# 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.