Links
My GitHub repository: https://github.com/LorenzoVenturello
Together with Alexander Lazar and Benjamin Schröter I organized the weekly combinatorics seminar at KTH.
Together with Alessio D'Alì (Universität Osnabrück) and Mariel Supina (UC Berkeley) I organized REACT - Online Workshop for Graduate Students. Check it out!
In an article with Hailun Zheng, we construct triangulations of the real projective d-dimensional space on a number of vertices which is (for d>5) the smallest currently known. Here you can find an implementation of the construction described in the paper, together with a list of facets of triangulations for d<8.
Bits of my code have been added to the packages SimplicialComplexes and GenericInitialIdeal in the latest version of Macaulay2. In particular it is now possible to compute a multigraded version of the generic initial ideal, in which the action on the polynomial ring is described by a block matrix. Comments or bug reports are more than welcome.
My project on balanced triangulations on few vertices was accepted for a computer demonstration at FPSAC 2019, which has been presented by Alexander Wang. Here are very few slides sketching the problem and the results.
Libraries of simplicial complexes:
The Manifold Page (by Frank H. Lutz): http://page.math.tu-berlin.de/~lutz/stellar/
Simplicial Complex library (by Masahiro Hachimori): http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/index_eng.html
Triangulations of Normal 3-Pseudomanifolds on 9 Vertices (by Tair Akhmejanov): http://pi.math.cornell.edu/~takhmejanov/pseudoManifolds.html
Pseudomanifold Triangulations on 10 Vertices (from the Cornell University's website): https://twiki.math.cornell.edu/do/view/EBS/Pseudomanifold10Vertex
Balanced triangulations on few vertices: https://github.com/LorenzoVenturello/Cross-flips_and_balanced_library/blob/master/Library_of_balanced_simplicial_complexes
Balanced normal 3-pseudomanifolds on few vertices: https://github.com/LorenzoVenturello/Cross-flips_and_balanced_library/blob/master/Pseudomanifolds