Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, February 3, 2016.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2016          February 2016            March 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6          1  2  3  4  5
3  4  5  6  7  8  9    7  8  9 10 11 12 13    6  7  8  9 10 11 12
10 11 12 13 14 15 16   14 15 16 17 18 19 20   13 14 15 16 17 18 19
17 18 19 20 21 22 23   21 22 23 24 25 26 27   20 21 22 23 24 25 26
24 25 26 27 28 29 30   28 29                  27 28 29 30 31
31


Wednesday, February 3, 2016

3:00 pm in 243 Altgeld,Wednesday, February 3, 2016

#### Nakajima's quiver varieties

###### Matej Penciak (UIUC Math)

Abstract: This will follow Section 1 (especially 1.3) of Victor Ginzburg's lectures on Nakajima quiver varieties: http://arxiv.org/pdf/0905.0686v2.pdf

4:00 pm in 245 Altgeld Hall,Wednesday, February 3, 2016

#### Approximating freeness under constraints

###### Sorin Popa (UCLA)

Abstract: I will discuss a method for constructing Haar unitaries $u$ in a subalgebra $B$ of a von Neumann II$_1$ factor $M$ that are "as free-independent as possible" (approximately) with respect to a given finite set of elements in $M$. This technique had most surprising applications over the years: to Kadison-Singer type problems, to proving vanishing cohomology results for II$_1$ factors (e.g., compact valued derivations and the Connes-Shlyakhtenko 1-cohomology), as well as in subfactor theory (notably, to the discovery of the proper axiomatisation of the group-like objects arising from subfactors). After explaining this method, which I call incremental patching, I will comment on all these applications and its potential for future use.