Mexican Mathematicians in the World : Trends and Recent Contributions.

Format:

Book

Author/Creator:

Galaz-García, Fernando.

Contributor:

González-Tokman, Cecilia.

Pardo, Juan Carlos.

Series:

Contemporary Mathematics

Contemporary Mathematics ; v.775

Language:

English

Subjects (All):

Mathematics--Mexico--Congresses.

Mathematics.

Mathematicians--Mexico--Congresses.

Mathematicians.

Women mathematicians--Mexico--Congresses.

Women mathematicians.

Physical Description:

1 online resource (336 pages)

Edition:

1st ed.

Other Title:

Mexican Mathematicians in the World

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

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.

Contents:

Cover

Title page

Contents

Preface

List of Talks and Speakers

A survey on extensions of Riemannian manifolds and Bartnik mass estimates

1. Mathematical relativity

2. The Mantoulidis-Schoen construction

3. Collar extensions, gluing procedures, and Bartnik mass estimates

4. Recent results on Bartnik mass estimates

5. Conclusions and open problems

Acknowledgments

References

Four-dimensional homogeneous Kähler Ricci solitons

1. Introduction

2. Preliminaries

3. Homogeneous Kähler surfaces. The proof of Theorem 1.1

4. The proof of Corollary 1.2

*-algebras and their nuclear dimension

Introduction

1. Basics of *-algebras

2. Nuclear dimension

3. Zero dimensional objects

4. *-algebras associated to groups

5. *-algebras associated to dynamical systems

6. Cuntz algebras

7. General simple *-algebras

8. Nuclear dimension of commutative algebras

Short survey on the existence of slices for the space of Riemannian metrics

3. Proofs of the Slice Theorem and Theorem B

4. Consequences of the Slice Theorem

Acknowledgment

Model theory and metric convergence II: Averages of unitary polynomial actions

1. PET structures

2. Leibman sequences

3. An ergodic theorem for unitary polynomial actions of ℤ

4. A Mean Ergodic Theorem for unitary polynomial actions of abelian groups

Appendix A. A Dominated Convergence Theorem for notions of integration in Banach spaces

A survey on the blow-up method for fast-slow systems

Notation

3. Survey

4. Summary and outlook

Langlands program and Ramanujan Conjecture: A survey

Introduction.

1. Artin -functions and number theory

2. Reductive groups and representation theory

3. The Langlands-Shahidi method

4. Local Langlands

5. Global Langlands

6. Globalization methods

7. Ramanujan Conjecture

The least quadratic non-residue

2. History and heuristics

3. The Pólya-Vinogradov inequality

4. The Burgess inequality

5. Explicit results on the least quadratic non-residue

6. The large sieve and Linnik's theorem

7. Ankeny's Theorem

8. Conclusion

Thin homotopy and the holonomy approach to gauge theories

2. Brief survey

3. Thin homotopy and groups of based loops on a manifold

4. Results

5. Conclusion and further remarks

On fractional higher-order Dirichlet boundary value problems: Between the Laplacian and the bilaplacian

2. Pointwise evaluations

3. Variational framework

4. Positivity preserving properties

5. Explicit formulas for the inhomogeneous Dirichlet problem in balls

6. Asymptotic behavior of solutions

Appendix A. On the composition of Green functions

¹ solutions on curve integrable spacetimes

2. Preliminaries and notation

3. Curve integrable spacetimes

On the pseudospectra of Schrödinger operators on Zoll manifolds

1. Introduction and statement of results

2. Proof of Theorem 1.2

3. Proof of Theorem 1.3

4. Proof of Theorem 1.4

5. Examples on ²

On a conjecture of Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux

1. Notation for the Lie algebras

2. Tableaux, words and their paths

3. Restriction of paths that come from words.

4. The Naito-Sagaki conjecture

5. Littlewood-Richardson tableaux and n-symplectic Sundaram tableaux: branching

6. On the proof of the Naito-Sagaki conjecture

7. Symplectic combinatorics of King, Berele and Sundaram

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

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.

ISBN:

9781470467289

1470467283

OCLC:

1285170590