# Spaces of resultants and toric varieties

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Andrzej Kozlowski, University of Warsaw

Over 40 years ago Graeme Segal in a seminal paper  proved that the space of holomorphic maps from the Riemann sphere S^2 to the complex projective space $CP^n$ approximates the spaces of corresponding continuous maps, with the approximation getting better as the degree $d$ increases. Segal made several conjectures about generalizing his theorem. A number such generalizations have been found, and many different techniques have been used in proving them, but the  general phenomenon remains mysterious. In this talk I will discuss the generalizations of Segal's theorem to the case when $CP^n$ is replaced by a toric variety and also to certain spaces that were defined by Farb and Wolfson in an algebraic context. I will also discuss some  real analogues of these results.