diff --git a/_data/participants.yml b/_data/participants.yml index 922712b..cc24842 100644 --- a/_data/participants.yml +++ b/_data/participants.yml @@ -7,6 +7,11 @@ - name: Jan De Beule affiliation: Ghent University + links: + "slides": ../talks/jdebeule_gapdays_fall2015.pdf + "demo 1": ../talks/demo1.g + "demo 2": ../talks/demo2.g + "demo 3": ../talks/demo3.g - name: Martin Bies affiliation: Institute for Theoretical Physics, Heidelberg diff --git a/talks/demo1.g b/talks/demo1.g new file mode 100644 index 0000000..e85a30b --- /dev/null +++ b/talks/demo1.g @@ -0,0 +1,50 @@ +q := 25; +pg := PG(2,q); +pts := Points(pg); +List(pts); +p := Random(pts); +lines := List(Lines(pg)); +l := Random(lines); +p * l; +Lines(p); +List(last); +Points(l); +List(last); + +conic := ParabolicQuadric(2,q); +EquationForPolarSpace(conic); +pts := Points(conic); +pts := List(pts); + +group := CollineationGroup(pg); +g := Random(group); +p^g; +OnProjSubspaces(l,g); + +Stabilizer(group,pts[1],\^); +time; +FiningStabiliser(group,pts[1]); +time; + +stab := FiningSetwiseStabiliser(group,pts); +CollineationGroup(conic); + +mat := IdentityMat(3,GF(q)); +form := QuadraticFormByMatrix(mat,GF(q)); +conic2 := PolarSpace(form); + +EquationForPolarSpace(conic2); +pts := List(Points(conic2)); +p := Random(pts); + +stab := FiningSetwiseStabiliser(group,pts); +CollineationGroup(conic2); + +ppts := List(Points(pg));; +orbs := FiningOrbits(stab,ppts); +o1 := orbs[1]; +p := Random(o1); +List(Lines(p),x->Number(pts,y->y in x)); +Collected(last); + + diff --git a/talks/demo2.g b/talks/demo2.g new file mode 100644 index 0000000..6415a22 --- /dev/null +++ b/talks/demo2.g @@ -0,0 +1,20 @@ +q := 2; +ps := HermitianPolarSpace(4,q^2); +EquationForPolarSpace(ps); +CategoriesOfObject(ps); +group := CollineationGroup(ps); +graph := IncidenceGraph(ps);; +Diameter(graph); +Girth(graph); + +adj := function(x,y) +return ProjectiveDimension(Meet(x,y))=-1; +end; + +lines := AsList(Lines(ps));; + +graph := Graph(group,lines,\^,adj,true);; + +size := q^5+1; +cliques := CompleteSubgraphs(graph,size); + diff --git a/talks/demo3.g b/talks/demo3.g new file mode 100644 index 0000000..be9ec24 --- /dev/null +++ b/talks/demo3.g @@ -0,0 +1,14 @@ +LoadPackage( "AtlasRep" ); +titsgroup:=AtlasGroup("2F4(2)'"); +g1:=AtlasSubgroup(titsgroup,3); +g2:=AtlasSubgroup(titsgroup,5); +conj:=ConjugacyClassSubgroups(titsgroup,g1);; + # Now look for the conjugate of g1 with maximal intersection +g1:=First(conj, sg -> Size(Intersection(sg,g2))=2048); +cg:=CosetGeometry(titsgroup,[g1,g2]);; +Rank2Parameters(cg); +[ [ 8, 8, 8 ], [ 2, 1755 ], [ 4, 2925 ] ] +pts := Set(ElementsOfIncidenceStructure(cg,1));; +lines := Set(ElementsOfIncidenceStructure(cg,2));; +gp := GeneralisedPolygonByElements(pts,lines,\*,titsgroup,OnCosetGeometryElement); + diff --git a/talks/jdebeule_gapdays_fall2015.pdf b/talks/jdebeule_gapdays_fall2015.pdf new file mode 100644 index 0000000..69679ba Binary files /dev/null and b/talks/jdebeule_gapdays_fall2015.pdf differ