papers and presentations

silviana amethyst
11/13/25

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

Papers ¶

The most current list of my papers is available on my Google Scholar

Published papers

Computing complex and real tropical curves using monodromy.
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.
Numerically 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.

Submitted papers

The most current list of my papers is available on my Google Scholar

Undergraduate research reports

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.

Unpublished papers or works

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

Talks and presentations ¶

These are large in bitsize, in general. Not optimized for web. I am sorry there are no more recent than this, I am working on it (Jan 16, 2025)

todo: update this list

Applications of computational algebraic geometry - UWEC Meals with Honors, September 2017
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, November 2015
Workspace Multiplicity and Fault Tolerance of Cooperating Robots - MACIS 2015, November 2015
Applications of Monodromy - TAMU, NCSU, October 2015 (chalk talk)
Advances in Software in Numerical Algebraic Geometry - SIAM AG15, August 2015
Parametrized Polynomial Systems and Real Numerical Algebraic Geometry - Notre Dame Applied Math Seminar, March 2015
Applications of Real Algebraic Varieties - AMS Spring Sectional, March 2015
Numerical Challenges to Decomposition of Real Algebraic Surfaces - De Paul University, January 2015
Numerically Decomposing Algebraic Surfaces with an Infinite Number of Singularities - The Ohio State University, November 2014
Printing Algebraic Surfaces with Singularities - AMS Fall Western Sectional, Fall 2014
Bertini_real: Software for Real Algebraic Sets - The Simons Institute for the Theory of Computing, October 2014
Bertini_real: Software for Real Algebraic Sets - IMCS 2014, August 2014
Multistability and Criticality of Real Sets - NCSU Symbolic Computation Seminar, April 2014
From Polynomials to 3D Printing: How to Print an Algebraic Surface - NCSU SUM Series (chalk talk)
Paramotopy - SIAM AG13, August 2013
Using Paramotopy to study chemical reaction networks - Harvard Medical School, Gunawardena Group, July 2013
Simplified Models for ILMs - NOLTA 2012
Cooperative Robotic Workspaces - SIAM DS11, May 2011, Snowbird
Illustration of numerical algebraic methods for workspace estimation of cooperating robots after joint failure - IASTED 2010

Posters ¶

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

Tutorials ¶

Python for Data Science, October 2017

The tutorial consisted 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.

I have some slides, and a GitHub repo

Git, using LaTeX, Fall 2018 @ ICERM

Git for mathematicians. Taught using a LaTeX paper as the basis, because I assume mathematicans know how to use LaTeX, and git cannot be taught without doing something. It’s a meta-skill, so an actual skill must be performed for git to mean anything.