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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
arXiv:1512.06033

Gordon's inequality and condition numbers in conic optimization
with Dennis Amelunxen
Preprint (being revised)
arXiv:1408.3016

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.
arXiv:1303.6672
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
arXiv:1210.3742

Adversarial Smoothed Analysis
with Felipe Cucker and Raphael Hauser
Journal of Complexity 26: 255-262 (2010)
arXiv:0903.3499v1

Coverage Processes of Spheres and Condition Numbers of Linear Programming
with Peter Bürgisser and Felipe Cucker
Annals of Probability 38(2): 570-604 (2010)
arXiv:0712.2816

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)
arXiv:math/0610270

The Complexity of Computing the Hilbert Polynomial of Smooth Equidimensional Complex Projective Varieties
with Peter Bürgisser
Foundations of Computational Mathematics7(1): 51-86 (2007).
arXiv:cs.SC/0502044

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).
arXiv:cs.CC/0301016

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.