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Some Publications

The dynamics of mutation rate, ageing and differential risk in melanoma development
with Amaya Virós and Simon Furney
Preprint, 2017

Persistent homology for low-complexity models
Preprint, 2017

Effective condition bounds for convex regularization
with Dennis Amelunxen and Jake Walvin
Preprint, 2017

Average-case analysis without the black swans
with Dennis Amelunxen
Journal of Complexity, 2016

Intrinsic volumes of polyhedral cones: a combinatorial perspective
with Dennis Amelunxen
To appear in Discrete and Computational Geometry, 2017

Gordon's inequality and condition numbers in conic optimization
with Dennis Amelunxen
Preprint (being revised)

Living on the edge: Phase transitions in convex programs with random data.
with Dennis Amelunxen, Mike McCoy and Joel Tropp
Information and Inference, 3(3), pp. 224-294., 2014.
Code for generating the figures.
Winner of inaugural best paper prize

On the Volume of Tubular Neighborhoods of Real Algebraic Varieties
Proceedings of the AMS, 2013

Adversarial Smoothed Analysis
with Felipe Cucker and Raphael Hauser
Journal of Complexity 26: 255-262 (2010)

Coverage Processes of Spheres and Condition Numbers of Linear Programming
with Peter Bürgisser and Felipe Cucker
Annals of Probability 38(2): 570-604 (2010)

The probability that a small perturbation of a numerical analysis problem is difficult
with Peter Bürgisser and Felipe Cucker
Mathematics of Computation 77: 1559-1583, (2008)

The Complexity of Computing the Hilbert Polynomial of Smooth Equidimensional Complex Projective Varieties
with Peter Bürgisser
Foundations of Computational Mathematics7(1): 51-86 (2007).

General formulas for the smoothed analysis of condition numbers
with Peter Bürgisser and Felipe Cucker
C. R. Acad. Sci. Paris, Ser. I 343, pp.145-150 (2006).

Smoothed analysis of complex conic condition numbers
with Peter Bürgisser and Felipe Cucker
Journal de Mathématiques Pures et Appliquées 86: 293-309 (2006).

On Numerical Invariants in Algebraic Complexity Theory
PhD Thesis, July 2005.

Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets
with P.Bürgisser and Felipe Cucker
Foundations of Computational Mathematics 5(4): 351-387 (2005)

The Complexity of Computing the Euler Characteristic of Complex Varieties
with Peter Bürgisser and Felipe Cucker
C. R. Acad. Sci. Paris, Ser. I 339 (2004)

Lower Bounds on the Bounded Coefficient Complexity of Bilinear Maps
with Peter Bürgisser
Journal of the ACM 51(3):464-482 (2004).

On the algebraic complexity of some families of coloured Tutte polynomials
with Johann A. Makowsky
Advances in Applied Mathematics 32 (1-2), pp. 327-349, 2004.