Department of

Mathematics


Seminar Calendar
for Graduate Student Colloquium events the year of Thursday, September 20, 2018.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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                        30                                         

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".

Wednesday, September 5, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, September 5, 2018

65 Years of Orthogonal Projections

Fernando Yahdiel Roman-Garcia (UIUC Math)

Abstract: In 1954 John Marstrand published a paper where he related the Hausdorff dimension of a planar set to the Hausdorff dimension of its orthogonal projections. This paper motivated so much work in subsequent years that the topic of “projection theorems” developed into its own subfield of metric geometry. Over 60 years later this continues to be a thriving area of research with many modern adaptations of the original problem solved by Marstrand. In this talk I will give an overview of many different results obtained over the years, including some of my ongoing work on intersections of horizontal projections on the Heisenberg group.

Wednesday, October 3, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, October 3, 2018

Connecting the upper half plane, geodesic flows, and continued fractions

Claire Merriman (UIUC Math)

Abstract: Continued fractions are frequently studied in number theory, but they can also be described geometrically. I will talk about continued fraction expansions as dynamical systems, and connect this symbolic system to tessellations. The first part will focus on the "regular" or "simple" continued fractions, where all of the numerators are 1. Then, I will show what happens when all of the numerators are $\pm 1$ and the denominators are all even or all odd.

Wednesday, October 31, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, October 31, 2018

Basics of Coding Theory and Some Applications

Xiao Li (UIUC Math)

Abstract: In this talk I will be presenting some basics of coding theory and some applications to error correcting code. I will then focus on algebraic coding theory and give some examples with interesting algebraic and combinatorial properties. If time permits, I will give some applications in distributed storage.

Wednesday, December 5, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, December 5, 2018

Orders of infinities: asymptotic valued differential fields

Nigel Pynn-Coates (UIUC Math)

Abstract: Asymptotic valued differential fields go back to work of Hardy and are motivated by comparing the asymptotic behaviour of solutions to differential equations. I will introduce valued differential fields and discuss some of this history. We will see how versions of l’Hôpital’s Rule show up as key properties in the subject. Along the way, I will draw some pictures to illustrate the topology of valued fields. Time permitting, I may mention some of my results or ongoing work.