ML@UPB

Martin Lotz

Department of Mathematics
City University of Hong Kong

About...

Currently, I am working in the department of mathematics at City University of Hong Kong. I am a former member of the research group of Prof. Peter Bürgisser at Paderborn, were I obtained my PhD in mathematics with a thesis on numerical invariants in algebraic complexity theory. Before coming to Paderborn, I studied mathematics at the Universität Basel (1995-1997) and ETH Zürich (1997-2001).

Interests

My main research interests are in complexity theory and algorithmic algebra. At the moment I am working on the probabilistic analysis of condition numbers for problems in numerical analysis and optimization. Other topics of interest include complexity theoretic questions in algebraic geometry and topology, and topological methods in algebraic complexity theory (towards lower bounds).

Teaching

Work

[ ps | pdf ] P.Bürgisser, F.Cucker, M.Lotz
The probability that a small perturbation of a numerical analysis problem is difficult
To appear in Mathematics of Computation.

[ ps | pdf ] P.Bürgisser, M.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 ] P.Bürgisser, F.Cucker, M.Lotz
General formulas for the smoothed analysis of condition numbers
C. R. Acad. Sci. Paris, Ser. I 343, pp.145-150 (2006).

[ ps | pdf ] P.Bürgisser, F.Cucker, M.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, F.Cucker, M.Lotz
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets
Foundations of Computational Mathematics, 2005.
[ ps | pdf ] P.Bürgisser, F.Cucker, M.Lotz
The Complexity of Computing the Euler Characteristic of Complex Varieties,
C. R. Acad. Sci. Paris, Ser. I 339 (2004).
[ ps | pdf ] P.Bürgisser, M.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 ] M.Lotz, J.A.Makowsky
On the algebraic complexity of some families of coloured Tutte polynomials,
Advances in Applied Mathematics 32 (1-2), pp. 327-349, 2004.

[ ps \| pdf ]	P.Bürgisser, F.Cucker, M.Lotz The probability that a small perturbation of a numerical analysis problem is difficult To appear in Mathematics of Computation.
[ ps \| pdf ]	P.Bürgisser, M.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 ]	P.Bürgisser, F.Cucker, M.Lotz General formulas for the smoothed analysis of condition numbers C. R. Acad. Sci. Paris, Ser. I 343, pp.145-150 (2006).
[ ps \| pdf ]	P.Bürgisser, F.Cucker, M.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, F.Cucker, M.Lotz Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets Foundations of Computational Mathematics, 2005.
[ ps \| pdf ]	P.Bürgisser, F.Cucker, M.Lotz The Complexity of Computing the Euler Characteristic of Complex Varieties, C. R. Acad. Sci. Paris, Ser. I 339 (2004).
[ ps \| pdf ]	P.Bürgisser, M.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 ]	M.Lotz, J.A.Makowsky On the algebraic complexity of some families of coloured Tutte polynomials, Advances in Applied Mathematics 32 (1-2), pp. 327-349, 2004.