Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 14, 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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Friday, October 14, 2016

2:00 pm in 443 Altgeld Hall,Friday, October 14, 2016

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

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

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

4:00 pm in 241 Altgeld Hall,Friday, October 14, 2016

#### Additive decompositions of Linear Operators

###### Alexi Gorman (UIUC Math)

Abstract: There are many operator algebras important to the study of analysis, geometry and various fields that are unwieldy as algebras, and understanding their action on the space can be cumbersome. The study of additive decompositions makes use of both the additive and multiplicative structures on a space of linear operators to understand the action of the transformation on a vector as the sum of the images of a few "well-behaved" operators acting on that vector. The utility and applicability of the additive decomposition can vary based on what kind of "well-behaved" operators we can decompose each map into. In particular, this talk will examine examples of endomorphism rings over vector spaces of varying cardinality, and some interesting sub-algebras of their endomorphisms. We will consider decompositions of operators into various sums that include the sum of an invertible operator and a projection, invertible and nilpotent, and the sum of invertible operator, projection, and nilpotent transformation.

4:00 pm in 345 Altgeld Hall,Friday, October 14, 2016

#### On "Regularity lemma for distal structures" by A. Chernikov and S. Starchenko: Epilogue

###### Erik Walsberg (UIUC Math)

Abstract: Motivated by problems in discrete geometry, Alon, Pach, Pinchasi, Radoičić, and Sharir (2005) established a strong version of the bipartite Ramsey theorem for semialgebraic graphs: any such graph or its complement contains a complete bipartite subgraph with parts of linear size. Eventually, this result led to a generalization due to Chernikov and Starchenko (2015), who extended it to graphs definable in distal structures. In this series of talks, we are planning to give an overview of the Chernikov–Starchenko result. This is the final talk of this series.