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Mathematics & Statistics
Colloquium Archive

# Colloquia — Fall 2017

## Friday, November 17, 2017

Title
Speaker

Time
Place

TBA
Ian McQuillan
Department of Computer Science
3:00pm-4:00pm
CMC 130
Nataša Jonoska

Abstract

TBA

## Friday, October 13, 2017

Title
Speaker

Time
Place

Towards Spectral Sparsification of Simplicial Complexes based on Generalized Effective Resistance
Bei Wang
Scientific Computing and Imaging Institute
University of Utah
3:00pm-4:00pm
CMC 130
Masahiko Saito

Abstract

As a generalization of the use of graphs to describe pairwise interactions, simplicial complexes can be used to model higher-order interactions between three or more objects in complex systems. There has been a recent surge in activity for the development of data analysis methods applicable to simplicial complexes, including techniques based on computational topology, higher-order random processes, generalized Cheeger inequalities, isoperimetric inequalities, and spectral methods. In particular, spectral learning methods (e.g. label propagation and clustering) that directly operate on simplicial complexes represent a new direction emerging from the confluence of computational topology and machine learning. Similar to the challenges faced by massive graphs, computational methods that operate on simplicial complexes are severely limited by computational costs associated with massive datasets.

To apply spectral methods in learning to massive datasets modeled as simplicial complexes, we work towards the sparsification of simplicial complexes based on preserving the spectrum of the associated Laplacian operators. We show that the theory of Spielman and Srivastava for the sparsification of graphs extends to the generality of simplicial complexes via the up Laplacian. In particular, we introduce a generalized effective resistance for simplexes; provide an algorithm for sparsifying simplicial complexes at a fixed dimension; and gives a specific version of the generalized Cheeger inequalities for weighted simplicial complexes under the sparsified setting. In addition, we demonstrate via experiments the preservation of up Laplacian during sparsification, as well as the utility of sparsification with respect to spectral clustering.

This is a joint work with Braxton Osting and Sourabh Palande.

## Friday, October 6, 2017

Title
Speaker

Time
Place

On exceptional sets of some operator sequences
Grigori Karagulyan
Institute of Mathematics
National Academy of Sciences of Armenia
3:00pm-4:00pm
CMC 130
Arthur Danielyan

Abstract

We will consider general theorems characterizing the divergence sets of the operator sequences satisfying the localization property. Applying those theorems we deduce complete characterizations of the divergence sets of Fourier series and their Cesaro means in classical orthonormal systems.

## Friday, September 1, 2017

Title
Speaker

Time
Place
The topic of this lecture is a group functor which we introduced in 1980. Precisely, given a group $$G$$ and an isomorphic copy of it $$G^\psi$$ where $$\psi$$ is the isomorphism, we defined $$\chi(G)=\langle G,G^\psi\mid gg^\psi=g^\psi g\text{ for all }g\in G\rangle.$$ It was shown that the group $$\chi(G)$$ has a section isomorphic to the second homology group $$H_2(G,ℤ)$$. The functor $$\chi$$ preserves a number of classes of groups such as: finite $$\pi$$-groups ($$\pi$$ a set of primes); finite nilpotent groups; solvable groups; nilpotent groups; polycyclic-by-finite groups. Recently, Bridson and Kochloukova added to this list the important class of finitely presented groups.