Preface: Many of these works deadname me. Just ignore it. Curious?

# Papers

### Published

Paramotopy: Parameter homotopies in parallel. A version of this paper appeared in ICMS 2018

Arc length based maximal lyapunov functions and domains of attraction estimation for polynomial nonlinear systems. A version of this paper appeared in Automatica, Volume 90, April 2018

Bertini_real: numerical decomposition of real algebraic curves and surfaces. A version of this paper has been accepted to ACM ToMS in 2017.

Decomposing solution sets of polynomial systems using derivatives. A version appeared as an ICMS 2016 extended abstract.

Validating the completeness of the real solution set of a system of polynomial equations. A version appeared in ISSAC 2016.

Numerical Local Irreducible Decomposition. A version appears as a MACIS 2015 extended abstract.

Bertini_real: software for one- and two-dimensional real algebraic sets. A version appears as an ICMS 2014 Extended Abstract

On computing a cell decomposition of a real surface containing infinitely many singularities. A version appears as an ICMS Extended Abstract

Reduced systems for Intrinsic Localized Modes on an infinite oscillator array. A version appears in IEICE NOLTA 2013.

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars and their application for sensing. A version appears in JAP 2012.

Simplified models for Intrinsic Localized Mode dynamics. A version appears in NOLTA 2012 Proceedings.

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars. A version appears in NOLTA 2011 Proceedings.

Arc length based maximal lyapunov functions and domains of attraction estimation for polynomial nonlinear systems. A version of this paper appeared in Automatica, Volume 90, April 2018

Bertini_real: numerical decomposition of real algebraic curves and surfaces. A version of this paper has been accepted to ACM ToMS in 2017.

Decomposing solution sets of polynomial systems using derivatives. A version appeared as an ICMS 2016 extended abstract.

Validating the completeness of the real solution set of a system of polynomial equations. A version appeared in ISSAC 2016.

__The complete solution of Alt-Burmester synthesis problems for four-bar linkages. A version appears in J. Mechanisms Robots 2016.__

__Workspace multiplicity and Fault tolerance of cooperating robots. A version appears as a MACIS 2015 paper.__

Numerical Local Irreducible Decomposition. A version appears as a MACIS 2015 extended abstract.

Bertini_real: software for one- and two-dimensional real algebraic sets. A version appears as an ICMS 2014 Extended Abstract

On computing a cell decomposition of a real surface containing infinitely many singularities. A version appears as an ICMS Extended Abstract

Reduced systems for Intrinsic Localized Modes on an infinite oscillator array. A version appears in IEICE NOLTA 2013.

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars and their application for sensing. A version appears in JAP 2012.

Simplified models for Intrinsic Localized Mode dynamics. A version appears in NOLTA 2012 Proceedings.

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars. A version appears in NOLTA 2011 Proceedings.

### Undergraduate research

Matplotlib and Bertini_real. Nicolle Ho, ND '18

3D-Printable algebraic Mobius strips. Travis Wert, ND '17

Preventing substitution of symbolic expressions in Matlab. Sam Cavender, ND '18

Bertini_real documentation, how-to videos, and 3D printing. Chris Lembo, ND '19

Rendering video of surface decompositions in Blender. Alec Sievern, ND '17.

3D-Printable algebraic Mobius strips. Travis Wert, ND '17

Preventing substitution of symbolic expressions in Matlab. Sam Cavender, ND '18

Bertini_real documentation, how-to videos, and 3D printing. Chris Lembo, ND '19

Rendering video of surface decompositions in Blender. Alec Sievern, ND '17.

### Unpublished

Waves Interacting on an Annulus, with a Fibonacci style resonance - Informal CSU Horsetooth Journal

Homotopy Continuation Methods, Intrinsic Localized Modes, and Cooperative Robotic Workspaces - Dissertation

Homotopy Continuation Methods, Intrinsic Localized Modes, and Cooperative Robotic Workspaces - Dissertation

# Presentations

### Invited

These are large in bitsize, in general. Not optimized for web.

- Regularizing Numerical Cell Decompositions - AMS Fall Sectional, Denver, Colorado, October 2016
- Numerically Decomposing Real and Complex Tropical Curves in Any Number of Dimensions - ICMS July 2016, Berlin
- Printing Algebraic Geometry - Bertini workshop, Notre Dame, May 2016
- The Development of Bertini 2 - Bertini workshop, Notre Dame, May 2016
- The Complete Solution of Alt-Burmester Synthesis Problems for Four-bar Linkages - AMS Sectional -- Georgia, March 2016
- Numerical Local Irreducible Decomposition - MACIS 2015
- Workspace Multiplicity and Fault Tolerance of Cooperating Robots - MACIS, November 2015
- Applications of Monodromy - TAMU, NCSU, October 2015 (chalk talk)
- Advances in Software in Numerical Algebraic Geometry - SIAM AG15
- Parametrized Polynomial Systems and Real Numerical Algebraic Geometry - Notre Dame Applied Math Seminar
- Applications of Real Algebraic Varieties - AMS Spring Sectional
- Numerical Challenges to Decomposition of Real Algebraic Surfaces - De Paul University
- Numerically Decomposing Algebraic Surfaces with an Infinite Number of Singularities - The Ohio State University
- Printing Algebraic Surfaces with Singularities - AMS Fall Western Sectional
- Bertini_real: Software for Real Algebraic Sets - The Simons Institute for the Theory of Computing
- Bertini_real: Software for Real Algebraic Sets - IMCS 2014
- Multistability and Criticality of Real Sets - NCSU Symbolic Computation
- From Polynomials to 3D Printing: How to Print an Algebraic Surface - NCSU SUM Series (chalk talk)
- Paramotopy - SIAM AG 2013
- Using Paramotopy to study chemical reaction networks - Harvard Medical School, Gunawardena Group
- Simplified Models for ILMs - NOLTA 2012
- Cooperative Robotic Workspaces - SIAM DS 2011
- Cooperative Robotic Workspaces - IASTED 2010

# Posters

These are large in bitsize, in general. Not optimized for web.

- Robotics, Kinematics, and Polynomials (png) (pdf)
- Bertini Workshop Poster
- Notre Dame Research Symposium 2015 fullresolution rasterized_and_small
- NCSU Postdoc Research Symposium 2014
- ECCAD 2014
- DTRA Annual Conference 2012
- NOLTA 2011 Poster Session
- DTRA Annual Conference 2011

# Tutorials

### Python for Data Science, October 2017

Consists of a quick show of ways of interacting with Python, a Jupyter notebook doing stuff with the BoardGameGeek.com Keggle dataset, and a little language tutorial.

### Git, using LaTeX, Fall 2018 @ ICERM

- I made some slides. Here they are.
- I also have a nifty diagram for explaining Git and Github.