Department of

# Mathematics

Seminar Calendar
for events the day of Friday, August 28, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2015             August 2015           September 2015
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1  2  3  4                      1          1  2  3  4  5
5  6  7  8  9 10 11    2  3  4  5  6  7  8    6  7  8  9 10 11 12
12 13 14 15 16 17 18    9 10 11 12 13 14 15   13 14 15 16 17 18 19
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26 27 28 29 30 31      23 24 25 26 27 28 29   27 28 29 30
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Friday, August 28, 2015

8:00 am in Altgeld Hall,Friday, August 28, 2015

#### Geometry Labs United meeting

Abstract: The Geometry Labs United meeting will be held August 28-30, 2015. The meeting will include an undergraduate poster sessions, panel discussion on running labs, and talks by Saul Schleimer (University of Warwick), Henry Segerman (Oklahoma State University), and Hugo Parlier (University of Fribourg). See the conference schedule at http://www.math.illinois.edu/glu2015/schedule.html

2:00 pm in 143 Altgeld Hall,Friday, August 28, 2015

#### The role of the Jacobi Identity in solving the Maurer-Cartan Equation

###### Ori Yudilevich   [email] (Utrecht University)

Abstract: In this talk I will describe a straightforward 2-step method for solving the Maurer-Cartan equation associated with a Lie algebra, an equation whose solution is equivalent to an integration of the Lie algebra to a local Lie group. The novelty of the method is in shedding light on the role of the Jacobi identity as an obstruction to integration. In the talk, I will also discuss applications of this method to Poisson geometry, local integration of Lie algebroids and, my main personal motivation, Cartan's realization problem.

4:00 pm in 345 Altgeld Hall,Friday, August 28, 2015

#### Organizational Meeting

4:00 pm in 241 Altgeld Hall,Friday, August 28, 2015

#### Lattice Properties of Oriented Exchange Graphs

###### Alexander Garver   [email] (University of Minnesota)

Abstract: The exchange graph of a quiver is the graph whose vertices are mutation-equivalent quivers and whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph, which is determined by fixing a particular quiver appearing in the exchange graph. The class of oriented exchange graphs contains interesting families of partially ordered sets such as the Tamari lattices and the Cambrian lattices introduced by Reading. In this talk, we will study oriented exchange graphs as partially ordered sets using quiver representations. We show that oriented exchange graphs with finitely many vertices are semidistributive lattices and that certain oriented exchange graphs with finitely many vertices are obtained by a lattice quotient of the lattice of biclosed subcategories, which we will introduce in this talk. The latter result generalizes Reading's Cambrian lattices in type A. No background on quivers and quiver representations will be assumed. This is joint work with Thomas McConville.