By Professor Catherine Hobbs, Sylvie Paycha

This quantity deals a different selection of impressive contributions from popular girls mathematicians who met in Cambridge for a convention lower than the auspices of eu ladies in arithmetic (EWM). those contributions function very good surveys in their topic parts, together with symplectic topology, combinatorics and quantity concept. the quantity in addition sheds mild on widespread ladies mathematicians who labored in Cambridge within the past due nineteenth and early twentieth centuries via offering an insightful historic advent first and foremost of the quantity. the amount concludes with brief contributions from girls mathematicians from throughout Europe operating in quite a few parts of arithmetic starting from team idea to magnetic fields.

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This quantity bargains a distinct choice of awesome contributions from well known girls mathematicians who met in Cambridge for a convention below the auspices of ecu ladies in arithmetic (EWM). those contributions function first-class surveys in their topic parts, together with symplectic topology, combinatorics and quantity conception.

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What other obstructions are there to performing such an embedding besides the obvious one of volume? Notice that because a, b, a are areas the volume obstruction to the existence of an embedding is that ab ≤ (a )2 . This question was nicely formulated in a paper by Cieliebak, Hofer, Latschev and Schlenk [3] called Quantitative Symplectic Geometry in terms of the following function: define c(a) for a ≥ 1 byh c(a) := inf{c : E(a, b) embeds symplectically in E(c , c )}. g We say that the set U embeds symplectically in V if there is a symplectomorphism φ such that φ(U ) ⊂ V .

Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Quantum mechanics as a deformation of classical mechanics, Lett. Math. Phys. 1 (1977) 521–530 and Deformation theory and quantization, part I, Ann. of Phys. 111 (1978) 61–110. 4. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, part II, Ann. of Phys. 111 (1978) 111–151 5. S. 144 (2002) 38–53. 6. A. Cattaneo, G. Felder and L. Tomassini, From local to global deformation quantization of Poisson manifolds, Duke Math.

Families of J-holomorphic curves: Holomorphic (or complex) objects are much more rigid than real ones. n There are infinitely many holomorphic functions if one just asks that they be defined in some small open subset of S 2 , but the condition that they be globally defined is very strong. Something very similar happens with complex curves. If one fixes a point x ∈ M there are infinitely many real curves through x. e. the set of all such curves can be given the topology of an infinite dimensional space.

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