Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 12, 2019.

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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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Tuesday, March 12, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, March 12, 2019

#### Hyperfiniteness and descriptive combinatorics

###### Clinton Conley (Carnegie Mellon)

Abstract: We survey some recent results on connections between descriptive set-theoretic properties of Borel graphs and hyperfiniteness of their connectedness equivalence relation. For convenience, we will focus on chromatic numbers with various measurability constraints. This talk will include joint work with Jackson, Marks, Miller, Seward, Tucker-Drob.

1:00 pm in 347 Altgeld Hall,Tuesday, March 12, 2019

#### The lattice bump multiplier problem

###### Loukas Grafakos (University of Missouri-Columbia)

Abstract: Given a smooth bump supported in a ball centered at the origin in $R^n$, we consider the multiplier formed by adding the translations of this bump by $N$ distinct lattice points. We investigate the behavior as $N$ tends to infinity of the $L^p$ norm of the multiplier operators associated with this finite sum of $N$ bumps.

2:00 pm in 243 Altgeld Hall,Tuesday, March 12, 2019

#### Learning on hypergraphs: spectral theory and clustering with applications

###### Pan Li (Illinois ECE)

Abstract: Learning on graphs is an important problem in machine learning, computer vision, and data mining. Traditional algorithms for learning on graphs primarily take into account only low-order connectivity patterns described at the level of individual vertices and edges. However, in many applications, high-order relations among vertices are necessary to properly model a real-life problem. In contrast to the low-order cases, in-depth algorithmic and analytic studies supporting high-order relations among vertices are still lacking. To address this problem, we introduce a new mathematical model family, termed inhomogeneous hypergraphs, which captures the high-order relations among vertices in a very extensive and flexible way. Specifically, as opposed to classic hypergraphs that treats vertices within a high-order structure in a uniform manner, inhomogeneous hypergraphs allow one to model the fact that different subsets of vertices within a high-order relation may have different structural importance. We propose a series of algorithmic and analytic results for this new model, including inhomogeneous hypergraph clustering, spectral hypergraph theory, and novel applications ranging from food-web and ranking analysis to subspace segmentation. All proposed algorithms come with provable performance guarantees and are evaluated on real datasets; the results demonstrate significant performance improvements compared to classical learning algorithms.

3:00 pm in 243 Altgeld Hall,Tuesday, March 12, 2019

#### To Be Announced

###### TBA

4:00 pm in 245 Altgeld Hall,Tuesday, March 12, 2019

#### Altgeld-Illini Renovation/Building Project Feedback Session

Abstract: This feedback session will focus on the Math Library.