Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 9, 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 9, 2015

2:00 pm in 143 Altgeld Hall,Friday, October 9, 2015

#### Coherent quantization using colored surfaces

###### David Li-Bland   [email] (UC Berkeley)

Abstract: Quantization - generally speaking, the process of deforming a classical’ state space to a quantum mechanical’ one - is a problem of fundamental importance. It becomes even more challenging when one wants to quantize not just a single space in isolation, but rather to simultaneously quantize a collection of spaces in a manner which is compatible with some key structural maps between them. In fact, this is generally not possible. Nevertheless, in this talk we will describe an approach to this problem which works for a large class of spaces and structural maps which are of interest both mathematically and physically (they generalize moduli spaces of flat connections). The trick is that these spaces can be understood in terms of `colored surfaces' (which we will introduce) which are both quite visual and easy to work with. As one application, we will explain how this allows one to quantize Lie bialgebras (thus, obtaining quantum groups) and to construct certain equivariant quantizations. This talk is based on joint work with Pavol Severa.

2:00 pm in 447 Altgeld Hall,Friday, October 9, 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 9, 2015

#### On "Surreal numbers, derivations and transseries" by A. Berarducci and V. Mantova [arXiv link]

###### Tigran Hakobyan   [email] (UIUC Math)

Abstract: In the fifth installment of this series of talks, we will review nested truncations of surreal numbers.

4:00 pm in 243 Altgeld Hall,Friday, October 9, 2015

#### Geometric properties of Higher Teichmüller Spaces

###### Georgios Kydonakis (UIUC Math)

Abstract: Higher Teichmüller Theory brings together different mathematical objects in describing the moduli space of fundamental group representations into a semisimple Lie group $G$. Realizing Teichmüller space as a subset of this moduli space in the case when $G=\text{PSL}\left( 2,\mathbb{R} \right)\,$, provides motivation to identify and study connected components of the representations variety, which share essential topological and geometric properties with the classical Teichmüller space. We will introduce particular examples of these components and point their special geometric significance.

4:00 pm in 241 Altgeld Hall,Friday, October 9, 2015

#### Bruhat Interval Polytopes

###### Emmanuel Tsukerman   [email] (University of California-Berkeley)

Abstract: In this talk, I will discuss the geometry of Bruhat Interval Polytopes, polytopes which generalize the classical Permutahedron and arise from the study of the moment map on the flag variety. In the process, I will demonstrate some techniques used in the study of Coxeter groups and touch upon their applications to R-polynomials, polynomials used in defining the famous Kazhdan-Lusztig polynomials. This talk is based on joint work with Lauren Williams.