**Title:** Exploring notions of "sameness"

**Speaker:** Maru Sarazola

**Speaker Info:** University of Minnesota

**Brief Description:**

**Special Note**:

**Abstract:**

When we start to do math, there is a very intuitive way to compare two mathematical objects X and Y: by asking whether X=Y. However, we soon find that the notion of equality is much too strict. For example, in linear algebra we don't really need two vector spaces to be equal to each other; instead, we want them to be "linearly isomorphic". Using tools from topology, we can take this one step further, and get an even weaker version of sameness called "equivalence". This leads to the old joke that, for a topologist, a coffee mug is the same as a donut!In this talk, we will explore these different notions of sameness with some examples, and we will see how they can be used to connect seemingly different mathematical structures.

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