Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 16, 2015.

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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 16, 2015

2:00 pm in 447 Altgeld Hall,Friday, October 16, 2015

#### Cannon's Conjecture and Analysis on Metric Spaces

###### Chris Gartland (UIUC Math)

Abstract: Cannon's conjecture is one of the main open problems in geometric group theory. It states that every Gromov hyperbolic group with boundary topologically equivalent to the 2-sphere acts geometrically on hyperbolic 3-space. It turns out that this conjecture is equivalent to a uniformization problem in analysis on metric spaces - that every Gromov hyperbolic group with boundary topologically equivalent to the 2-sphere has its boundary quasisymmetrically equivalent to the 2-sphere. We will identify the major players in these two conjectures and outline a proof of their equivalence.

4:00 pm in 345 Altgeld Hall,Friday, October 16, 2015

#### On "Reducibility and nonreducibility of between $\ell^p$ equivalence relations" by R. Dougherty and G. Hjorth [pdf]

###### Mary Angelica Gramcko-Tursi (UIUC Math)

Abstract: For $1 \le p < \infty$, we call two sequences of reals $\ell^p$-equivalent if their difference is in $\ell^p$. In the paper mentioned in the title, the authors prove that for $p < q$, the $\ell^p$-equivalence is strictly below the $\ell^q$-equivalence in the Borel reducibility hierarchy of equivalence relations. In this talk, we will introduce the notion of Borel reducibility of equivalence relations and prove the reducibility of the $\ell^p$-equivalence to the $\ell^q$-equivalence, leaving the proof of strictness for the following talk. Interestingly enough, the proof of reducibility involves a generalized version of the Koch snowflake curve.

4:00 pm in 243 Altgeld Hall,Friday, October 16, 2015

#### Some Constructions in Stable Homotopy Theory

###### Dileep Menon (UIUC Math)

Abstract: In this talk we’ll investigate some of the structure within the stable homotopy groups of spheres. We’ll start somewhere near the beginning. After introducing some basic notions, I’ll construct the Toda bracket which gives a way of creating new elements from old in the homotopy groups of spheres. We’ll use these explicit constructions to motivate some important global phenomena.

4:00 pm in 241 Altgeld Hall,Friday, October 16, 2015

#### Involution words - a survey

###### Zachary Hamaker   [email] (University of Minnesota-IMA)

Abstract: The combinatorics of Coxeter groups has long been a rich area of study with important applications to representation theory and geometry. Many of the key ideas in this realm have natural analogues when we restrict our attention to involutions in Coxeter groups. Based on pioneering work of Richardson and Springer, we will survey many results translated through the lens of involution words, which are the natural analog of reduced words for involutions. Some highlights include a new insertion algorithm, an intuitive combinatorial interpretation of the Chinese monoid and applications to the geometry of spherical varieties. These results only scratch the surface, and many open problems remain! This is joint work with Eric Marberg and Brendan Pawlowski.