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Preface; Contents; Part I From the Plenary Talks; Floer Field Philosophy; 1 Introduction; 1.1 A Brief Introduction to Invariants of Manifolds; 2 Floer Field Theory; 2.1 Categories and Functors; 2.2 The Symplectic Category; 2.3 Categories with Cerf Decompositions; 2.4 Construction Principle for Floer Field Theories; 2.5 2+1 Floer Field Theories Arising from Gauge Theory; 2.6 Atiyah
Floer Type Conjectures for 3-Manifold Invariants; 3 Extensions of Floer Field Theories; 3.1 2-Categories and Bicategories; 3.2 Higher Bordism Categories; 3.3 Functors Between Bi- and 2-Categories
3.4 Adjunctions, Quilt Diagrams, and Quilted Bicategories3.5 The Symplectic 2-Category; 3.6 Gauge Theoretic 2-Categories and Quilted Atiyah Floer Conjectures; 4 Known Issues in the Bibliography; References; Part II Low Dimensional Topology; An Elementary Fact About Unlinked Braid Closures; 1 Khovanov Homology Proof of Proposition 1; 2 Fibred Links in #n(S1 timesS2); 2.1 Heegaard
Floer Homology Proof of Proposition 2; References; Symmetric Unions Without Cosmetic Crossing Changes; 1 Introduction; 2 Symmetric Unions; 2.1 Knot Floer Homology; 2.2 Main Examples; 3 Proof of Main Theorem
3.1 Khovanov Homology3.2 Proof of Main Theorem; 3.3 Observations; References; The Total Thurston
Bennequin Number of Complete and Complete Bipartite Legendrian Graphs; 1 Introduction; 2 The Total Thurston
Bennequin Number for Complete Graphs; 2.1 Remarks About K4; 2.2 Remarks About K5; 3 The Total Thurston
Bennequin Number for Complete Bipartite Graphs; 4 Questions and Examples of Embeddings; References; Coverings of Open Books; 1 Introduction; 2 Giroux Correspondence and Coverings; 3 The Overtwisted Complexity, Depth of Bindings and Open Book Coverings
4 Illustration of Overtwisted Coverings and a Pants PatternReferences; Part III Mathematical Biology; Understanding Locomotor Rhythm in the Lamprey Central Pattern Generator; 1 Introduction; 2 Experimental Results; 3 Mathematical Modeling Results; 4 Entrainment Ranges; 5 Discussion; References; Applications of Knot Theory: Using Knot Theory to Unravel Biochemistry Mysteries; 1 Knots and Links; 1.1 Knot and Link Invariants; 2 Biology Background; 2.1 Replication; 2.2 Topoisomerase; 2.3 Recombinase; References; Metapopulation and Non-proportional Vaccination Models Overview; 1 Introduction
2 Methodology2.1 Metapopulation Model; 2.2 Non-proportional Vaccination Model; 3 Results and Simulations; 3.1 Metapopulation Model; 3.2 Non-proportional Vaccination Model; 4 Final Remarks; References; Controlling a Cockroach Infestation; 1 Introduction; 2 The Mathematical Model; 2.1 The Basic Model; 2.2 The Effect of Pesticides; 2.3 Pesticide Parameters; 2.4 Population Growth Parameters; 3 Results; 3.1 Stability Analysis; 3.2 Genetic Algorithm; 4 Discussion; References; The Impact of Violence Interruption on the Diffusion of Violence: A Mathematical Modeling Approach; 1 Introduction
Floer Type Conjectures for 3-Manifold Invariants; 3 Extensions of Floer Field Theories; 3.1 2-Categories and Bicategories; 3.2 Higher Bordism Categories; 3.3 Functors Between Bi- and 2-Categories
3.4 Adjunctions, Quilt Diagrams, and Quilted Bicategories3.5 The Symplectic 2-Category; 3.6 Gauge Theoretic 2-Categories and Quilted Atiyah Floer Conjectures; 4 Known Issues in the Bibliography; References; Part II Low Dimensional Topology; An Elementary Fact About Unlinked Braid Closures; 1 Khovanov Homology Proof of Proposition 1; 2 Fibred Links in #n(S1 timesS2); 2.1 Heegaard
Floer Homology Proof of Proposition 2; References; Symmetric Unions Without Cosmetic Crossing Changes; 1 Introduction; 2 Symmetric Unions; 2.1 Knot Floer Homology; 2.2 Main Examples; 3 Proof of Main Theorem
3.1 Khovanov Homology3.2 Proof of Main Theorem; 3.3 Observations; References; The Total Thurston
Bennequin Number of Complete and Complete Bipartite Legendrian Graphs; 1 Introduction; 2 The Total Thurston
Bennequin Number for Complete Graphs; 2.1 Remarks About K4; 2.2 Remarks About K5; 3 The Total Thurston
Bennequin Number for Complete Bipartite Graphs; 4 Questions and Examples of Embeddings; References; Coverings of Open Books; 1 Introduction; 2 Giroux Correspondence and Coverings; 3 The Overtwisted Complexity, Depth of Bindings and Open Book Coverings
4 Illustration of Overtwisted Coverings and a Pants PatternReferences; Part III Mathematical Biology; Understanding Locomotor Rhythm in the Lamprey Central Pattern Generator; 1 Introduction; 2 Experimental Results; 3 Mathematical Modeling Results; 4 Entrainment Ranges; 5 Discussion; References; Applications of Knot Theory: Using Knot Theory to Unravel Biochemistry Mysteries; 1 Knots and Links; 1.1 Knot and Link Invariants; 2 Biology Background; 2.1 Replication; 2.2 Topoisomerase; 2.3 Recombinase; References; Metapopulation and Non-proportional Vaccination Models Overview; 1 Introduction
2 Methodology2.1 Metapopulation Model; 2.2 Non-proportional Vaccination Model; 3 Results and Simulations; 3.1 Metapopulation Model; 3.2 Non-proportional Vaccination Model; 4 Final Remarks; References; Controlling a Cockroach Infestation; 1 Introduction; 2 The Mathematical Model; 2.1 The Basic Model; 2.2 The Effect of Pesticides; 2.3 Pesticide Parameters; 2.4 Population Growth Parameters; 3 Results; 3.1 Stability Analysis; 3.2 Genetic Algorithm; 4 Discussion; References; The Impact of Violence Interruption on the Diffusion of Violence: A Mathematical Modeling Approach; 1 Introduction