Date of the event: Friday, March 31, 2017
Location: Wilfrid Laurier University, Waterloo Campus, Career Center, Room CC101
Website: http://www.cargo.wlu.ca/15years
Website at the Fields Institute: http://www.fields.utoronto.ca/activities/1617/CARGO15
Schedule of the event:9:30 a.m. Opening Remarks,
(1) Dr. Max Blouw, President and vicechancellor, Wilfrid Laurier University
(2) Dr. Laurent Bernardin, Executive VicePresident of Research and Development, Maplesoft
9:4510:45 Prof. Frank Sottile, Texas A&M, College Station, USA "The trace test in numerical algebraic geometry"
10:45  11:15 a.m. Coffee Break
11:00  12:15 Dr. Jürgen Gerhard, Senior Director of Research, Maplesoft, Waterloo, Canada "What's New in Maple 2016"
12:15
(1) Closing Remarks, Ilias Kotsireas, Director, CARGO Lab
(2) Oxford University Press 6 books raffle:
Prof. Frank Sottile, Texas A&M, College Station, USA 

Title: "The trace test in numerical algebraic geometry" 

Abstract:  
Numerical algebraic geometry uses tools from numerical analysis to study algebraic varieties on a computer. Its origins were in homotopy methods, which used Newton iterations and homotopy continuation to solve systems of equations. Early homotopy algorithms exploited combinatorial structures, such as multihomogeneity, for efficiency. In numerical algebraic geometry, a variety X is represented by a witness set, which is a linear section of X in a projective or affine space. 

A fundamental step is to decompose a witness set for a variety X into subsets corresponding to the irreducible components of X. An algorithm for this numerical irreducible decomposition uses monodromy to compute a possible decomposition which is verified using the trace test. 

In this talk I will introduce numerical algebraic geometry and witness sets, and describe numerical irreducible decomposition, including a new and elementary proof of the trace test. I will then explain versions of witness sets, the trace test, and numerical irreducible decomposition for multihomogeneous varieties X that take advantage of this structure. 

This is joint work with Anton Leykin and Jose Rodriguez. 

Short Bio:  
Sottile is a Professor of Mathematics at Texas A&M University. He holds a Masters degree from Cambridge University (1986) and a MSc. (1989) and Ph.D. from the University of Chicago (1994). His research interests are in algebraic combinatorics and the applications of algebraic geometry. He was the founding chair of the SIAM Activity Group on Algebraic Geometry and is a corresponding editor of the SIAM Journal on Applied Algebra and Geometry. He has published over 100 peerreviewed articles and one book. He was a Churchill Scholar, held a NSF Career award, and is a Fellow of the American Mathematical Society. 
Dr. Jürgen Gerhard, Senior Director of Research, Maplesoft 

Title: What's New in Maple 2016 

Abstract:  
We will present some of the new features in Maple 2016, including data frames, Math apps, series and limit computations, symbolic integration and summation, symbolic PDE solving, Statistics, and more. See the Maple 2016 Research Datasheet. 

Short Bio:  
Maplesoft (http://www.maplesoft.com) is the leading provider of highperformance software tools for engineering, science, and mathematics. Maplesoft's flagship product, Maple, combines the world's most powerful mathematics engine with an interface that makes it extremely easy to analyze, explore, visualize, and solve mathematical problems. 

Jürgen Gerhard holds a PhD from University of Paderborn, Germany. He has been with Maplesoft since 2003, and is currently Senior Director of Research. His areas of interest are symbolic computation and its applications in engineering, and he is coordinating research and consulting projects in these areas at Maplesoft. Together with Joachim von zur Gathen, he is the coauthor of the reference textbook "Modern Computer Algebra", which as of 2013 is in its 3rd edition. 