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exposition
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publications
Lower bounds on the bounded coefficient complexity of bilinear maps
Journal of the ACM (JACM) 51 (3), 464-482, 2004
On the algebraic complexity of some families of coloured Tutte polynomials
Advances in Applied Mathematics 32 (1-2), 327-349, 2004
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets
Foundations of Computational Mathematics 5 (4), 351-387, 2005
General formulas for the smoothed analysis of condition numbers
Comptes Rendus Mathematique 343 (2), 145-150, 2006
Smoothed analysis of complex conic condition numbers
Journal de mathématiques pures et appliquées 86 (4), 293-309, 2006
The complexity of computing the Hilbert polynomial of smooth equidimensional complex projective varieties
Foundations of Computational Mathematics 7 (1), 59-86, 2007
The probability that a slightly perturbed numerical analysis problem is difficult
Mathematics of Computation 77 (263), 1559-1583, 2008
Adversarial smoothed analysis
Journal of Complexity 26 (3), 255-262, 2010
Coverage processes on spheres and condition numbers for linear programming
The Annals of Probability 38 (2) 570-604, 2010
Living on the edge: Phase transitions in convex programs with random data
Information and Inference: A Journal of the IMA 3 (3), 224-294, 2014
On the volume of tubular neighborhoods of real algebraic varieties
Proceedings of the AMS 143, 1875-1889, 2015
Average-case complexity without the black swans
Journal of Complexity 41, 82-101, 2017
Intrinsic volumes of polyhedral cones: a combinatorial perspective
Discrete & Computational Geometry 58 (2), 371-409, 2017
The dynamics of mutation rate, aging and extrinsic risk in melanoma development
Cancer Research, 2018
Biological sex and age shape melanoma tumour evolution
bioRxiv, 828038, 2019
Chronic UV damage of the stroma improves melanoma survival
Cancer Research 79 (13_Supplement), 2022-2022, 2019
On the error in phase transition computations for compressed sensing
IEEE Transactions on Information Theory 65 (10), 6620-6632, 2019
Persistent homology for low-complexity models
Proceedings of the Royal Society A 475 (2230), 20190081, 2019
Concentration of the intrinsic volumes of a convex body
Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 …, 2020
Dimensionality reduction for k-distance applied to persistent homology
36th International Symposium on Computational Geometry (SoCG 2020), 10: 1-10: 15, 2020
Effective condition number bounds for convex regularization
IEEE Transactions on Information Theory 66 (4), 2501-2516, 2020
Wilkinson’s bus: Weak condition numbers, with an application to singular polynomial eigenproblems
Foundations of Computational Mathematics 20 (6), 1439-1473, 2020
Dimensionality reduction fork-distance applied to persistent homology
Journal of Applied and Computational Topology 5 (4), 671-691, 2021
Molecular subtype, biological sex and age shape melanoma tumour evolution
British Journal of Dermatology 184 (2), 328-337, 2021
Categorising SME Bank Transactions with Machine Learning and Synthetic Data Generation
arXiv preprint arXiv:2508.05425, 2025
A Neural Difference-of-Entropies Estimator for Mutual Information
ECAI 2025 - 28th European Conference on Artificial Intelligence, 2243-2250, 2025
Performance-Efficiency Trade-off for Fashion Image Retrieval
ECAI 2025 - 28th European Conference on Artificial Intelligence, 5264-5271, 2025
Partitioning Theorems for Sets of Semi-Pfaffian Sets, with Applications
Forum of Mathematics, Sigma 14, e5, 2026
Sharp phase transitions in Euclidean integral geometry
High Dimensional Probability X, Springer, 187-258, 2026
Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
arXiv preprint arXiv:2607.08370, 2026
Khovanskii’s Bezout-type Theorem for Pfaffian Functions: A Self-Contained Proof, and Applications
arXiv preprint arXiv:2607.29267, 2026
talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
MA254/354 Theory of ODEs
Lecture, Warwick University, Mathematics Institute, 2026