Recent important results in Maths and Logic

Decidability and undecidability

1. The integers are first order definable by a universal formula in the field of rationals.
   By Jochen Koenigsmann,
   Survey Published in Lecture Notes in Mathematics, vol. 2111
   preprint

Knot theory

1. Explicit upper bounds for Reidemeister moves for recognizing unknots and not equivalence.
   unknots by Marc Lackenby, and
   knotequivalence by Alexander Coward and Marc Lackenby.
   slidesby A. Coward.
   slidesby A. Lackenby.

• A polynomial upper bound on Reidemeister moves Annals Math. (accepted) http://people.maths.ox.ac.uk/lackenby/pol19514.pdf
• (With Alexander Coward) An upper bound on Reidemeister moves Amer. J. Math. (accepted) http://people.maths.ox.ac.uk/lackenby/rei09n11.pdf
• (with Alexander Coward) Unknotting genus one knots Comment. Math. Helv. 86 (2011) 383-399. httP://PEOPle.maths.ox.ac.uk/lackenby/ugo05059.pdf