# Alex Pieloch : Moduli Spaces of Real Algebraic Curves

There is a natural relationship between moduli spaces of Riemann surfaces, mapping class groups of surfaces, and intersection patterns of simple closed curves on surfaces. In this talk, we describe an analogous relationship between moduli spaces of real algebraic curves, mapping class groups of surfaces with orientation reversing involutions, and intersection patterns of involution invariant simple closed curves on surfaces. After establishing these relationships, we obtain that the homology and cohomology groups of mapping class groups of surfaces with orientation reversing involutions satisfy duality relationships analogous to those for compact manifolds. We also obtain that higher homotopy groups associated to the moduli spaces of real algebraic curves relative to its boundary vanish in all degrees less than a determinable constant.

**Category**: Geometry and Topology**Duration**: 01:34:33**Date**: April 10, 2017 at 3:10 PM**Views**: 142-
**Tags:**seminar, Geometry/topology Seminar

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