Neal Bushaw

In August 2022 this was declared a “highlights” section, and is no longer guaranteed to be exhaustive. There are talks which are lost to the sands of time — if you have a hint of a memory of a vision of seeing me give a talk somewhere and it isn't in this list, it is best to assume it probably happened. Or you could invite me for a repeat.

• Aug 2026“Cyclic and Möbius Pianos”. Bridges 2026, University of Galway, Ireland.
• Mar 2026“The Saturation Spectrum of Berge Stars”. VCU Discrete Math Seminar, Richmond VA.
• Nov 2025“I heard there was a secret chord…”. Shenandoah Undergraduate Mathematics and Statistics Conference, James Madison University, Harrisonburg VA. (Plenary.)
• Oct 2025“Bootstrap Percolation on Grids and Tori”. AMS Special Session on Recent Trends in Graph Theory (virtual).
• Oct 2025“Bootstrap Percolation on Grids and Tori”. VCU Discrete Math Seminar, Richmond VA. Abstract.
• Oct 2025“The Hypergraph Saturation Spectrum for Berge Stars”. AMS Special Session on Recent Trends in Graph Theory, New Orleans LA.
• Apr 2025“Maximally Even Sets”. UVm–Dartmouth Discrete Math Day, Burlington VT.
• Apr 2025“I Heard There Was a Secret Chord”. Colloquium, University of Vermont, Burlington VT.
• Feb 2025“Intersecting Families of Paths”. VCU Discrete Math Seminar, Richmond VA. Abstract.
• Dec 2024“Intersecting Families of Graphs”. Discrete Mathematics Seminar, Centre for Mathematical Modeling, Santiago, Chile.
• Sep 2024“Combinatorial Music Theory”. DIMAG Lunch Seminar, Institute for Basic Science, Daejeon, Korea.
• Sep 2024“Edge-Colored Extremal Problems”. Discrete Mathematics Seminar, Institute for Basic Science, Daejeon, Korea.
• Aug 2024“The Music and Mathematics of Maximal Evenness in Graphs” (presented by co-author Brent Cody). Bridges Conference 2024, Richmond VA.
• Aug 2024“Coloring with Forbidden Subgraphs”. MAA MathFest, Indianapolis IN.
• Apr 2024“I heard there was a secret chord…”. VCU Discrete Math Seminar, Richmond VA.
• Oct 2023“Thresholds for Zero-Sums”. AMS Special Session on Extremal and Probabilistic Combinatorics, Fall Sectional Meeting, Mobile AL.
• Sep 2023“Combinatorial Music Theory”. VCU Discrete Math Seminar, Richmond VA.
• Mar 2023“Even vs. Odd Independent Sets”. AMS Special Session on Recent Trends in Structural and Extremal Graph Theory, Atlanta GA.
• Mar 2023“Extremal Problems with Forbidden Color Classes”. 54th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton FL.
• Oct 2022“Rainbow Saturated Graphs”. Discrete Math Seminar, Auburn University, Auburn AL.
• Sep 2022“Threshold Pebbling”. VCU Discrete Math Seminar, Richmond VA.
• Jun 2022“Partial Rainbows”. SIAM Conference on Discrete Mathematics.
• Apr 2022“Bridging the Gap Between Monochrome and Rainbow”. AMS Special Session on Topics in Extremal Combinatorics, Joint Mathematics Meetings.
• Nov 2021“Rainbow Saturation”. Combinatorics Seminar, University of Manitoba, Winnipeg, Canada.
• Sep 2021“One of My Favorites: The Sandglass Conjecture via Entropy”. VCU Discrete Math Seminar, Richmond VA.
• Jun 2021“Rainbow Saturation”. SIAM Conference on Discrete Mathematics, mini-symposium on Ramsey, Anti-Ramsey and Extremal Problems.
• Mar 2021“Bootstrap Percolation and Automated Conjecturing”. 52nd Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton FL.
• Feb 2021“A Gentle Introduction to Extremal Graph Theory”. VCU Discrete Math Seminar, Richmond VA.
• Mar 2020“Rainbow Saturation”. 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton FL.
• Jan 2020“What is Additive Combinatorics?”. VCU Discrete Math Seminar, Richmond VA.
• Nov 2019“Musical Mathematics”. VCU Discrete Math Seminar, Richmond VA.
• Oct 2019“Variations on a Theme of Turán”. Mississippi Discrete Math Workshop, Oxford MS.
• Oct 2019“Small Percolating Sets”. Mathematics Colloquium, University of Montana, Missoula MT.
• Aug 2019“Small Percolating Sets”. VCU Discrete Math Seminar, Richmond VA.
• Mar 2019“Even Cycles in Dense Graphs”. 50th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton FL.
• Feb 2019“The Taming of the Hypergraph”. VCU Discrete Math Seminar, Richmond VA.
• Nov 2018“Extremal Graph Theory”. Colloquium, University of Richmond, Richmond VA.
• Nov 2018“Automated Conjecturing and Hamiltonian Graphs”. MAA Sectional Meeting, University of Mary Washington, Fredericksburg VA.
• Oct 2018“Bootstrap Percolation on Infinite Graphs”. Mathematics Colloquium, Virginia State University, Petersburg VA.
• Oct 2018“Extremal Graph Theory”. Mathematics Colloquium, Randolph-Macon College, Ashland VA.
• Oct 2018“Bootstrap Percolation on Planar Tilings”. Mathematics Colloquium, James Madison University, Harrisonburg VA.
• Sep 2018“Bootstrap Percolation on Planar Tilings”. Mathematics Colloquium, College of William & Mary, Williamsburg VA.
• Sep 2018“Hypergraph Containers, or: How I Learned to Stop Worrying and Love Independent Sets”. VCU Discrete Math Seminar, Richmond VA.
• Jul 2018“The Even Cycle Spectrum of Dense Graphs”. 10th International Colloquium on Graph Theory and Combinatorics, Université Lyon 1, La Doua, Lyon, France.
• Jun 2018“Thresholds for Random Pebbling”. SIAM Discrete Math, University of Colorado at Denver, Denver CO.
• Apr 2018“Bootstrap Percolation on Polygonal Tilings”. MAA Sectional Meeting, Virginia Military Institute, Lexington VA.
• Mar 2018“Automated Conjecturing and Collaborative Mathematics”. 49th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton FL.
• Jan 2018“2-Connected Graphs Have Many Cycle Lengths”. Discrete Math Seminar, Virginia Commonwealth University, Richmond VA.
• Sep 2017“Turán Numbers and Their Variants”. Discrete Math Seminar, Virginia Commonwealth University, Richmond VA.
• Apr 2017“The Even Cycle Spectrum of Dense Graphs”. AMS Special Session on Extremal Problems in Graphs, Hypergraphs and Other Combinatorial Structures, Spring Central Sectional Meeting, Indiana University, Bloomington IN.
• Jan 2017“Variations on a Theme: The Forbidden Subgraph Problem”. Mathematics Colloquium, Virginia Commonwealth University, Richmond VA.
• Apr 2016“Minimum Codegree Conditions for Tiling by Tight Cycles”. AMS Special Session on Probabilistic and Extremal Combinatorics, Spring North Sectional Meeting, North Dakota State University, Fargo ND. (Invited)
• Jan 2016“Extremal Numbers for Forestable Graphs”. AMS–MAA Joint Meetings, Seattle WA.
• Nov 2015“The Forbidden Subgraph Problem and Its Variants”. Postdoc Lunch Seminar Series, Arizona State University, Tempe AZ.
• Oct 2015“Threshold Pebbling on Grids of Arbitrary Dimension”. AMS Special Session on Probabilistic Combinatorics, Fall Southeastern Sectional Meeting, University of Memphis, Memphis TN. (Invited)
• Sep 2015“Pebbling Problems on Graphs”. Discrete Math Seminar, Arizona State University, Tempe AZ.
• Jun 2015“Threshold Pebbling for Grids”. Connections in Discrete Mathematics, Simon Fraser University, Burnaby BC, Canada.
• Mar 2015“Introduction to Hypergraph Containers”. Discrete Math Seminar, Arizona State University, Tempe AZ.
• Jan 2015“Supersaturation Theorems, Hypergraph Containers, and Typical Structures”. Discrete Math Seminar, Arizona State University, Tempe AZ.
• Oct 2014“Typical Structure of Graphs with No Large Clique”. Postdoc Lunch Seminar Series, Arizona State University, Tempe AZ.
• Jan 2014“Random Markov Processes”. Mathematics and Computer Science Seminar, Universidade Federal do Ceará, Fortaleza, Brazil.
• Nov 2013“Random Markov Processes”. Probability Seminar, Arizona State University, Tempe AZ.
• Oct 2013“The Sharp Threshold for Maximum-Size Sum-Free Subsets in Even-Order Abelian Groups”. Discrete Math Seminar, Arizona State University, Tempe AZ.
• Sep 2013“Turán Numbers of Linear and Equibipartite Forests”. Discrete Math Seminar, Arizona State University, Tempe AZ.
• Dec 2012“Turán Numbers of Equibipartite Forests and Forests of Hyperpaths”. Theoretical Computer Science and Combinatorics Seminar, Universidade de São Paulo, São Paulo, Brazil.
• Dec 2012“Turán Numbers of Linear and Equibipartite Forests”. Mathematics and Computer Science Seminar, Universidade Federal do Ceará, Fortaleza, Brazil.
• Nov 2011“Turán Numbers for Multiple Paths”. Atlanta Lecture Series in Combinatorics and Graph Theory IV, Georgia State University, Atlanta GA.
• Oct 2011“Turán Numbers for Multiple Paths and Some Forests”. Discrete Mathematics Seminar, University of Nebraska, Lincoln NE.
• Aug 2011“Turán Numbers for Multiple Paths and Equibipartite Trees”. Paul Turán Memorial Conference, Rényi Institute of Mathematics, Budapest, Hungary.
• Apr 2011“Turán Numbers for Multiple Paths and Equibipartite Trees”. Combinatorics Seminar, University of Memphis, Memphis TN.
• May 2008“Ramsey Theory and Applications”. Mathematics Colloquium, Western Washington University, Bellingham WA.

• Feb 2022“Mathematical Music Theory”. VCU Math Circle, Virginia Commonwealth University, Richmond VA. (High school students.)
• Nov 2019“Musical Mathematics”. University of Vermont Mathematics Colloquium, Burlington VT.
• Apr 2019“Pizza Problems”. VCU Math Club, Virginia Commonwealth University, Richmond VA.
• Dec 2018“Conway's Rational Tangles”. Sonya Kovalevsky Girls in Math Day, Virginia Commonwealth University, Richmond VA. (Junior high / middle school students.)
• May 2018“Percolation Among Zombies”. VCU Math Circle, Virginia Commonwealth University, Richmond VA. (High school students.)
• Apr 2018“Bootstrap Percolation”. Society of Physics Students, Virginia Commonwealth University, Richmond VA. (Physics majors and graduate students.)
• Dec 2017“Conway's Rational Tangles”. Sonya Kovalevsky Girls in Math Day, Virginia Commonwealth University, Richmond VA. (Junior high / middle school students.)
• Apr 2016“Mad Scientists, Permutations, and Combinatorics”. ASU Math Circle, Arizona State University, Tempe AZ. (High school students.)
• Apr 2016“Conway's Rational Tangles”. Mathematics Awareness Day Workshop, Arizona State University, Tempe AZ. (High school students.)
• Sep 2015“Winning Strategies”. ASU Math Circle, Arizona State University, Tempe AZ. (High school students.)
• Sep 2015“Intro to Extremal Graph Theory”. ASU Math Club, Arizona State University, Tempe AZ. (Undergraduate mathematics majors.)
• Apr 2015“The Mathematics of Billiards and Reflections”. Mathematics Awareness Day Workshop, Arizona State University, Tempe AZ. (High school students. Joint with T. Stepien and M. Kawski.)
• Nov 2011“Voting Theory: Why It Isn't Fair”. Cantor Sect Undergraduate Mathematics Club, University of Memphis, Memphis TN.

Virginia Commonwealth University

• MATH 200 Calculus with Analytic Geometry I
  Spring 2020, Spring 2022, Fall 2025
  Limits, continuity, derivatives, differentials, antiderivatives and definite integrals.
• MATH 300 Introduction to Mathematical Reasoning
  Fall 2017, Fall 2018, Fall 2019, Fall 2020, Fall 2021, Fall 2022, Spring 2023, Fall 2025, Fall 2026
  An introduction to basic concepts of mathematical reasoning and the writing of proofs in an elementary setting. Direct, indirect and induction proofs. Illustrations of the concepts include basic proofs from mathematical logic, elementary set theory, elementary number theory, number systems, foundations of calculus, relations, equivalence relations, functions and counting with emphasis on combinatorial proofs.
• MATH 310 Linear Algebra
  Spring 2026
  Systems of linear equations, vector spaces, linear dependence, bases, dimensions, linear mappings, matrices, determinants, quadratic forms, orthogonal reduction to diagonal form, eigenvalues and geometric applications.
• MATH 350 Introductory Combinatorics
  Fall 2017, Fall 2022, Fall 2026
  An introduction to basic combinatorial concepts such as combinations, permutations, binomial coefficients, Fibonacci numbers and Pascal's triangle; basic theorems such as the pigeonhole principle and Newton's binomial theorem; algorithms such as bubble sort and quicksort; and discussion of basic applications such as chessboard problems, combinatorial games, magic squares and Latin squares.
• MATH 356 Graphs and Algorithms
  Spring 2019, Spring 2020
  An introduction to basic graph theoretic concepts such as trees, colorings and matchings; basic theorems such as the handshaking lemma and the Gallai identities; algorithms such as Dijkstra's and Kruskal's; and discussion of famous open problems such as finding shortest tours for a traveling salesman.
• MATH 490 Mathematical Expositions
  Spring 2019
  A senior capstone course in the major designed to help students attain proficiency in expository mathematical writing and oral presentation, which require the efficient and effective use of mathematics and the English language. Students will learn a variety of topics in mathematics, write reviews of selected award-winning mathematics papers and write a senior paper.
• MATH 556 Graph Theory
  Fall 2018, Fall 2021, Fall 2023
  Introduction to graph classes, graph invariants, graph algorithms, graph theoretic proof techniques and applications.
• MATH 650 Advanced Combinatorics
  Fall 2019, Fall 2023
  Topics include advanced applications of the pigeonhole principle and inclusion–exclusion principle, recurrence relations, generating functions, special counting sequences, Ramsey theory, and combinatorial designs and codes.
• MATH 656 Advanced Graph Theory
  Spring 2018, Spring 2023, Spring 2026
  This course lays a rigorous theoretical foundation for further advanced study in graph theory. Topics may include connectivity, matching, planarity, coloring, Hamiltonian cycles and topological graph theory, as well as further advanced material.
• MATH 756 Topics in Graph Theory
  Fall 2020
  A detailed study of selected topics, which may include extremal graph theory, spectral graph theory, infinite graphs, random graphs and graph minors. Fall 2020 focus: extremal graph theory.

University of Vermont

• MATH 3230 Ordinary Differential Equations
  Spring 2025
  Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations.
• MATH 6678 Topics in Combinatorics
  Spring 2025
  Topics will vary each semester and may include combinatorial designs, coding theory, topological graph theory, cryptography.

Arizona State University

• MAT 194 CLAS Early Start Program Mathematics
  Summer/Fall 2016
  Intensive two-week program for incoming mathematics majors. Focuses on building problem solving skills and mathematical background, as well as tools to help ensure academic success and to ease the transition to college life.
• MAT 210 Business Calculus
  Online, Spring 2017
• MAT 243 Discrete Mathematical Structures
  Fall 2016
  Logic, sets, functions, elementary number theory and combinatorics, recursive algorithms, and mathematical reasoning, including induction. Emphasizes connections to computer science.
• MAT 265 Calculus for Engineers I
  Fall 2016
  Limits and continuity, differential calculus of functions of one variable, introduction to integration.
• MAT 266 Calculus for Engineers II
  Fall 2016
  Methods of integration, applications of calculus, elements of analytic geometry, improper integrals, Taylor series.
• MAT 275 Modern Differential Equations
  Fall 2013 (2 sections)
  Introduces differential equations, theoretical and practical solution techniques. Applications. Problem solving using MATLAB.
• MAT 300 Mathematical Structures
  Fall 2014, Fall 2015
  Logic and set theory, induction, functions, order and equivalence relations, cardinality. Emphasizes writing proofs.
• MAT 416/513 Introduction to Graph Theory
  Spring 2017
• MAT 516 Graph Theory I
  Fall 2014, Fall 2015
  First semester of a systematic development of graph theory, including matchings, connectivity, arboricity, planarity, coloring, network flows.
• MAT 517 Graph Theory II
  Spring 2015, Spring 2016
  Second semester of a systematic development of graph theory, including dense and sparse graphs, Ramsey theory, hamiltonicity, random graphs, minors.

University of Memphis

• MATH 1710 College Algebra
  Spring 2011 (2 sections)
  Analysis of functions (linear, quadratic, polynomial, root, rational, exponential, logarithmic) using graphing calculators; partial fractions; synthetic division; conic sections; theory of equations; inequalities; applications.

Western Washington University

• MATH 112 Functions and Algebraic Methods
  Fall 2006
  Pattern recognition and generalization, building mathematical models and problem solving are emphasized. Supporting topics include polynomials, linear and quadratic equations, inequalities, graphs, rational expressions, radicals and functions.
• MATH 114 Precalculus I
  Winter 2007, Spring 2007, Fall 2008
  Data analysis, functions as mathematical models, functions and their graphs.
• MATH 115 Precalculus II
  Winter 2008
  Data analysis, modeling, trigonometry, inverse functions.
• MATH 157 Business Calculus
  Spring 2008
  Limits, rates of change, differentiation, graphing and optimization, integration, business applications, partial differentiation.