Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 13, 2015.

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Friday, November 13, 2015

4:00 pm in 243 Altgeld Hall,Friday, November 13, 2015

Nielsen-Thurston Classification of Mapping Classes of Closed Surfaces

Sarah Mousley (UIUC Math)

Abstract: The mapping class group of a closed surface $S$, denoted by $Mod(S)$, is the collection of all orientation-preserving homeomorphisms of $S$ up to homotopy. We will begin by explicitly computing the mapping class group of the torus $T^2$ and see that there are three types of elements in $Mod(T^2)$: finite order, powers of Dehn twists, and Anosov. We will then look at closed surfaces of genus $g \geq 2$ and learn that a similar classification statement (known as the Nielsen-Thurston classification) holds. I hope to convince you that the Nielsen-Thurston classification is meaningful. After all, any small child can arbitrarily place objects into bins and call the result a classification. Were Nielsen and Thurston just a pair of toddlers? Come to my talk and find out.

4:00 pm in 345 Altgeld Hall,Friday, November 13, 2015

On "Surreal numbers, derivations and transseries" by A. Berarducci and V. Mantova [arXiv link]

Lou van den Dries   [email] (UIUC Math)

Abstract: This is the last talk on the paper mentioned in the title. I'll define the Berarducci-Mantova derivation on the field of surreal numbers, and indicate its main properties. Using infinite products, this can be presented a bit more directly than in that paper.

4:30 pm in 239 Altgeld Hall,Friday, November 13, 2015

Department of Mathematics Retirement Party

Abstract: The Department of Mathematics will hold a retirement reception for Lori Dick, celebrating her 30 years with the department.