Department of

# Mathematics

Seminar Calendar
for Graduate Student Colloquium events the year of Tuesday, March 13, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2018            March 2018             April 2018
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Wednesday, February 14, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, February 14, 2018

#### Hyperbolicity in geometric group theory

###### Heejoung Kim (Illinois Math)

Abstract: In geometric group theory, we study a finitely generated group by looking at how the group acts on a metric space, using the topological or geometric properties of the metric space to shed light on the group. In particular, there has been lots of study about a finitely generated group acting nicely on a hyperbolic space based on properties of hyperbolic geometry. However, an arbitrary group does not admit a nice action on a hyperbolic space in general. Hence, many people have tried to generalize the techniques of hyperbolic geometry to study a more general metric space where a group might act nicely. In this talk, we will discuss hyperbolic geometry and how to use it to understand a finitely generated group. Moreover, we will talk about some generalizations of hyperbolic geometry with examples.

Monday, March 12, 2018

1:00 pm in 163 Noyes Laboratory,Monday, March 12, 2018

#### Kirwan-Ness stratifications for Cyclic quivers

###### Itziar Ochoa de Alaiza Gracia (Illinois Math)

Abstract: Mathematical and physical problems can often be simplified by making use of symmetries: for example, by taking a space with symmetries and forming a quotient (“dividing out by the symmetries”). Starting with elementary examples, I will explain difficulties that can arise in forming such quotients, and outline a scientific procedure in algebraic geometry that builds reasonable quotients by cutting up spaces into “stable” and “unstable” orbits. I will then explain that, by refining the “stable/unstable” dichotomy to measure “just how unstable each orbit is,” one can get a lot of topological/geometric information about the quotient.

Wednesday, April 4, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, April 4, 2018

#### Measurable Differentiable Structures

###### Chris Gartland (Illinois Math)

Abstract: We'll discuss Lipschitz differentiable structures on a metric measure spaces. The structures consist of a Borel cover of the space, together with Lipschitz maps from the elements of the cover to $\mathbb{R}^n$, such that any real-valued Lipschitz function is differentiable almost everywhere with respect to the maps. Lipschitz differentiable structures were defined in a paper by Cheeger in '99, where he also proved the fundamental theorem that any doubling metric measure space satisfying a Poincare inequality admits such a structure. A corollary of this theorem is a criterion for the non-biLipschitz embedability of these metric spaces in $\mathbb{R}^n$ which generalizes the known results for Carnot groups and Laakso space. These structures allow for interesting constructions on the space such as the $L^\infty$ cotangent bundle and $L^\infty$ cohomology.

Wednesday, April 25, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, April 25, 2018

#### Randomness in 3-Dimensional Geometry and Topology

###### Malik Obeidin (Illinois Math)

Abstract: The probabilistic method, pioneered by Paul Erdos, has proven to be one of the most powerful and versatile tools in the field of combinatorics. Mathematicians working in diverse fields, from graph theory to number theory to linear algebra, have found the probabilistic toolset valuable. However, 3-manifold topology has only been recently approached from this angle, though the field itself is full of intricate combinatorics. In this talk, I'll describe some of the ways one might define a "random 3-manifold" and the subtleties that arise in the definition. I'll also talk about how one can use these ideas to experiment computationally with 3-manifolds, to help us get a handle on what is "common", and what is "rare".