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:20260422T212752Z 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\nAbstr act\nIn 1973\, Brown\, Erdős and Sós proved that if H is a 3-uniform hyp ergraph 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 possible up to a constant factor. Resolving a conjecture of Linial\, also reiterated by Keevash\, Long\, Narayanan\, and Scott\, we show that the same result h olds for triangulations of the torus. Furthermore\, we extend our result t o every closed orientable surface S. Joint work with Alexandr Polyanskii\, István Tomon and Dmitriy Zakharov.\n LOCATION:https://researchseminars.org/talk/DCGParis/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Raman Sanyal (Goethe University Frankfurt) DTSTART:20210128T130000Z DTEND:20210128T140000Z DTSTAMP:20260422T212752Z UID:DCGParis/2 DESCRIPTION:Title: Inscribable polytopes\, routed trajectories\, and reflection arrangements \nby Raman Sanyal (Goethe University Frankfurt) as part of Discrete an d Computational Geometry Seminar in Paris\n\n\nAbstract\nSteiner posed the question if any 3-dimensional polytope had a realization\nwith vertices o n a sphere. Steinitz constructed the first counter examples and\nRivin gav e a complete answer to Steiner's question. In dimensions 4\nand up\, the U niversality Theorem indicates that certifying inscribability is\ndifficult if not hopeless. In this talk\, I will address the following\nrefined que stion: Given a polytope P\, is there a continuous deformation of P\nto an inscribed polytope that keeps corresponding faces parallel? In other\nword s\, is there an inscribed polytope P’ that is normally equivalent (or st rongly\nisomorphic) to P?\n\nThis question has strong ties to deformations of Delaunay subdivisions and\nideal hyperbolic polyhedra and its study re veals a rich interplay of algebra\,\ngeometry\, and combinatorics. In the first part of the talk\, I will discuss\nrelations to routed trajectories of particles and reflection groupoids and\nshow that that the question is polynomial time decidable.\n\nIn the second part of the talk\, we will foc us on class of zonotopes\, that is\,\npolytopes representing hyperplane ar rangements. It turns out that inscribable\nzonotopes are rare and intimate ly related to reflection groups and\nGrünbaum's quest for simplicial arra ngements. This is based on joint work\nwith Sebastian Manecke.\n LOCATION:https://researchseminars.org/talk/DCGParis/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Dauvergne (Princeton University) DTSTART:20210225T130000Z DTEND:20210225T140000Z DTSTAMP:20260422T212752Z UID:DCGParis/3 DESCRIPTION:Title: The Archimedean limit of random sorting networks\nby Duncan Dauvergne (Princeton University) as part of Discrete and Computational Geometry Sem inar in Paris\n\n\nAbstract\nConsider a list of n particles labelled in in creasing order. A sorting\nnetwork is a way of sorting this list into decr easing order by swapping\nadjacent particles\, using as few swaps as possi ble. Simulations of\nlarge-n uniform random sorting networks reveal a surp rising and\nbeautiful global structure involving sinusoidal particle traje ctories\, a\nsemicircle law\, and a theorem of Archimedes. Based on these simulations\,\nAngel\, Holroyd\, Romik\, and Virag made a series of conjec tures about the\nlimiting behaviour of sorting networks. In this talk\, I will discuss how\nto use the local structure and combinatorics of random s orting networks\nto prove these conjectures.\n LOCATION:https://researchseminars.org/talk/DCGParis/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Emo Welzl (ETH Zurich) DTSTART:20210325T130000Z DTEND:20210325T140000Z DTSTAMP:20260422T212752Z UID:DCGParis/4 DESCRIPTION:Title: Triangulation Flip Graphs of Planar Point Sets\nby Emo Welzl (ETH Zur ich) as part of Discrete and Computational Geometry Seminar in Paris\n\n\n Abstract\nFull triangulations of a finite planar point set P are maximal s traight-line embedded plane graphs on P. In partial triangulations some no n-extreme points can be skipped. Flips are minimal changes in triangulatio ns. They define an adjacency relation on the set of triangulations of P\, giving rise to the flip graph of all (full or partial) triangulations of P . In the seventies Lawson showed that flip graphs are always connected. Ou r goal is to investigate the structure of flip graphs\, with emphasis on t heir vertex-connectivity. We obtain similar bounds as they follow for regu lar triangulations from secondary polytopes via Balinski’s Theorem. Join t work with Uli Wagner\, IST Austria\n LOCATION:https://researchseminars.org/talk/DCGParis/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Avvakumov (University of Copenhagen) DTSTART:20210422T120000Z DTEND:20210422T130000Z DTSTAMP:20260422T212752Z UID:DCGParis/5 DESCRIPTION:Title: A subexponential size triangulation of ${\\mathbb R}P^n$\nby Sergey A vvakumov (University of Copenhagen) as part of Discrete and Computational Geometry Seminar in Paris\n\n\nAbstract\nA practical way to encode a manif old is to triangulate it.\nAmong all possible triangulations it makes sens e to look for the minimal one\, which for the purpose of this talk means u sing the least number of vertices.\n\nConsider a family of manifolds 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 f ar 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 the gold en ratio.\nIn this talk I will present the first triangulation of ${\\math bb R}P^n$ with a subexponential\, approximately $\\sqrt{n}^\\sqrt{n}$\, nu mber of vertices.\nI will also state several open problems related to the topic.\n\nThis is a joint work with Karim Adiprasito and Roman Karasev.\n LOCATION:https://researchseminars.org/talk/DCGParis/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Zuzana Patáková (Charles University) DTSTART:20210520T120000Z DTEND:20210520T130000Z DTSTAMP:20260422T212752Z 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 Par is\n\n\nAbstract\nRadon theorem plays a basic role in many results of comb inatorial convexity. It says that any set of d+2 points in R^d can be spli t into two parts so that their convex hulls intersect. It implies Helly th eorem and as shown recently also its more robust version\, so-called fract ional Helly theorem. By standard techniques this consequently yields an ex istence of weak epsilon nets and a (p\,q)-theorem.\n\nWe will show that we can obtain these results even without assuming convexity\, replacing it w ith very weak topological conditions. More precisely\, given an intersecti on-closed family F of subsets of R^d\, we will measure the complexity of F by the supremum of the first d/2 Betti numbers over all elements of F. We show that bounded complexity of F guarantees versions of all the results mentioned above.\n\nBased on joint work with Xavier Goaoc and Andreas Holm sen.\n LOCATION:https://researchseminars.org/talk/DCGParis/6/ END:VEVENT END:VCALENDAR