Adam Van TuylDepartment of Mathematics and StatisticsMcMaster University Hamilton, ON, Canada L8S 4L8 vantuyl@math.mcmaster.ca 

My research is primarily in commutative algebra. My current research interests are: homological invariants, edge ideals, simplicial complexes, sets of points in (multi)projective spaces, and toric ideals.
Lecture Notes (Classes and Workshops)
 In JuneJuly 2017, I was one of the instructors for the PRAGMATIC summer school at the Universita di Catania, Italy. Here are a copy of my lecture notes for the workshop These lectures, along with my coinstructors, formed the basis of our monograph Ideal of Powers and Powers of Ideals
 During the Winter 2013 semester, J. Biermann and I ran a weekly seminar: (You can only see the website via the Wayback Machine)
 In July 2011, I will be giving three one hour lectures on edge and cover ideals. These lectures are part of a workshop held at Castro Urdiales, Spain, as part of MONICA (Monomial Ideals, Compuations, and Applications). For more on this workshop, see These lecture notes will appear in Springer Lecture Notes in Mathematics sometime in Fall 2013.
 During the Fall 2007 semester, I cotaught a graduate course on Operations Research with Dr. W. Huang. As part of the course, the students and instructors typed up their lecture notes. You can see more about our seminar below:
 In July 2006, I will be giving one of the workshop lectures at the Fields Institute on Computational and Combinatorial Commutative Algbera. For more on this workshop, see
 During second sememster of the 20052006 school year, I ran a seminar on combinatorial commutative algebra. For more on this seminar, see Included on this page are lecture notes typed up by my M.Sc. student Jing He.
 In two papers with Enrico Carlini and Elena Guardo,
I studied problems related to star configurations. In both
papers, we were required to compute a few special cases via
computer. You can find the relevant
code here:
 Star configurations on generic hypersurfaces
 Plane curves containing star configuration sets of points
 In the paper
Revisiting the spreading and covering numbers,
Ben Babock and
I looked at the problem of computing some invariants of a graph that
arises in a problem in algebraic geometry. As part of his summer
NSERC USRA, Ben wrote a number of programs to compute and bound
these invariants. You can find some this code here
 In my paper
Zerononzero patterns for nilpotent matrices over finite fields
with
Kevin N. Vander Meulen, we looked
at the problem of determining what zerononzero patterns
allow nilpotence. As part of this project, we showed that one
could use results from commutative algebra to elminate
possible patterns as being potentially nilpotent. One
can use computer programs, like CoCoA and Macaulay 2,
to carry out the necessary computations. You can
see worked out examples here:

With Chris Francisco
and
Andrew Hoefel, I
wrote
a Macaulay 2 package, entitled EdgeIdeals,
that allows users to use experiment with hypergraphs
and graphs via the edge ideal correspondence.
See the papge
for more information.
 With Fabrizio Zanello, I introduced the notion of a levelable simplicial complex. We showed that a simplicial complex is levelable if and only if there existed a integral solution to a system of equations constructed from the facets of the complex. Please see for more on this, and a Mathematica program to determine if a complex is levelable.
 In my paper ACM sets of points in multiprojective space
(joint with Elena Guardo) we looked for necessary and sufficient
conditions for a set of points to be ACM. Our paper
contains a number of examples to show that results
in P
1 x P1 cannot be easily extended to the general setting. To see the code CoCoA for our examples please see  In a recent paper with Elena Guardo, we described an algorithm to compute the minimal resolution of double points in P^{1} x P^{1} with an ACM support. We have implemented this program into CoCoA and Macaulay 2. To see this code, please go to
 PostDocs
 Jay Wang (jointly supervised with M. Harada and J. Rajchgot) 20212023
 Sergio Da Silva (jointly supervised with M. Haradaand J. Rajchgot) 20202022
 Jeremy Lane (jointly supervised with M. Harada) 20192022
 Johannes Hofscheier (jointly supervised with M. Harada) 20172019
 Federico Galetto (jointly supervised with M. Harada) 20152018
 Jennifer Biermann 20112013
 PhD Students
 Craig Kohne (cosupervised with A. Deza) Sept. 2017  Aug. 2022 (expected)
Thesis title: TBD  Graham Keiper, Sept. 2016  December. 2021 (expected)
Thesis title: Toric ideals of finite simple graphs  Eduardo Camps, Jan. 2020June 2020
(Visiting Ph.D. student from Escuela Superior de Fsica y Matemticas, IPN, Mexico)  Beatrice Picone (cosupervised with E. Guardo) Sept. 2015December 2018 (Completed)
Thesis title: Homological invariants of some special varieties.
(Picone was a PhD student at the Universita di Catania, Italy.)  Miguel Eduardo Paczka, Jan. 2018June 2018
(Visiting Ph.D. student from Escuela Superior de Fsica y Matemticas, IPN, Mexico)
 Craig Kohne (cosupervised with A. Deza) Sept. 2017  Aug. 2022 (expected)
 MSc. Students
 Maryam Nowroozi, MSc (completed May 2021) cosupervsied with Dr. M. Harada
Thesis title: Virtual resolutions of sufficiently general points in P^{1} x P^{1}.  Jarvis, Kennedy, MSc (completed August 2020) cosupervised with Dr. M. Harada
Projecti title: An Algebraic Condition for a Complex to be Virtual  Michael Cox, MSc (completed December 2018) cosupervised with Dr. K.N. Vander Meulen
Project Title: On condition numbers of companion matrices.  Jason Palombaro, MSc (completed December 2017)
Project Title: On the Groebner bases of ideals of points in P^{1} x P^{1}.  Michael Riddell, MSc (completed June 2017) cosupervised with Dr. K.N. Vander Meulen
Project Title: Zero forcing number of circulant graphs.  Sam Budd, MSc (Completed June 2017)
Project Title: A introduction to fideals and their complements.  Becky Hooper, MSc (Completed June 2017)
Project Title: Shellability of the van der Waerden complex.  Ashwini Bhat, M.Sc. (Completed May 2012)
Project: Associated Primes of Powers of the Alexander Dual of Path Ideals of Trees.
(Update: A. Bhat, J. Biermann and myself turned this results into this journal article which appeared in the Journal of Pure and Applied Algebra.)  Kevin Jurcik, M.Sc. (Completed May 2009) cosupervised with
W. Huang
Project: Open Shop Scheduling to Minimize Makespan.  Jing (Jane) He, M.Sc. (Completed May 2007)
Project: The path ideal of a tree and its properties.
(Update: Jane and I turned her project into a this journal article which appeared in Comm. Alg.)
 Maryam Nowroozi, MSc (completed May 2021) cosupervsied with Dr. M. Harada
 NSERC USRA Students
 Olivia Wdowiak, Summer 2003
Project: Regularity of fat points.  John Kimball, (cosupervised with Greg Lee) Summer 2005
Project: Graded Betti numbers of edge ideals.  Natalie Campbell, (cosupervised with Kevin N. Vander Meulen)
Summer 2009
Project: Nilpotent Patterns over Finite Fields.  Hannah Bergsma, (cosupervised with Kevin N. Vander Meulen)
Summer 2010
Project: Construction of Nilpotent Patterns.  Ben Babcock, Summer 2010
Project: Revisiting the spreading and covering numbers.  Hannah Bergsma, (cosupervised with Kevin N. Vander Meulen)
Summer 2011
Project: Inertially artbitary patterns.  Ben Babcock, Summer 2011
Project: Combinatorial Commutative Algebra.  Catriona Watt, (cosupervised with Kevin N. Vander Meulen) Summer
2012
Project: Graded Betti numbers of some edge ideals.  Jonathan Earl, (cosupervised with Kevin N. Vander Meulen) Summer
2014
Project: Independence complexes of circulant graphs.  Jonathan Baker, (cosupervised with Kevin N. Vander Meulen) Summer
2015
Project: TBD  Jonathan Earl, (cosupervised with Kevin N. Vander Meulen) Summer
2015
Project: TBD
 Olivia Wdowiak, Summer 2003
 Honours Projects
 Jessica Reinikka, Sept. 2011April 2012
Project: Mutually orthogonal Latin Squares and their applications.  Jesse Krauel, (cosupervised with Dr.
J. Biermann) Sept 2012April 2013
Project: Some methods of primality testing. 
Mitchell Gallinger, (cosupervised with Dr.
J. Biermann) Sept 2012April 2013
Project: Groebner Bases: ideal membership and graph colouring. 
Lindsey Daniels, (cosupevised with
Dr. G. Lee) Sept 2013April 2014
Project: Group Theory and the Rubik's Cube.
 Jessica Reinikka, Sept. 2011April 2012