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We are all familiar with the three-dimensional space in which we live, but to solve problems, mathematicians need spaces with 4, 5 or many more dimensions. We cannot visualize these higher dimensional spaces, but it is nevertheless very important to describe their shape. Moreover, these spaces are often full of holes and these holes can sometimes tell us something surprising about our own three-dimensional world. Raf Bocklandt (UvA) will guide you through it!
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