This volume contains the proceedings of the IV Meeting of Mexican Mathematicians Abroad (IV Reuni'on de Matem'aticos Mexicanos en el Mundo), held at Casa Matem'atica Oaxaca (CMO) in Oaxaca, Mexico, on June 10-15, 2018--Preface.

Includes bibliographical references.

A survey on extensions of Riemannian manifolds and Bartnik mass estimates / Armando J. Cabrera Pacheco and Carla Cederbaum -- Four-dimensional homogeneous Kähler Ricci solitons / Esteban Calviño-Louzao, Eduardo García-Río, Ixchel Gutiérrez-Rodríguez, and Ramón Vázquez-Lorenzo -- C∗-algebras and their nuclear dimension / Jorge Castillejos -- Short survey on the existence of slices for the space of Riemannian metrics / Diego Corro and Jan-Bernhard Kordass -- Model theory and metric convergence II: Averages of unitary polynomial actions / Eduardo Dueñez and José N. Iovino -- A survey on the blow-up method for fast-slow systems / Hildeberto Jardón-Kojakhmetov and Christian Kuehn -- Langlands Program and Ramanujan Conjecture: A survey / Luis Alberto Lomelí -- The least quadratic non-residue / Kevin McGown and Enrique Treviño -- Thin homotopy and the holonomy approach to gauge theories / Claudio Meneses -- On fractional higher-order Dirichlet boundary value problems: Between the Laplacian and the bilaplacian / Alberto Saldaña -- H¹ solutions on curve integrable spacetimes / Yafet Sanchez Sanchez -- On the pseudospectra of Schrödinger operators on Zoll manifolds / David Sher, Alejandro Uribe, and Carlos Villegas-Blas -- On a conjecture of Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux / Jacinta Torres.

"Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10-15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields."--page 4 of cover.