Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, October 5, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, October 5, 2016

2:00 pm in 443 Altgeld Hall,Wednesday, October 5, 2016

#### Measurable versions of the Lovász Local Lemma and measurable graph colorings, Part I

###### Anton Bernshteyn (UIUC Math)

Abstract: We will begin working through the paper "Measurable versions of the Lovász Local Lemma and measurable graph colorings" by Anton Bernshteyn.

4:00 pm in 243 Altgeld Hall,Wednesday, October 5, 2016

#### Model Theory of Logarithmic Transseries

###### Allen Gehret   [email] (UIUC Math)

Abstract: Transseries are formal series which naturally arise as formal asymptotic expansions of solutions of differential equations at infinity. The kind of transseries I study are logarithmic transseries, for example the formal series $2/\log\log x+2/(\log\log x)^2+2/(\log\log x)^3+\cdots+1/\log x+1/(\log x)^2+1/(\log x)^3+\cdots +7/x+5/x^2$ is a logarithmic transseries. In this talk I will overview my research into the algebra and model theory of the field of logarithmic transseries. I will begin by broadly discussing model theory. Then I will explicitly define the object I'm studying, $\mathbb{T}_{\log}$, the differential-valued field of logarithmic transseries. Finally, I will mention various results from the past few years about this object that will go into my thesis as well as things I still have left to do. In this talk I will assume familiarity with basic concepts from abstract algebra (groups, fields, vector spaces, formal power series), but everything else I'll define from scratch. In particular, I don't assume any prior knowledge of model theory.

4:00 pm in 245 Altgeld Hall,Wednesday, October 5, 2016
###### Mathematics graduate students (UIUC Mathematics)

Abstract: All department members are welcome at these short presentations from students in the PI4 program from Summer 2016. The talks will report on industrial and scientific internships, and the on-campus working groups. Refreshments provided. Drop in and out between talks as needed. Time: 4-6pm.