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My talks:

(pdf / with pauses) 3D Printed Mathematical Art

  • Queens College Math Club, May 2017.
Abstract: 3D Printing is happening at Queens College! Professor Hanusa will show how he uses the computer program Mathematica to design and 3D print pieces of Mathematical Art. The art will be on display and be passed around, so you will have the chance to see and touch objects 3D printed in plastic, sandstone, and even metal!

(pdf / with pauses) The power and pitfalls of Mathematica for 3D design

Abstract: Mathematica has amazing graphics and design capabilities that I have been using to design 3D works of art and teach my students the same. I will discuss the commands and techniques that I have found useful, along with the frustrations and work-arounds that I have has to institute in order to cajole Mathematica into creating (and then exporting!) the desired artwork. I will also focus on how I teach my students these same methods.

(pdf / with pauses) A q-Queens Problem

Abstract: The n-Queens Problem asks in how many ways you can place n queens on an n×n chessboard so that no two attack each other. There has been no formula for the answer to this question ... until now! We develop a mathematical theory to address the more general question "In how many ways can you place q chess pieces on a polygonal chessboard so that no two pieces attack each other?"

The theory is geometrical and combinatorial in nature and involves counting lattice points that avoid certain hyperplanes. This is joint work with Thomas Zaslavsky and Seth Chaiken.

(pdf) Pondering Pencil Puzzles

Abstract: In Spring 2016, I taught MATH 555: Games and Puzzles as a class exploration of pencil puzzles, which are logic-based puzzles in the vein of Sudoku. We'll discuss how students were able to flex their creativity and take ownership of their learning in this class.

Course Materials are available online at http://qc.edu/~chanusa/courses/555/16/

(pdf) Teaching Mathematical Art: Coordinating Design and 3D Printing

Abstract: I teach Queens College MATH 213: Math with Mathematica as a student-driven project-based class. Our second project this Spring 2015 was to design and print a piece of three-dimensional mathematical art using Mathematica. We'll discuss the project with a focus on what worked, and present the fruits of the students' labor.

Course Materials and a Virtual Art Gallery are available online at http://qc.edu/~chanusa/courses/213/15/

(pdf) Posters you can count on

Abstract: In my Combinatorics class (Math 636), students answer a counting question of their choosing. They present their individual research at a poster session held at the end of the semester. The students see the diversity of ideas that can be understood using the techniques learned in our class.

(pdf) Applications of abacus diagrams

Abstract: A t-core partition is a partition whose Young diagram has no box with hook length a multiple of t. Partitions that are both s-core and t-core for integers s and t are called simultaneous core partitions. We will discuss the applications of simultaneous core partitions—we visit with lattice paths, alcoves in a hyperplane arrangement, and a "major index" statistic that recovers a q-analog for Catalan numbers. This is joint work with Brant Jones and Drew Armstrong.

(pdf) Self-conjugate core partitions: It's storytime!

Abstract: A t-core partition is an integer partition whose Young diagram has no box with hook length a multiple of t. Self-conjugate core partitions arise in the combinatorics of affine Coxeter groups and in the representation theory of the alternating group.

In this talk, I will discuss the investigation of self-conjugate core partitions that I carried out with Rishi Nath. I will present results and conjectures concerning positivity, monotonicity, and unimodality. We have found more questions than answers and I will conclude with questions and directions for future work.

(pdf) Combinatorial interpretations in affine Coxeter groups

Abstract: In this talk we will investigate various combinatorial models that arise in the study of Coxeter groups. A stepping-off point will be the notion of one-line notation; when we write a finite permutation, we often write it in one-line notation as with 15243. I will discuss a generalization for affine permutations, and then bijections with other combinatorial families such as abacus models, core partitions, and bounded partitions.

Then I will describe how Brant Jones and I have generalized these combinatorial models to affine Coxeter groups of types B, C, and D. No previous understanding of Coxeter groups is necessary to enjoy this talk. A healthy appetite for interesting combinatorics will suffice.
See also: Interactive animations

(pdf) A combinatorial introduction to reflection groups

Abstract: What do permutations, snowflakes, M.C. Escher prints, and a kaleidoscope all have in common? They are all related to reflection groups. We'll explore these groups (which you might encounter in abstract algebra) through the lens of combinatorics. That means we'll do some counting and there will be plenty of pretty pictures to see. Once we have discussed some background, I'll share some of my recent research on the topic. Come join us!

(pdf) A quasi-polynomial q-Queens result and related Kronecker products of matrices

  • CUNY Combinatorics Seminar, February 2012.
  • University of California, Davis, May 2009.
  • Queens College, May 2009.
Abstract: For a fixed number of nonattacking queens placed on a square board of varying size, we show that the number of solutions is a quasipolynomial function of the size of the board using Ehrhart theory. This result generalizes to other real and fairy pieces on a polygonal board. Determining the period of each quasipolynomial function requires calculating the least common multiple of all subdeterminants of a matrix. This matrix has the form of a Kronecker product of a matrix involving the moves of the piece and the incidence matrix of a complete graph. Investigation of this quantity gives a new linear algebraic result proved using graph theory. No background knowledge is necessary to enjoy this talk.

(pdf) Combinatorial Interpretations in affine Coxeter groups of type B, C, and D

Abstract: Core partitions and abacus diagrams are two useful combinatorial objects in bijection with minimal length coset representatives in the parabolic quotient of the affine symmetric group modulo the finite symmetric group. In joint work with Brant Jones, we extend cores, abaci, and other combinatorial interpretations to types affine B, C, and D.

See also: Interactive animations

(pdf) Combinatorial interpretations in affine Coxeter groups

Abstract: In this talk I will investigate various combinatorial models which arise in the study of Coxeter groups. (This is joint work with Brant C. Jones.) A stepping-off point will be the notion of one-line notation; when we write a finite permutation, we often write it in one-line notation as 15243. I will discuss a generalization for affine permutations, and then bijections with other combinatorial families such as abacus models, core partitions, and bounded partitions. If time permits, I will discuss an application of the abacus model—the enumeration of fully commutative affine permutations. No previous understanding of Coxeter groups is necessary to enjoy this talk. A healthy appetite for interesting combinatorics will suffice.

(pdf) Let's Count: Domino Tilings

Abstract: Interesting mathematics lie behind the dominoes and chessboards that live in your games closet. In this talk, we'll explore counting questions related to the arrangements of dominoes that completely tile a rectangular chessboard. Our exploration will lead us to famous number sequences, linear algebra, graph theory, and combinatorics. All are invited to come and enjoy this talk!

(pdf) The enumeration of fully commutative affine permutations

(pdf) An introduction to LaTeX for students (Presentation TeX source) (Empty.tex) (NotEmpty.tex) (Practice your skills)

(pdf) How Mathematica improves my teaching (Mathematica supplement)

(pdf) Voting Methods and Colluding Voters

  • Gettysburg College, January 2008.
  • Binghamton University, December 2007.

Five days of five speakers in (roughly) fifty minutes

  • Binghamton University, February 2007.

(pdf) Let's Count: Enumeration through matrix methods.

  • Queens College, February 2008.
  • Temple University Colloquium, March 2006.

(pdf) A Gessel-Viennot-Type Method for Cycle Systems in a Directed Graph.

  • Gettysburg College, January 2008.
  • LaBRI (Bordeaux, France), June 2006.
  • Cornell University, November 2005.
  • Binghamton University, September 2005.
  • Carnegie Mellon University, March 2005.
  • University of Washington, February 2005.
  • University of California, Berkeley, February 2005.

(pdf) Matrix types and operations arising in matching theory.

  • Binghamton University, September 2005.
  • University of Washington, April 2005.

An Introduction to Tilings.

  • University of Washington, February 2005.

The Traffic Assignment Problem.

  • University of Washington, May 2003.

A Binet's Form for Generalized Fibonacci Numbers through Random Tilings and Markov Chains.

  • University of Washington, May 2002.
  • Harvey Mudd College, April 2001.