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Prof Miklos Laczkovich

Appointment

- Emeritus Professor of Mathematics
- Dept of Mathematics
- Faculty of Maths & Physical Sciences

Research Groups

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Research Summary

My main research interests cover much of combinatorial and set theoretic analysis. Some particular areas are as follows:

Problems in geometric measure theory; e.g. is it true that the ball in Rn is the Lipschitz image of every measurable set of positive Lebesgue measure?

Problems of equidecomposability: Is it true that two bounded measurable sets of the same positive measure and with rectifiable boundaries are always equidecomposable with finitely many measurable pieces? Is this true for the cube and the tetrahedron in R3? Is it true that if two measurable sets are equidecomposable under a commutative group of isometries then they are equidecomposable with measurable pieces?

Problems concerning the difference operator: can we characterise those topological groups (in particular, those Banach spaces) where it is true that if the differences of a function are continuous then it is the sum of a continuous function and an additive function? Can we represent every Lp function on the circle with vanishing integral as the sum of finitely many differences of Lp functions?

Miscellaneous: Does there exist an algorithm that decides, for every given polynomial with integer coefficients of the functions sin xn and cos xn whether or not it has a real root?

Problems in geometric measure theory; e.g. is it true that the ball in Rn is the Lipschitz image of every measurable set of positive Lebesgue measure?

Problems of equidecomposability: Is it true that two bounded measurable sets of the same positive measure and with rectifiable boundaries are always equidecomposable with finitely many measurable pieces? Is this true for the cube and the tetrahedron in R3? Is it true that if two measurable sets are equidecomposable under a commutative group of isometries then they are equidecomposable with measurable pieces?

Problems concerning the difference operator: can we characterise those topological groups (in particular, those Banach spaces) where it is true that if the differences of a function are continuous then it is the sum of a continuous function and an additive function? Can we represent every Lp function on the circle with vanishing integral as the sum of finitely many differences of Lp functions?

Miscellaneous: Does there exist an algorithm that decides, for every given polynomial with integer coefficients of the functions sin xn and cos xn whether or not it has a real root?