# Topology

Monday, April 24, 2017 - 2:30pm - 3:30pm

Florian Marquardt (Friedrich-Alexander-Universität Erlangen-Nürnberg)

Topological transport of sound waves and vibrations in solids has attracted considerable attention in the past two years. Several approaches have been proposed and some have been demonstrated. However, it remains an outstanding challenge to create platforms for topological transport of phonons at the nanoscale. In this talk, I will describe three possible approaches that we have proposed. In the first, time-reversal is broken explicitly, with the help of an external laser field containing optical vortices.

Monday, March 13, 2017 - 2:00pm - 2:50pm

Ying Wu (King Abdullah University of Science & Technology)

As one of the most fundamental concepts in wave physics, resonance can give rise to a lot of interesting phenomena including low frequency band gaps. Because of its “divergent” nature, resonance also adds complexity into the modeling, and may even cause the failure of some widely adopted theories like quasi-static homogenization. In this talk, I will introduce my contributions in modeling classical wave systems with resonances by emphasizing on two major aspects: homogenization and linear dispersion relations.

Tuesday, June 7, 2016 - 1:15pm - 2:30pm

Kurt Maute (University of Colorado)

1. Basic Concepts

2. Brief Historical Overview

3. Density Method in Solid Mechanics

a. Homogenization and Explicit Interpolation Approaches

b. Ill-posedness issues

c. Regularization Methods

4. Level-set Methods in Solid Mechanics

a. Explicit Methods and Hamilton-Jacobi Approaches

b. Ersatz and Immersed boundary Methods

5. Overview of Applications in Solid and Fluid Mechanics and heat transfer

Recommended Papers:

2. Brief Historical Overview

3. Density Method in Solid Mechanics

a. Homogenization and Explicit Interpolation Approaches

b. Ill-posedness issues

c. Regularization Methods

4. Level-set Methods in Solid Mechanics

a. Explicit Methods and Hamilton-Jacobi Approaches

b. Ersatz and Immersed boundary Methods

5. Overview of Applications in Solid and Fluid Mechanics and heat transfer

Recommended Papers:

Thursday, February 11, 2016 - 11:00am - 12:00pm

Yoonsoo Kim (Gyeongsang National University)

This talk is about the speaker's recent research work which offers ideas on how a network of dynamical systems is affected by its network topology from the performance and stability perspective. Unlike many existing works, the present talk focuses on the interplay between network topology and 'local dynamics'. More specifically, the present talk is mainly concerned with two issues.

Wednesday, May 20, 2015 - 10:20am - 11:10am

Yihong Wu (University of Illinois at Urbana-Champaign)

This talk focuses on the problem of finding the underlying communities

within a network using only knowledge of network topology. We consider a

generative model for a network, namely the planted cluster model, which is a

within a network using only knowledge of network topology. We consider a

generative model for a network, namely the planted cluster model, which is a

Friday, May 2, 2014 - 9:00am - 9:50am

Tamal Dey (The Ohio State University)

Recent data sparsification strategies in topological data analysis such as Graph Induced Complex and sparsified Rips complex give rise to a sequence of simplicial complexes connected by simplicial maps rather than inclusions. As a result, the need for computing topological persistence under such maps arises. We propose a practical algorithm for computing such persistence in Z2-homology.

Thursday, November 6, 2008 - 8:45am - 9:30am

William Noid (The Pennsylvania State University)

Coarse-grained (CG) models provide a promising computational tool for investigating slow complex processes that cannot be adequately studied using more detailed models. However, unless the CG model is consistent with an accurate high-resolution model, the results of CG modeling may be misleading. The present talk describes a statistical mechanical framework that provides a rigorous “multiscale bridge” connecting models with different resolution.

Wednesday, October 29, 2008 - 3:00pm - 3:50pm

Gunnar Carlsson (Stanford University)

The nature and quantity of data arising out of scientific applications requires novel methods, both for exploratory analysis as well as analysis of significance and validation. One set of new methods relies on ideas and methods from topology. The study of data sets requires an extension of standard methods, which we refer to as persistent topology. We will survey this area, and show that algebraic methods can be applied both to the exploratory and the validation side of investigations, and show some examples.

Wednesday, March 5, 2014 - 11:30am - 12:20pm

Michael Farber (University of Warwick)

I will discuss several probabilistic models producing simplicial complexes, manifolds and discrete

groups. Random simplicial complexes are high dimensional analogues of random graphs and can be

used for studying the behaviour of large systems or networks depending on many random

parameters. We are interested in properties of random spaces which are satisfies with probability

tending to one. Using probabilistic models one may also test probabilistically the validity of open

groups. Random simplicial complexes are high dimensional analogues of random graphs and can be

used for studying the behaviour of large systems or networks depending on many random

parameters. We are interested in properties of random spaces which are satisfies with probability

tending to one. Using probabilistic models one may also test probabilistically the validity of open

Thursday, March 6, 2014 - 10:15am - 11:05am

Elizabeth Munch (University of Minnesota, Twin Cities)

In order to understand the properties of a real-valued function on a topological space, we can study the Reeb graph of that function. The Reeb graph is a construction which summarizes the connectivity of the level sets. Since it is efficient to compute and is a useful descriptor for the function, it has found its place in many applications. As with many other constructions in computational topology, we are interested in how to deal with this construction in the context of noise.