Organizing Committee
Abstract

This workshop will focus on core algorithms in the three crucial areas in nonlinear algebra: numerical algebraic geometry, symbolic computation, and combinatorial methods. There have been tremendous advances in algorithms in these areas. As applications become more sophisticated, and require more computing resources, the basic algorithms and implementations need to step up to match the demand from applications. This workshop will bring together experts to exchange ideas on new algorithms that are needed and on improvement of existing ones. It will incite collaboration on hybrid algorithms involving computational methods from the three areas. Examples of open problems to be addressed include: certification of numerical methods, and combining numerical, symbolic and combinatorial methods to allow a much larger reach for decomposition algorithms.

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Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, September 17, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50am EDTComputing Subschemes of the Border Basis Scheme - Martin Kreuzer, University of Passau11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTTime-Varying Semidefinite Programs - Amir Ali Ahmadi, Princeton University11th Floor Lecture Hall
11:30 - 12:20pm EDTCoCoA News 2018 - Anna Bigatti, Universita' degli Studi di Genova11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTPolyhedral computations in polynomial system solving - Anders Jensen, Aarhus Universitet11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTsage.geometry.polyhedron - Matthias Koeppe, University of California Davis11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, September 18, 2018
TimeEventLocationMaterials
9:00 - 9:50am EDT"Chordal" package- Exploiting graphical structure in polynomial ideals - Diego Cifuentes, Massachusetts Institute of Technology11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTSegre-Driven Algorithms to Test Ideal Membership and Compute Algebraic Multiplicity - Martin Helmer, University of Copenhagen11th Floor Lecture Hall
11:30 - 12:20pm EDTComputing Multiple Zeros of Polynomial Systems - Lihong Zhi, Academy of Mathematics and Systems Science, CAS11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTMultiprecision- solving and causing problems - Danielle Brake, University of Wisconsin - Eau Claire11th Floor Lecture Hall
3:30 - 5:30pm EDTPoster Session and Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, September 19, 2018
TimeEventLocationMaterials
9:00 - 9:50am EDTAlgorithms in tropical geometry - Diane Maclagan, University of Warwick11th Floor Lecture Hall
10:00 - 10:30am EDTComputer vision working group10th Floor Classroom 
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTCore computational methods in tropical algebraic geometry - Yue Ren, Max Planck Institute11th Floor Lecture Hall
11:30 - 12:20pm EDTTropical Principal Component Analysis and its Application to Phylogenetics - Ruriko Yoshida, Naval Postgraduate School11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTAlgebraic Biology with Macaulay2 - Elizabeth Gross, University of Hawaii at Manoa11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, September 20, 2018
TimeEventLocationMaterials
9:00 - 9:50am EDTNumerical Function Patches for 1D and 2D Real Algebraic Cell Decompositions - Charles Wampler, General Motors R&D11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTFiber product homotopy method for multiparameter eigenvalue problems - Jose Rodriguez, University of Wisconsin-Madison11th Floor Lecture Hall
11:30 - 12:20pm EDTRandom Monomial Ideals - Lily Silverstein, University of California Davis11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
1:00 - 2:00pm EDTMatrix completion working group10th Floor Classroom 
2:30 - 3:20pm EDTComputational tools for FI-algebras - Robert Krone, University of California Davis11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTNumerical approximations- sometimes being close is good enough - Chris Peterson, Colorado State University11th Floor Lecture Hall
Friday, September 21, 2018
TimeEventLocationMaterials
9:00 - 9:50am EDTBKK bound and polyhedral homotopy - Tianran Chen, Auburn University at Montgomery11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTProof-of-work Certificates for High Complexity Mathematical Computations - Erich Kaltofen, NCSU and Duke University11th Floor Lecture Hall
11:30 - 1:30pm EDTBreak for Lunch / Free Time  
3:30 - 7:00pm EDTAGNES Conference at Brown University 

Associated Semester Workshops

Nonlinear Algebra
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Nonlinear Algebra Bootcamp
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Real Algebraic Geometry and Optimization
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Nonlinear Algebra in Applications
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Lecture Videos

Proof-of-work Certificates for High Complexity Mathematical Computations

Erich Kaltofen
North Carolina State University
September 21, 2018

BKK bound and polyhedral homotopy

Tianran Chen
Auburn University at Montgomery
September 21, 2018

Numerical Approximations: sometimes close is good enough

Chris Peterson
Colorado State University
September 20, 2018

Computational tools for Fl-algebras

Robert Krone
UC Davis
September 20, 2018

Random monomial ideals

Lily Silverstein
University of California Davis
September 20, 2018

Fiber product homotopy method for multiparameter eigenvalue problems

Jose Rodriguez
University of Wisconsin-Madison
September 20, 2018

Algebraic Biology with Macaulay2

Elizabeth Gross
University of Hawai'i at Manoa
September 19, 2018

Gröbner bases from tropical geometry

Diane Maclagan
University of Warwick
September 19, 2018

Multiprecision- solving and causing problems

Danielle Brake
University of Wisconsin - Eau Claire
September 18, 2018

sage.geometry.polyhedron

Matthias Köppe
UC Davis
September 17, 2018

CoCoA News 2018

Anna Bigatti
University of Genova
September 17, 2018

Time-Varying Semidefinite Programs

Amir Ali Ahmadi
Princeton University
September 17, 2018

Computing Subschemes of the Border Basis Scheme

Martin Kreuzer
University of Passau
September 17, 2018