Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 21, 2014.

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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, November 21, 2014

9:00 am in Altgeld Hall and Illini Union,Friday, November 21, 2014

#### MoSAIC Festival

Abstract: A MoSAIC Festival will be held on the Illinois campus Friday, November 21 through Sunday, November 23. MoSAIC Festivals are art/math mini-conferences that incorporate lectures, hands-on workshops, an art exhibition, video screenings, and space for participants to display works which they bring. The festival is open to the public. High school teachers and students are encouraged to attend. Schedule of events is at http://www.math.illinois.edu/MOSAIC/

4:00 pm in 243 Altgeld Hall,Friday, November 21, 2014

#### Quasi-Hamiltonian G-Spaces

###### Yang Song (UIUC Math)

Abstract: Atiyah and Bott gave a way to describe the moduli space of flat connection as a symplectic manifolds by doing a Hamiltonian reduction to an infinitely dimensional space. Quasi-Hamiltonian G-space, on the other hand, can be used to attack the same problem without the infinite dimensional space. In this talk, we will introduce lie group valued moment map and quasi-Hamiltonian G-spaces. If times allows, we will briefly sketch the construction of moduli spaces of flat connection using quasi-Hamiltonian G-spaces.

4:00 pm in 345 Altgeld Hall,Friday, November 21, 2014

#### Treeable equivalence relations

###### Anush Tserunyan (UIUC)

Abstract: Given a Borel equivalence relation $E$ on a Polish space $X$, a useful way to present it is via a Borel graphing; that is, a Borel graph $\mathcal{G}$ (i.e. antireflexive symmetric Borel subset of $X^2$) such that $E$ is exactly the equivalence relation of being in the same connected component of $\mathcal{G}$. Of course, such a graphing always exists: take $\mathcal{G} := E \setminus \text{Diag}(X)$, but it contains redundant information (lots of cycles), not necessary for reconstructing $E$. A minimal graphing of $E$ would be an acyclic Borel graphing; in other words, each $E$-class is spanned by a tree. The Borel equivalence relations that admit such a graphing are called treeable. In this talk, we will discuss the class of treeable equivalence relations, focusing on a particular open question about a certain closure property of this class and its connections with Borel combinatorics, ergodic theory, and geometric group theory.

4:00 pm in 245 Altgeld Hall,Friday, November 21, 2014

#### Panel for mentoring assistant professor and postdocs

Abstract: Jayadev Athreya and Kay Kirkpatrick will lead a panel for mentoring assistant professors and postdocs.

4:00 pm in 343 Altgeld Hall,Friday, November 21, 2014

#### Equivariant Cohomology of Flags and Partial Flags

###### Elizabeth Drellich   [email] (University of Massachusetts Amherst)

Abstract: We start with a flag variety G/B and a partial flag variety G/P and examine the relationship between the T-equivariant cohomology of each of these spaces. This talk will present several descriptions of this relationship, including the GKM fiber bundle model of Guillemin-Sabatini-Zara and a recent combinatorial linear algebraic construction that is joint work with J. Tymoczko.