Outputs (6)

Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey (2020)
Book Chapter
Galaz-García, F., Guijarro, L., & Núñez-Zimbrón, J. (2020). Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey. In O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, & D. Crowley (Eds.), Differential geometry in the large (291-310). Cambridge University Press. https://doi.org/10.1017/9781108884136.017

We survey two recent developments in the topic of three-dimensional Alexandrov spaces: the topological classification of closed collapsed threedimensional Alexandrov spaces and the geometrization of sufficiently collapsed closed three-dimensional Ale... Read More about Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey.

Fake Lens Spaces and Non-Negative Sectional Curvature (2020)
Book Chapter
Goette, S., Kerin, M., & Shankar, K. (2020). Fake Lens Spaces and Non-Negative Sectional Curvature. In O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, & D. Crowley (Eds.), Differential Geometry in the Large (285-290). Cambridge University Press. https://doi.org/10.1017/9781108884136.016

In this short note we observe the existence of free, isometric actions of finite cyclic groups on a family of 2-connected 7-manifolds with non-negative sectional curvature. This yields many new examples including fake, and possible exotic, lens space... Read More about Fake Lens Spaces and Non-Negative Sectional Curvature.

Uncertainty Quantification in Lasso-Type Regularization Problems (2020)
Book Chapter
Basu, T., Einbeck, J., & Troffaes, M. C. (2021). Uncertainty Quantification in Lasso-Type Regularization Problems. In Optimization Under Uncertainty with Applications to Aerospace Engineering (81-109). Springer Verlag. https://doi.org/10.1007/978-3-030-60166-9_3

Signatures, Lifts, and Eigenvalues of Graphs (2020)
Book Chapter
Liu, S., Peyerimhoff, N., & Vdovina, A. (2020). Signatures, Lifts, and Eigenvalues of Graphs. In F. M. Atay, P. B. Kurasov, & D. Mugnolo (Eds.), Discrete and continuous models in the theory of networks : operator theory : advances and applications (255-269). Birkhäuser Verlag. https://doi.org/10.1007/978-3-030-44097-8_13

We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite tower of 3-cyclic lifts, each of which is again Ramanujan.

Bions and Instantons in Triple-well and Multi-well Potentials (2020)
Book Chapter
Dunne, G. V., Sulejmanpasic, T., & Ünsal, M. (2020). Bions and Instantons in Triple-well and Multi-well Potentials. In A. Niemi, T. Tomboulis, & K. K. Phua (Eds.), Roman Jackiw: 80th Birthday Festschrift (119-148). World Scientific Publishing. https://doi.org/10.1142/9789811210679_0015

Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the triple-well potenti... Read More about Bions and Instantons in Triple-well and Multi-well Potentials.

Curvature Calculations for Antitrees (2020)
Book Chapter
Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Curvature Calculations for Antitrees. In M. Keller, D. Lenz, & R. K. Wojciechowski (Eds.), Analysis and geometry on graphs and manifolds (21-54). Cambridge University Press. https://doi.org/10.1017/9781108615259.003

In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalized and non-normalized Bakry-Émery setting as well in the Ollivier-Ricci... Read More about Curvature Calculations for Antitrees.