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I will talk about mathematical objects that have two seemingly contradictory attributes. On the one hand, they are generic within a given class, in the sense that if most objects within the class have a property, then our object has it as well. So generic objects are common. On the other hand, they are very special if they exist, for example, there is always, in essence, at most one such object within a given class. Generic objects show up in various areas of mathematics, for example, in topology, geometry, and analysis. They tend to have astonishing mathematical features. Can you imagine a curve C with the property that if you cover it by the union of two curves C1 and C2, then either C1 or C2 must be equal to the whole C? There is a curve like that and it is one of the generic objects.

Photo from the University of Illinois's Department of Mathematics

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Applied Mathematics | Mathematics


Event location: Farley Auditorium

Generic Special Objects



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