Luc Lapointe's Books

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

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The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082187294X

ISBN 13

9780821872949

k-Schur Functions and Affine Schubert Calculus

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki

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k-Schur Functions and Affine Schubert Calculus

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.

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Page Count

226

Publisher

Springer

Published Date

ISBN 10

1493906828

ISBN 13

9781493906826

The Killing Tide

A Brittany Mystery

By: Jean-Luc Bannalec

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The Killing Tide

A Brittany Mystery

By: Jean-Luc Bannalec

The Killing Tide by Jean-Luc Bannalec is the fifth novel in the internationally bestselling Commissaire Dupin series. Deep sea fishers, dolphin researchers, smugglers, and an island shrouded in myth in the middle of the rough Atlantic ocean: Commissaire Dupin had sworn he would never again investigate on the ocean, but his fifth case takes him offshore, off the west coast of Brittany on a beautifully sunny day in June. He lands on the unique Île de Sein, populated by more rabbits than people, where the hairdresser arrives by boat and which was formerly inhabited by powerful witches and even the devil himself. In front of this impressive backdrop—between the islands of Molène, Ouessant, and the bay of Douarnenez—Dupin and his team follow a puzzling case that pushes them to their very limits.

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Page Count

324

Publisher

Minotaur Books

Published Date

ISBN 10

1250173396

ISBN 13

9781250173393

Evidence-Based Cybersecurity

Foundations, Research, and Practice

By: Pierre-Luc Pomerleau,David Maimon

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Evidence-Based Cybersecurity

Foundations, Research, and Practice

By: Pierre-Luc Pomerleau,David Maimon

The prevalence of cyber-dependent crimes and illegal activities that can only be performed using a computer, computer networks, or other forms of information communication technology has significantly increased during the last two decades in the USA and worldwide. As a result, cybersecurity scholars and practitioners have developed various tools and policies to reduce individuals' and organizations' risk of experiencing cyber-dependent crimes. However, although cybersecurity research and tools production efforts have increased substantially, very little attention has been devoted to identifying potential comprehensive interventions that consider both human and technical aspects of the local ecology within which these crimes emerge and persist. Moreover, it appears that rigorous scientific assessments of these technologies and policies "in the wild" have been dismissed in the process of encouraging innovation and marketing. Consequently, governmental organizations, public, and private companies allocate a considerable portion of their operations budgets to protecting their computer and internet infrastructures without understanding the effectiveness of various tools and policies in reducing the myriad of risks they face. Unfortunately, this practice may complicate organizational workflows and increase costs for government entities, businesses, and consumers. The success of the evidence-based approach in improving performance in a wide range of professions (for example, medicine, policing, and education) leads us to believe that an evidence-based cybersecurity approach is critical for improving cybersecurity efforts. This book seeks to explain the foundation of the evidence-based cybersecurity approach, review its relevance in the context of existing security tools and policies, and provide concrete examples of how adopting this approach could improve cybersecurity operations and guide policymakers' decision-making process. The evidence-based cybersecurity approach explained aims to support security professionals', policymakers', and individual computer users' decision-making regarding the deployment of security policies and tools by calling for rigorous scientific investigations of the effectiveness of these policies and mechanisms in achieving their goals to protect critical assets. This book illustrates how this approach provides an ideal framework for conceptualizing an interdisciplinary problem like cybersecurity because it stresses moving beyond decision-makers' political, financial, social, and personal experience backgrounds when adopting cybersecurity tools and policies. This approach is also a model in which policy decisions are made based on scientific research findings.

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Page Count

251

Publisher

CRC Press

Published Date

ISBN 10

1000600874

ISBN 13

9781000600872

Algebraic Methods and $q$-Special Functions

By: Jan Felipe Van Diejen,Luc Vinet

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Algebraic Methods and $q$-Special Functions

By: Jan Felipe Van Diejen,Luc Vinet

There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

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Page Count

290

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820265

ISBN 13

9780821820261

Bible and Canon

A Modern Historical Inquiry

By: Luc Zaman

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Bible and Canon

A Modern Historical Inquiry

By: Luc Zaman

Several decades ago canonical criticism came to dominate the study of the canon and even indeed all of biblical studies by its emphasis on the biblical canon's dogmatic content. An investigation of this canonical criticism brings its weak points to light: most notably the insufficient attention that is given to the canon's historical development. This new historical study begins with the earliest stages of the process of forming the canon rather than its final stages as most studies do. It shows how the canon, in essence, was already formed in the early stages of its historical development. It is essentially, synchronically, an authoritative unification of a range of traditions within the faith community, and diachronically, the guide that draws the dynamics of these traditions beyond their discontinuities to produce a continuity.

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Page Count

730

Publisher

BRILL

Published Date

ISBN 10

9047433548

ISBN 13

9789047433545

Synthetic Biology

Volume 2

By: Luc Brunsveld,Hiroaki Suga

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Synthetic Biology

Volume 2

By: Luc Brunsveld,Hiroaki Suga

Leading researchers draw on the recent literature in Synthetic Biology, from both dedicated journals and broader sources, making this an essential reference to any library supporting this research in this emerging field.

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Page Count

196

Publisher

Royal Society of Chemistry

Published Date

ISBN 10

1782621202

ISBN 13

9781782621201

Nitric Oxide

By: Jean-Luc Balligand

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Nitric Oxide

By: Jean-Luc Balligand

Nitric oxide (NO) has been discovered to play a fundamental role in a number of biological phenomena. This book describes various aspects of nitric oxide biology, physiology and pharmacology. It is divided into three sections. The first part deals with the basic chemistry and enzymology of NO, thus laying a molecular basis for what follows. The middle part surveys the physiological roles of NO under normal conditions. The concluding part explores the relevance of NO to disease, both as a pathogenic factor and a therapeutic target. The book thus provides detailed information on NO biology to the reader unfamiliar with the field and represents a reference work for scientists working in an NO-related field of biomedical research. Each chapter, written by experts in their fields, gives a broad introduction followed by a comprehensive review of the current knowledge and a detailed reference list.

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Page Count

718

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540661220

ISBN 13

9783540661221

Theoretical Physics at the End of the Twentieth Century

Lecture Notes of the CRM Summer School, Banff, Alberta

By: Yvan Saint-Aubin,Luc Vinet

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Theoretical Physics at the End of the Twentieth Century

Lecture Notes of the CRM Summer School, Banff, Alberta

By: Yvan Saint-Aubin,Luc Vinet

The Centre de recherches matMmatiques (CRM) was created in 1968 by the Universite de Montreal to promote research in the mathematical sciences. It is now a national institute that hosts several groups and holds special theme years, summer schools, workshops, and a postdoctoral program. The focus of its scientific activities ranges from pure to applied mathematics and includes statistics, theoretical computer science, mathematical methods in biology and life sciences, and mathematical and theoretical physics. The CRM also promotes collaboration between mathematicians and industry. It is subsidized by the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR of the Province de Quebec, and the Canadian Institute for Advanced Research and has private endowments. Current ac tivities, fellowships, and annual reports can be found on the CRM Web page at www.CRM.UMontreal.CA. The CRM Series in Mathematical Physics includes monographs, lecture notes, and proceedings based on research pursued and events held at the Centre de recherches matMmatiques.

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Page Count

660

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387953116

ISBN 13

9780387953113

k-Schur Functions and Affine Schubert Calculus

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki

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k-Schur Functions and Affine Schubert Calculus

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Anne Schilling,Mark Shimozono,Mike Zabrocki

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Page Count

226

Publisher

Springer

Published Date

ISBN 10

1493906828

ISBN 13

9781493906826

The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

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The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian GrSLk into Schubert homology classes in GrSLk+1. This is achieved by studying the combinatorics of a new class of partitions called k-shapes, which interpolates between k k-cores and kk+1-cores. We define a symmetric function for each k-shape, and show that they expand positively in terms of dual k-Schur functions. We obtain an explicit combinatorial description of the expansion of an ungraded k k-Schur function into k+1-Schur functions. As a corollary, we give a formula for the Schur expansion of an ungraded k-Schur function.

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Page Count

101

Published Date

ISBN 10

0821898744

ISBN 13

9780821898741

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

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The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

By: Thomas Lam,Luc Lapointe,Jennifer Morse,Mark Shimozono

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Solve jigsaw puzzle

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082187294X

ISBN 13

9780821872949

Book's by Luc Lapointe

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

k-Schur Functions and Affine Schubert Calculus

k-Schur Functions and Affine Schubert Calculus

The Killing Tide

The Killing Tide

Evidence-Based Cybersecurity

Evidence-Based Cybersecurity

Algebraic Methods and $q$-Special Functions

Algebraic Methods and $q$-Special Functions

Bible and Canon

Bible and Canon

Synthetic Biology

Synthetic Biology

Nitric Oxide

Nitric Oxide

Theoretical Physics at the End of the Twentieth Century

Theoretical Physics at the End of the Twentieth Century

k-Schur Functions and Affine Schubert Calculus

k-Schur Functions and Affine Schubert Calculus

The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions

The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions

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