (MACIS, 2015)

Permanent versus determinant, obstructions, and Kronecker coefficients. - Peter Bürgisser (CoRR, 2015)

Fundamental invariants of orbit closures. - Peter Bürgisser; Christian Ikenmeyer (CoRR, 2015)

Permanent versus determinant: not via saturations of monoids of representations. - Peter Bürgisser; Christian Ikenmeyer; Jesko Hüttenhain (CoRR, 2015)

Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242). - Peter Bürgisser; Felipe Cucker; Marek Karpinski; Nicolai N. Vorobjov Jr. (Dagstuhl Reports, 2015)

Probabilistic Analysis of the Grassmann Condition Number. - Dennis Amelunxen; Peter Bürgisser (Found. Comput. Math., 2015)

Intrinsic volumes of symmetric cones and applications in convex programming. - Dennis Amelunxen; Peter Bürgisser (Math. Program., 2015)

No Occurrence Obstructions in Geometric Complexity Theory. - Peter Bürgisser; Christian Ikenmeyer; Greta Panova (FOCS, 2016)

Condition Length and Complexity for the Solution of Polynomial Systems. - Diego Armentano; Carlos Beltrán 001; Peter Bürgisser; Felipe Cucker; Michael Shub (Found. Comput. Math., 2016)

On the condition of the zeros of characteristic polynomials. - Peter Bürgisser; Felipe Cucker; Elisa Rocha Cardozo (J. Complex., 2017)

Condition of Intersecting a Projective Variety with a Varying Linear Subspace. - Peter Bürgisser (SIAM J. Appl. Algebra Geom., 2017)

Membership in Moment Polytopes is in NP and coNP. - Peter Bürgisser; Matthias Christandl; Ketan D. Mulmuley; Michael Walter 005 (SIAM J. Comput., 2017)

Efficient Algorithms for Tensor Scaling, Quantum Marginals, and Moment Polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (FOCS, 2018)

Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory. - Peter Bürgisser; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (ITCS, 2018)

Towards a Theory of Non-Commutative Optimization: Geodesic 1st and 2nd Order Methods for Moment Maps and Polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (FOCS, 2019)

Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (CoRR, 2019)

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time. - Peter Bürgisser; Felipe Cucker; Pierre Lairez (J. ACM, 2019)

On the Number of Real Zeros of Random Fewnomials. - Peter Bürgisser; Alperen Ali Ergür; Josué Tonelli-Cueto (SIAM J. Appl. Algebra Geom., 2019)

Interior-point methods for unconstrained geometric programming and scaling problems. - Peter Bürgisser; Yinan Li; Harold Nieuwboer; Michael Walter 005 (CoRR, 2020)

Rigid continuation paths II. Structured polynomial systems. - Peter Bürgisser; Felipe Cucker; Pierre Lairez (CoRR, 2020)

Correction To: The Complexity of Factors of Multivariate Polynomials. - Peter Bürgisser (Found. Comput. Math., 2020)

Computing the Homology of Semialgebraic Sets. I: Lax Formulas. - Peter Bürgisser; Felipe Cucker; Josué Tonelli-Cueto (Found. Comput. Math., 2020)

The real tau-conjecture is true on average. - Irénée Briquel; Peter Bürgisser (Random Struct. Algorithms, 2020)

Polynomial Time Algorithms in Invariant Theory for Torus Actions. - Peter Bürgisser; M. Levent Dogan; Visu Makam; Michael Walter 005; Avi Wigderson (CCC, 2021)

Optimization, Complexity and Invariant Theory (Invited Talk). - Peter Bürgisser (STACS, 2021)

Computing the Homology of Semialgebraic Sets. II: General Formulas. - Peter Bürgisser; Felipe Cucker; Josué Tonelli-Cueto (Found. Comput. Math., 2021)

Real zeros of mixed random fewnomial systems. - Peter Bürgisser (ISSAC, 2023)

Complexity of Robust Orbit Problems for Torus Actions and the abc-Conjecture. - Peter Bürgisser; Mahmut Levent Dogan; Visu Makam; Michael Walter 005; Avi Wigderson (CCC, 2024)

On the Hardness of PosSLP. - Peter Bürgisser; Gorav Jindal (SODA, 2024)

Completeness classes in algebraic complexity theory. - Peter Bürgisser (CoRR, 2024)