Programme

Anyone interested is welcome: please e-mail mrc@maths.warwick.ac.uk so that we can estimate the numbers involved.

ABSTRACTS

Alexei Gorinov (Nijmegen)

Division theorems for the cohomology of discriminant complements and applications to enumerative geometry.

The linear group $\mathrm{GL}_{n+1}(\mathbb{C})$ acts in a natural way on the space of equations of smooth complete intersections of given multidegree in the complex projective space $\mathbb{P}^n$. We generalize a theorem of C. Peters and J. Steenbrink by showing that the Leray spectral sequence of the corresponding quotient map degenerates in the second term over the rationals. As a by-product of the proof, we obtain explicit expressions divisible by the order the automorphism group of any smooth projective hypersurface of given dimension and degree.

Jonathan Woolf (Liverpool)

Witt groups of constructible sheaves

The algebra of symmetric bilinear forms in the constructible derived category of sheaves of a space X can be geometrically interpreted in terms of the bordism theory of Witt spaces over X. (A Witt space is a space whose intersection cohomology satisfies Poincare duality, for instance a manifold or a complex variety.) I will discuss this correspondence and then illustrate it by giving sketches of parallel geometric and algebraic proofs of a theorem due toCappell and Shaneson which can be interpreted as a generalised Novikovadditivity for signatures.

Farid Tari (Durham)

Asymptotic curves on surfaces in $R^5$

(Joint work with M. C. Romero-Fuster and M. A. S. Ruas) We study asymptotic curves on generically immersed surfaces in $R^5$. We characterise asymptotic directions via the contact of the surface with flat objects ($k$-planes, $k=1$--$4$), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.