Martin Lotz


School of Mathematics
James Clerk Maxwell Building
The King's Buildings
The University of Edinburgh
Edinburgh, EH9 3JZ

e-mail: first dot last at ed dot ac dot uk

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About...

After growing up in Germany, Argentina and Mexico, I studied Mathematics in Basel, the ETH (Swiss Federal Institute of Technology) in Zürich, and the University of Paderborn, where I finished my doctorate in Algebraic Complexity Theory. I have worked as a post-doctoral researcher at the City University of Hong Kong, as a DFG Research Fellow at the University of Oxford, and currently as a Research Fellow at the University of Edinburgh, supported by a Leverhulme Trust and Seggie Brown Fellowship. I'm associated to the Compressed Sensing Group, the Algorithms and Complexity Group in the School of Informatics, and also maintain contact with the Edinburgh Research Group in Optimization.

Curriculum Vitae

Research Interests

My interests span a wide range of mathematics and its applications. My current work explores connections between conic optimization theory and compressed sensing thresholds. Past work has been in algebraic complexity theory, computational algebra and geometry, foundations of numerical analysis, combinatorics, and probability theory. Besides my fundamental research interests, I am also interested in practical applications of optimization methods.

Teaching

Last year I was teaching the Differential Equation Solution and Modelling (MATH08022) course for first year students.
Previous Teaching

Where you may find me (upcoming events)

3rd Conference on Optimization Methods and Software, May 13-17 2012, Chania, Crete
21st International Symposium on Mathematical Programming, August 19-24 2012, Berlin

Publications

Raphael Hauser, Martin Lotz
Smoothed Analysis of Distance Functions: A General Approach.
In preparation.
[ pdf ] Martin Lotz
On the Volume of Tubular Neighbourhoods of Real Algebraic Varieties.
Preprint.
[ ps | pdf ] Felipe Cucker, Raphael Hauser, Martin Lotz
Adversarial Smoothed Analysis
Journal of Complexity 26: 255-262 (2010)
Arxiv: 0903.3499v1
[ ps | pdf ] Peter Bürgisser, Felipe Cucker, Martin Lotz
Coverage Processes of Spheres and Condition Numbers of Linear Programming.
Annals of Probability 38(2): 570-604 (2010)
Arxiv: 0712.2816
[ ps | pdf ] Peter Bürgisser, Felipe Cucker, Martin Lotz
The probability that a small perturbation of a numerical analysis problem is difficult
Mathematics of Computation 77: 1559-1583, (2008)
Arxiv: math/0610270
[ ps | pdf ] Peter Bürgisser, Martin Lotz
The Complexity of Computing the Hilbert Polynomial of Smooth Equidimensional Complex Projective Varieties,
Foundations of Computational Mathematics7(1): 51-86 (2007).
Arxiv: cs.SC/0502044
[ ps | pdf ] Peter Bürgisser, Felipe Cucker, Martin Lotz
General formulas for the smoothed analysis of condition numbers
C. R. Acad. Sci. Paris, Ser. I 343, pp.145-150 (2006).
[ ps | pdf ] Peter Bürgisser, Felipe Cucker, Martin Lotz
Smoothed analysis of complex conic condition numbers
Journal de Mathématiques Pures et Appliquées 86: 293-309 (2006).
[ ps | pdf ] M.Lotz
On Numerical Invariants in Algebraic Complexity Theory,
PhD Thesis, July 2005.
[ ps | pdf ] P.Bürgisser, Felipe Cucker, Martin Lotz
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets
Foundations of Computational Mathematics 5(4): 351-387 (2005)
[ ps | pdf ] Peter Bürgisser, Felipe Cucker, Martin Lotz
The Complexity of Computing the Euler Characteristic of Complex Varieties,
C. R. Acad. Sci. Paris, Ser. I 339 (2004).
[ ps | pdf ] Peter Bürgisser, Martin Lotz
Lower Bounds on the Bounded Coefficient Complexity of Bilinear Maps,
Journal of the ACM 51(3):464-482 (2004).
Arxiv: cs.CC/0301016
[ ps | pdf ] Martin Lotz, Johann A. Makowsky
On the algebraic complexity of some families of coloured Tutte polynomials,
Advances in Applied Mathematics 32 (1-2), pp. 327-349, 2004.