This workshop will be offered virtually. The in-person meeting has been cancelled due to the COVID-19 outbreak. A schedule for virtual talks will be posted soon. Accepted participants will be notified how to access the virtual presentations.
Organizing Committee
Abstract

Galois groups encode the internal structure of field extensions. Less well-known is that (families) of systems of polynomial equations or geometric problems also have Galois groups that encode the internal structure of the equations or geometric problems. During the 2018 Fall program at the ICERM on Nonlinear Algebra, different groups of researchers who were studying or using Galois groups in their work became more aware of their related interests. This common thread connects recent work in enumerative geometry, statistics, computer vision, number theory, and numerical nonlinear algebra. Further connections have subsequently been realized to arithmetic enhancements of intersection theory and to random real algebraic geometry. This workshop will bring representatives of these research groups together to deepen these interactions and chart new research goals.

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

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Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 31, 2020
TimeEventLocationMaterials
9:50 - 10:00am EDTWelcome - ICERM Director  
10:00 - 10:20am EDTOrganizer Welcome and Overview - Frank Sottile, Texas A&M University  
10:20 - 11:00am EDTIntroductions  
11:00 - 11:35am EDTBraid monodromy of univariate fewnomials - Lionel Lang, Stockholm University 
1:30 - 2:05pm EDTThere are 160,839 + 160,650 3-planes in a 7-dimensional cubic hypersurface - Kirsten Wickelgren, Duke University 
2:30 - 3:05pm EDTGalois groups in 3D Reconstruction - Timothy Duff, Georgia Institute of Technology 
3:30 - 4:00pm EDT"Make your own Coffee" break  
Tuesday, September 1, 2020
TimeEventLocationMaterials
10:00 - 10:35am EDTGalois theory in several variables - a number theory perspective - Andrew Bridy, Yale University 
11:00 - 11:35am EDT38406501359372282063949 and all that- Monodromy of Fano Problems - Sachi Hashimoto, Boston University 
12:00 - 1:30pm EDTFree time/ Unorganized Discussion  
1:30 - 2:05pm EDTGalois groups in Schubert calculus - Frank Sottile, Texas A & M University  
2:30 - 3:05pm EDTPolynomial systems of graphical models - Elizabeth Gross, University of Hawai'i at Manoa 
3:30 - 4:00pm EDT"Make your own Coffee" break  
Wednesday, September 2, 2020
TimeEventLocationMaterials
9:00 - 9:35am EDTHomotopyContinuation.jl - Solving systems of polynomial equations in Julia - Paul Breiding, TU Berlin 
10:00 - 10:35am EDTReal monodromy action - Margaret Regan, Duke University 
11:00 - 11:35am EDTToward rigorous monodromy and 1-parameter enumerative problems - John Voight, Dartmouth College 
12:00 - 1:30pm EDTFree time/ Unorganized Discussion  
1:30 - 2:05pm EDTWronskians and Monodromy in Real Schubert Calculus - Jake Levinson, Simon Fraser University 
2:30 - 3:05pm EDTMonodromy problems in Brill--Noether theory - Isabel Vogt, Stanford University and University of Washington 
3:30 - 4:00pm EDT"Make your own Coffee" break  

Lecture Videos

Monodromy problems in Brill--Noether theory

Isabel Vogt
Stanford University
September 2, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Wronskians and Monodromy in Real Schubert Calculus

Jake Levinson
University of Washington
September 2, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Toward rigorous monodromy and 1-parameter enumerative problems

John Voight
Dartmouth College
September 2, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Real monodromy action

Margaret Regan
Duke University
September 2, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Polynomial systems of graphical models

Elizabeth Gross
University of Hawai'i at Manoa
September 1, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Galois theory in several variables - a number theory perspective

Andrew Bridy
Yale University
September 1, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Galois groups in 3D Reconstruction

Timothy Duff
Georgia Institute of Technology
August 31, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

There are 160,839 + 160,650 3-planes in a 7-dimensional cubic hypersurface

Kirsten Wickelgren
Duke University
August 31, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play

Braid monodromy of univariate fewnomials

Lionel Lang
Stockholm University
August 31, 2020
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and...
Play