Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 5, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2019             April 2019              May 2019
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1  2       1  2  3  4  5  6             1  2  3  4
3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
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24 25 26 27 28 29 30   28 29 30               26 27 28 29 30 31
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Friday, April 5, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 5, 2019

#### Generic derivations on o-minimal structures

###### Elliot Kaplan (UIUC Math)

Abstract: We study derivations $\delta$ on o-minimal fields $K$. We introduce the notion of a $T$-derivation, which is a derivation which cooperates with the 0-definable $\mathcal{C}^1$-functions on $K$. For example, if $K$ is an elementarily equivalent to the real exponential field, we require that $\delta \exp(a) = \exp(a)\delta a$ for all $a \in K$. Let $T$ be the theory of $K$ in an appropriate language $L$ and let $T^\delta$ be the $L\cup \{\delta\}$ theory stating that $\delta$ is a $T$-derivation. We show that if $T$ has quantifier elimination, then $T^\delta$ has a model completion $T^\delta_G$. The derivation in models $K$ of $T^\delta_G$ behaves "generically," it is wildly discontinuous and its kernel is a dense elementary $L$-substructure of $K$. If $T$ is the theory of real closed ordered fields, then $T^\delta_G$ is the theory of closed ordered differential fields (CODF) as introduced by Michael Singer. We are able to recover many of the known facts about CODF in our setting. Among other things, we show that $T^\delta_G$ has $T$ as its open core and that $T^\delta_G$ is distal. This is joint work with Antongiulio Fornasiero.

4:00 pm in 145 Altgeld Hall,Friday, April 5, 2019

#### A pointless alternative to topological spaces

###### William Balderrama (UIUC)

Abstract: Fundamental to geometry and topology is the notion of a space. These are usually axiomatized as topological spaces, but there are alternative axiomatizations. In this talk, I will introduce one alternative, the locales, and describe some ways in which they can be better behaved than topological spaces.

4:00 pm in 314 Altgeld Hall,Friday, April 5, 2019

#### Integration Bee 2019 Day 1

###### Shyam Hari (UIUC Math)

Abstract: Participants will be tasked with solving 20 integrals in 30 minutes. However, these are not your ordinary Stewart's problems: these test your logic, critical thinking, mathematical intuition and knowledge! Those who perform the best will move on to day two of the Integration Bee!