BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrey Kupavskii (CNRS\, G-SCOP) DTSTART:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260404T094753Z UID:DCGParis/1 DESCRIPTION:Title: The extremal number of surfaces\nby Andrey Kupavskii (CNRS\, G -SCOP) as part of Discrete and Computational Geometry Seminar in Paris\n\n \nAbstract\nIn 1973\, Brown\, Erdős and Sós proved that if H is a 3-unif orm hypergraph on n vertices which contains no triangulation of the sphere \, then H has at most $O(n^{5/2})$ edges\, and this bound is the best poss ible up to a constant factor. Resolving a conjecture of Linial\, also reit erated by Keevash\, Long\, Narayanan\, and Scott\, we show that the same r esult holds for triangulations of the torus. Furthermore\, we extend our r esult to every closed orientable surface S. Joint work with Alexandr Polya nskii\, István Tomon and Dmitriy Zakharov.\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Raman Sanyal (Goethe University Frankfurt) DTSTART:20210128T130000Z DTEND:20210128T140000Z DTSTAMP:20260404T094753Z UID:DCGParis/2 DESCRIPTION:Title: Inscribable polytopes\, routed trajectories\, and reflection arran gements\nby Raman Sanyal (Goethe University Frankfurt) as part of Disc rete and Computational Geometry Seminar in Paris\n\n\nAbstract\nSteiner po sed the question if any 3-dimensional polytope had a realization\nwith ver tices on a sphere. Steinitz constructed the first counter examples and\nRi vin gave a complete answer to Steiner's question. In dimensions 4\nand up\ , the Universality Theorem indicates that certifying inscribability is\ndi fficult if not hopeless. In this talk\, I will address the following\nrefi ned question: Given a polytope P\, is there a continuous deformation of P\ nto an inscribed polytope that keeps corresponding faces parallel? In othe r\nwords\, is there an inscribed polytope P’ that is normally equivalent (or strongly\nisomorphic) to P?\n\nThis question has strong ties to defor mations of Delaunay subdivisions and\nideal hyperbolic polyhedra and its s tudy reveals a rich interplay of algebra\,\ngeometry\, and combinatorics. In the first part of the talk\, I will discuss\nrelations to routed trajec tories of particles and reflection groupoids and\nshow that that the quest ion is polynomial time decidable.\n\nIn the second part of the talk\, we w ill focus on class of zonotopes\, that is\,\npolytopes representing hyperp lane arrangements. It turns out that inscribable\nzonotopes are rare and i ntimately related to reflection groups and\nGrünbaum's quest for simplici al arrangements. This is based on joint work\nwith Sebastian Manecke.\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Dauvergne (Princeton University) DTSTART:20210225T130000Z DTEND:20210225T140000Z DTSTAMP:20260404T094753Z UID:DCGParis/3 DESCRIPTION:Title: The Archimedean limit of random sorting networks\nby Duncan Da uvergne (Princeton University) as part of Discrete and Computational Geome try Seminar in Paris\n\n\nAbstract\nConsider a list of n particles labelle d in increasing order. A sorting\nnetwork is a way of sorting this list in to decreasing order by swapping\nadjacent particles\, using as few swaps a s possible. Simulations of\nlarge-n uniform random sorting networks reveal a surprising and\nbeautiful global structure involving sinusoidal particl e trajectories\, a\nsemicircle law\, and a theorem of Archimedes. Based on these simulations\,\nAngel\, Holroyd\, Romik\, and Virag made a series of conjectures about the\nlimiting behaviour of sorting networks. In this ta lk\, I will discuss how\nto use the local structure and combinatorics of r andom sorting networks\nto prove these conjectures.\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Emo Welzl (ETH Zurich) DTSTART:20210325T130000Z DTEND:20210325T140000Z DTSTAMP:20260404T094753Z UID:DCGParis/4 DESCRIPTION:Title: Triangulation Flip Graphs of Planar Point Sets\nby Emo Welzl ( ETH Zurich) as part of Discrete and Computational Geometry Seminar in Pari s\n\n\nAbstract\nFull triangulations of a finite planar point set P are ma ximal straight-line embedded plane graphs on P. In partial triangulations some non-extreme points can be skipped. Flips are minimal changes in trian gulations. They define an adjacency relation on the set of triangulations of P\, giving rise to the flip graph of all (full or partial) triangulatio ns of P. In the seventies Lawson showed that flip graphs are always connec ted. Our goal is to investigate the structure of flip graphs\, with emphas is on their vertex-connectivity. We obtain similar bounds as they follow f or regular triangulations from secondary polytopes via Balinski’s Theore m. Joint work with Uli Wagner\, IST Austria\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Avvakumov (University of Copenhagen) DTSTART:20210422T120000Z DTEND:20210422T130000Z DTSTAMP:20260404T094753Z UID:DCGParis/5 DESCRIPTION:Title: A subexponential size triangulation of ${\\mathbb R}P^n$\nby S ergey Avvakumov (University of Copenhagen) as part of Discrete and Computa tional Geometry Seminar in Paris\n\n\nAbstract\nA practical way to encode a manifold is to triangulate it.\nAmong all possible triangulations it mak es sense to look for the minimal one\, which for the purpose of this talk means using the least number of vertices.\n\nConsider a family of manifold s such as $S^n$\, ${\\mathbb R}P^n$\, $SO_n$\, etc. A natural question is how the size of the minimal triangulation depends on $n$?\nSurprisingly\, except for the trivial case of $S^n$\, our best lower and upper bounds are very far apart.\n\nFor ${\\mathbb R}P^n$ the current best lower and upper bounds are around $n^2$ and $\\phi^n$\, respectively\, where $\\phi$ is t he golden ratio.\nIn this talk I will present the first triangulation of $ {\\mathbb R}P^n$ with a subexponential\, approximately $\\sqrt{n}^\\sqrt{n }$\, number of vertices.\nI will also state several open problems related to the topic.\n\nThis is a joint work with Karim Adiprasito and Roman Kara sev.\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Zuzana Patáková (Charles University) DTSTART:20210520T120000Z DTEND:20210520T130000Z DTSTAMP:20260404T094753Z UID:DCGParis/6 DESCRIPTION:Title: On Radon and fractional Helly theorems\nby Zuzana Patáková ( Charles University) as part of Discrete and Computational Geometry Seminar in Paris\n\n\nAbstract\nRadon theorem plays a basic role in many results of combinatorial convexity. It says that any set of d+2 points in R^d can be split into two parts so that their convex hulls intersect. It implies H elly theorem and as shown recently also its more robust version\, so-calle d fractional Helly theorem. By standard techniques this consequently yield s an existence of weak epsilon nets and a (p\,q)-theorem.\n\nWe will show that we can obtain these results even without assuming convexity\, replaci ng it with very weak topological conditions. More precisely\, given an int ersection-closed family F of subsets of R^d\, we will measure the complexi ty of F by the supremum of the first d/2 Betti numbers over all elements o f F. We show that bounded complexity of F guarantees versions of all the r esults mentioned above.\n\nBased on joint work with Xavier Goaoc and Andre as Holmsen.\n LOCATION:https://stable.researchseminars.org/talk/DCGParis/6/ END:VEVENT END:VCALENDAR