BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Manfred Scheucher (TU Berlin) DTSTART:20210121T150000Z DTEND:20210121T170000Z DTSTAMP:20260422T033703Z UID:CJCS/1 DESCRIPTION:Title: Usi ng SAT Solvers in Combinatorics and Geometry\nby Manfred Scheucher (TU Berlin) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\nAbstract : TBA\n LOCATION:https://researchseminars.org/talk/CJCS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Man-Wai Cheung (Harvard University) DTSTART:20210128T150000Z DTEND:20210128T170000Z DTSTAMP:20260422T033703Z UID:CJCS/2 DESCRIPTION:Title: Com pactifications of cluster varieties and convexity\nby Man-Wai Cheung ( Harvard University) as part of Copenhagen-Jerusalem Combinatorics Seminar\ n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CJCS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Benedetti (U Miami) DTSTART:20210204T150000Z DTEND:20210204T170000Z DTSTAMP:20260422T033703Z UID:CJCS/3 DESCRIPTION:Title: A d -dimensional version of interval graphs\, of Hamiltonian paths\, and of b inomial edge ideals\nby Bruno Benedetti (U Miami) as part of Copenhage n-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe study the d-dimensiona l generalization of three mutually-related\nnotions in graph theory: (unit )-interval graphs\, Hamiltonian cycles\, and\nbinomial edge ideals.\n\nThi s is joint work with Matteo Varbaro and Lisa Seccia (arXiv:2101.09243).\n LOCATION:https://researchseminars.org/talk/CJCS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Manecke (University of Frankfurt) DTSTART:20210211T150000Z DTEND:20210211T160000Z DTSTAMP:20260422T033703Z UID:CJCS/4 DESCRIPTION:Title: Ins cribable fans\, zonotopes\, and reflection arrangements\nby Sebastian Manecke (University of Frankfurt) as part of Copenhagen-Jerusalem Combinat orics Seminar\n\n\nAbstract\nSteiner posed the question if any 3-dimension al polytope had a\nrealization with vertices on a sphere. Steinitz constru cted the first\ncounter example and Rivin gave a complete resolution. In\n dimensions 4 and up\, universality theorems by Mnev/Richter-Gebert\nrender the question for inscribable combinatorial types hopeless.\n\nHowever\, f or a given complete fan N\, we can decide in polynomial time\nif there is an inscribed polytope with normal fan N. Linear\nhyperplane arrangements c an be realized as normal fans via zonotopes.\nIt turns out that inscribed zonotopes are rare and in this talk I\nwill focus on the question of class ifying the corresponding\narrangements. This relates to localizatons and r estrictions of\nreflection arrangements and Grünbaum's quest for the clas sification of \nsimplicial arrangements. The talk is based on joint work w ith Raman\nSanyal.\n LOCATION:https://researchseminars.org/talk/CJCS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Tancer (Charles University Prague) DTSTART:20210218T150000Z DTEND:20210218T170000Z DTSTAMP:20260422T033703Z UID:CJCS/5 DESCRIPTION:Title: The unbearable hardness of unknotting\nby Martin Tancer (Charles Universi ty Prague) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst ract\nDuring the talk\, I will sketch a proof that deciding if a diagram o f the unknot can be untangled using at most k Riedemeister moves (where k is part of the input) is NP-hard. (This is not the same as the unknot reco gnition but it reveals some difficulties.) Similar ideas can be also used for proving that several other similar invariants are NP-hard to recognize on links.\n\nJoint work with A. de Mesmay\, Y. Rieck and E. Sedgwick.\n LOCATION:https://researchseminars.org/talk/CJCS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasso Petrotou (University of Ioannina) DTSTART:20210225T150000Z DTEND:20210225T170000Z DTSTAMP:20260422T033703Z UID:CJCS/6 DESCRIPTION:Title: Tom & Jerry triples\nby Vasso Petrotou (University of Ioannina) as part o f Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nUnprojection i s a theory due to Reid which constructs and analyses more complicated ring s from simpler ones. The talk will be about a new format of unprojection w hich we call Tom & Jerry triples. As an application we will construct two families of codimension 6 Fano 3-folds in weighted projective space.\n\nWe will also give a brief introduction to Macaulay2.\n LOCATION:https://researchseminars.org/talk/CJCS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Parada (TU Eindhoven) DTSTART:20210311T150000Z DTEND:20210311T170000Z DTSTAMP:20260422T033703Z UID:CJCS/7 DESCRIPTION:Title: Ins erting edges into simple drawings\nby Irene Parada (TU Eindhoven) as p art of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nSimple dr awings of graphs are those in which each pair of edges share at most one p oint\, either a common endpoint or a proper crossing. Given a simple drawi ng D of a graph G\, in this talk we consider the problem of inserting a gi ven set of missing edges (edges of the complement of G) into D such that t he result is again a simple drawing. We show that it is NP-complete to dec ide whether one edge can be inserted into a simple drawing. On the positiv e side\, we present a Fixed-Parameter Tractable (FPT) algorithm for this p roblem parameterized by the number of crossings that the edge to be insert ed can have. This algorithm is tight under the Exponential Time Hypothesis . We also obtain an FPT algorithm for inserting a bounded number of edges with a bounded number of crossings. In these FPT algorithms\, after workin g in the drawing\, the problem boils down to finding an algorithm for a la beled abstract graph. To obtain these FPT algorithms we use different tool s including the sunflower lemma\, representative families for matroids\, a nd Courcelle's theorem. These techniques\, useful in many parameterized al gorithms\, will be briefly introduced during the talk.\n LOCATION:https://researchseminars.org/talk/CJCS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Pilar Cano (Université Libre de Bruxelles) DTSTART:20210304T150000Z DTEND:20210304T160000Z DTSTAMP:20260422T033703Z UID:CJCS/8 DESCRIPTION:Title: Fli ps in higher order Delaunay triangulations\nby Pilar Cano (Université Libre de Bruxelles) as part of Copenhagen-Jerusalem Combinatorics Seminar \n\n\nAbstract\nWe study the flip graph of higher order Delaunay triangula tions. A triangulation of a set S of n points in the plane is order-k Dela unay if for every triangle its circumcircle encloses at most k points of S . The flip graph of S has one vertex for each possible triangulation of S\ , and an edge connecting two vertices when the two corresponding triangula tions can be transformed into each other by a flip (i.e.\, exchanging the diagonal of a convex quadrilateral by the other one). The flip graph is an essential structure in the study of triangulations\, but until now it had been barely studied for order-k Delaunay triangulations. In this work we show that\, even though the order-k flip graph might be disconnected for k ≥ 3\, any order-k triangulation can be transformed into some other orde r-k triangulation by at most k − 1 flips\, such that the intermediate tr iangulations are of order 2k − 2\, in the following settings: (1) for an y k ≥ 0 when S is in convex position\, and (2) for any k ≤ 5 and any p oint set S. Our results imply that the flip distance between two order-k t riangulations is O(kn)\, as well as an efficient enumeration algorithm.\n LOCATION:https://researchseminars.org/talk/CJCS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Kühne (Max Planck Institute of Mathematics in the Sciences) DTSTART:20210318T151500Z DTEND:20210318T170000Z DTSTAMP:20260422T033703Z UID:CJCS/9 DESCRIPTION:Title: Inv estigating Terao's freeness conjecture with computer algebra\nby Lukas Kühne (Max Planck Institute of Mathematics in the Sciences) as part of C openhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMotivated by sing ularity theory\, Hiroaki Terao introduced a module of logarithmic derivati ons associated with a hyperplane arrangement. This talk is concerned with Terao’s freeness conjecture which asserts that the freeness of this deri vation module is determined by the underlying combinatorics of the arrange ment.\n\nTo investigate this conjecture\, we have enumerated all matroids of rank 3 with up to 14 hyperplanes whose characteristic polynomial splits over the integers and saved it in a public database. Using the GAP packag e ZariskiFrames we have computed the moduli space and the free locus of th e derivation module of each of these matroids as a quasi-affine set. As th e main result\, this yields a computational proof of Terao’s freeness co njecture for rank 3 arrangements with up to 14 hyperplanes in arbitrary ch aracteristic.\n\nIn this talk\, I will explain the background of this conj ecture without assuming prior knowledge and demonstrate the database and h ighlights of the computations.\n\nThis talk is based on joint work with Mo hamed Barakat\, Reimer Behrends\, Christopher Jefferson\, and Martin Lerne r.\n LOCATION:https://researchseminars.org/talk/CJCS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Soberon (CUNY) DTSTART:20210325T150000Z DTEND:20210325T170000Z DTSTAMP:20260422T033703Z UID:CJCS/10 DESCRIPTION:Title: Tv erberg's theorem beyond prime powers\nby Pablo Soberon (CUNY) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nTverberg-type theory aims to establish sufficient conditions for a simplicial complex $ \\Sigma$ such that every continuous map $f:\\Sigma \\to \\mathbb{R}^d$ map s $q$ points from pairwise disjoint faces to the same point in $\\mathbb{R }^d$. Such results are plentiful for $q$ a prime power. However\, for $q $ with at least two distinct prime divisors\, results that guarantee the e xistence of $q$-fold points of coincidence are non-existent— aside from immediate corollaries of the prime power case. Here we present a general method that yields such results beyond the case of prime powers. Joint wo rk with Florian Frick.\n LOCATION:https://researchseminars.org/talk/CJCS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Torsten Mütze (University of Warwick) DTSTART:20210506T140000Z DTEND:20210506T160000Z DTSTAMP:20260422T033703Z UID:CJCS/11 DESCRIPTION:Title: Co mbinatorial generation via permutation languages\nby Torsten Mütze (U niversity of Warwick) as part of Copenhagen-Jerusalem Combinatorics Semina r\n\n\nAbstract\nIn this talk I present a general and versatile algorithmi c framework for exhaustively generating a large variety of different combi natorial objects\, based on encoding them as permutations\, which provides a unified view on many known results and allows us to prove many new ones . This talk gives an overview over three main applications of our framewor k: (1) the generation of pattern-avoiding permutations\; (2) the generatio n of various classes of rectangulations\; (3) the generation of lattice co ngruences of the weak order on the symmetric group and of graph associahed ra.\n\nThis talk is based on joint work with Liz Hartung\, Hung P. Hoang\, and Aaron Williams (SODA 2020)\, and with Arturo Merino (SoCG 2021) and J ean Cardinal.\n LOCATION:https://researchseminars.org/talk/CJCS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Peluse (Princeton) DTSTART:20210408T140000Z DTEND:20210408T160000Z DTSTAMP:20260422T033703Z UID:CJCS/12 DESCRIPTION:Title: Mo dular zeros in the character table of the symmetric group\nby Sarah Pe luse (Princeton) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n \nAbstract\nIn 2017\, Miller conjectured\, based on computational evidence \, that for any fixed prime $p$ the density of entries in the character ta ble of $S_n$ that are divisible by $p$ goes to $1$ as $n$ goes to infinity . I’ll describe a proof of this conjecture\, which is joint work with K. Soundararajan. I will also discuss the (still open) problem of determinin g the asymptotic density of zeros in the character table of $S_n$\, where it is not even clear from computational data what one should expect.\n LOCATION:https://researchseminars.org/talk/CJCS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Felsner (TU Berlin) DTSTART:20210422T140000Z DTEND:20210422T160000Z DTSTAMP:20260422T033703Z UID:CJCS/13 DESCRIPTION:Title: Co mbinatorics of Pseudocircle Arrangements\nby Stefan Felsner (TU Berlin ) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn this talk we survey results for pseudocircle arrangements. Along the way w e present several open problems. Among others we plan to touch the followi ng topics:\n * The taxonomy of classes of pseudocircle arrangements.\n * T he facial structure with emphasis on triangles and digons.\n * Circulariza bility.\n * Coloring problems for pseudocircle arrangements.\nThe talk inc ludes work of Grünbaum\, Snoeyink\, Pinchasi\, Scheucher\, and others.\n LOCATION:https://researchseminars.org/talk/CJCS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Eberhard (University of Cambridge) DTSTART:20210513T140000Z DTEND:20210513T160000Z DTSTAMP:20260422T033703Z UID:CJCS/14 DESCRIPTION:by Sean Eberhard (University of Cambridge) as part of Copenhag en-Jerusalem Combinatorics Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CJCS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Yufei Zhao (MIT) DTSTART:20210429T140000Z DTEND:20210429T160000Z DTSTAMP:20260422T033703Z UID:CJCS/15 DESCRIPTION:Title: Th e geometry of transitive sets\, with applications to eigenbasis of Cayley graphs\nby Yufei Zhao (MIT) as part of Copenhagen-Jerusalem Combinator ics Seminar\n\n\nAbstract\nI will discuss some counterintuitive facts and conjectures about the width of a finite transitive subset of a high dimens ional sphere (here "transitive" means transitive under the orthogonal grou p). We were motivated by the question of whether Cayley graphs always have a bounded eigenbasis. I will explain this connection\, and mention severa l open problems.\n\nBased on joint work with Ashwin Sah and Mehtaab Sawhne y: https://arxiv.org/abs/2005.04502 and https://arxiv.org/abs/2101.11207\n LOCATION:https://researchseminars.org/talk/CJCS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Lackenby (University of Oxford) DTSTART:20210520T140000Z DTEND:20210520T160000Z DTSTAMP:20260422T033703Z UID:CJCS/16 DESCRIPTION:Title: Un knot recognition in quasi-polynomial time\nby Marc Lackenby (Universit y of Oxford) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb stract\nI will outline a new algorithm for unknot recognition that runs in quasi-polynomial time. The input is a diagram of a knot with n crossings\ , and the running time is 2^{O((log n)^3)}. The algorithm uses a wide vari ety of tools from 3-manifold theory\, including normal surfaces\, hierarch ies and Heegaard splittings. In my talk\, I will explain this background t heory\, as well as explain how it fits into the algorithm.\n LOCATION:https://researchseminars.org/talk/CJCS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Batyrev (Universität Tübingen) DTSTART:20210603T141500Z DTEND:20210603T160000Z DTSTAMP:20260422T033703Z UID:CJCS/17 DESCRIPTION:Title: Co mbinatorics of lattice polytopes and MMP\nby Victor Batyrev (Universit ät Tübingen) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\n Abstract\nThe Minimal Model Program (MMP) was born in 80-ties from attempt s to extend classical results on the birational classification of algebra ic surfaces to algebraic varieties of dimension >2. The problem of birat ional classification of higher dimensional algebraic varieties is so dif ficult that its complete solution is not even expected. However\, a signi ficant progress in understanding this \nproblem can be achieved if one re stricts attention to some special and simultaneously sufficiently rich cl ass of algebraic varieties under consideration.\n\nThe talk suggests to lo ok at the class of algebraic varieties that are birational to non-degenera te hypersurfaces Z in an algebraic torus T. It turns out that this class is sufficiently rich to illustrate \nmany important ideas of MMP using c ombinatorial properties of the Newton polytope P of the defining equation of Z. The purpose of the talk is to explain the interplay between the com binatorics of lattice polytopes and MMP which benefits from studing its “combinatorial shadows”.\n LOCATION:https://researchseminars.org/talk/CJCS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Oswin Aichholzer (TU Graz) DTSTART:20210610T141500Z DTEND:20210610T160000Z DTSTAMP:20260422T033703Z UID:CJCS/18 DESCRIPTION:Title: Or der Types\, Rotation Systems\, and Crossing Numbers of $K_n$\nby Oswin Aichholzer (TU Graz) as part of Copenhagen-Jerusalem Combinatorics Semina r\n\n\nAbstract\nIn the area of crossing numbers we ask for minimizing th e number of edge intersections in a drawing of a graph.\nThere is a rich v ariety of crossing number problems: Which graphs do we consider\, what exa ctly is a drawing of a graph\, and how are intersections counted? \nIn thi s talk we will concentrate on the crossing number of complete graphs embed ded in the plane as either geometric\nor simple drawing. We will have a cl oser look at two useful combinatorial concepts for these representations: order types for the\ngeometric case\, and rotation systes for the topologi cal case.\n LOCATION:https://researchseminars.org/talk/CJCS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Miloš Stojakovic (University of Novi Sad) DTSTART:20210624T141500Z DTEND:20210624T160000Z DTSTAMP:20260422T033703Z UID:CJCS/19 DESCRIPTION:Title: De aling with bichromatic non-crossing matchings\nby Miloš Stojakovic (U niversity of Novi Sad) as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\n\nAbstract\nGiven a set of n red and n blue points in the plane\, we are interested in matching red points with blue points by straight line s egments so that the segments do not cross. We develop a range of tools for dealing with the non-crossing matchings of points in convex position. It turns out that the points naturally partition into groups that we refer to as orbits\, with a number of properties that prove useful for studying an d efficiently processing the non-crossing matchings.\n\n\nBottleneck match ing is such a matching that minimizes the length of the longest segment. I llustrating the use of the developed tools\, we show how to solve the prob lem of finding bottleneck matchings of points in convex position faster th an before.\n\nJoint work with Marko Savić.\n LOCATION:https://researchseminars.org/talk/CJCS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Chaya Keller (Ariel University) DTSTART:20210527T140000Z DTEND:20210527T160000Z DTSTAMP:20260422T033703Z UID:CJCS/20 DESCRIPTION:Title: On multicolor Ramsey numbers and subset-coloring of hypergraphs\nby Chay a Keller (Ariel University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe multicolor hypergraph Ramsey number R_k(s\,r) i s the minimal n\, such that in any k-coloring of all r-element subsets of [n]\, there is a subset of size s\, all whose r-subsets are monochromatic. We present a new "stepping-up lemma" for R_k(s\,r): If R_k(s\,r)>n\, the n R_{k+3}(s+1\,r+1)>2^n. Using the lemma\, we improve some known lower bou nds on multicolor hypergraph Ramsey numbers.\nFurthermore\, given a hyperg raph H=(V\,E)\, we consider the Ramsey-like problem of coloring all r-subs ets of V such that no hyperedge of size >r is monochromatic. We provide up per and lower bounds on the number of colors necessary in terms of the chr omatic number \\chi(H). In particular\, we show that this number is O(log^ {(r-1)} (r \\chi(H)) + r)\, where log^{(m)} denotes m-fold logarithm.\n\nJ oint work with Bruno Jartoux\, Shakhar Smorodinsky\, and Yelena Yuditsky.\ n LOCATION:https://researchseminars.org/talk/CJCS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Linda Kleist (TU Braunschweig) DTSTART:20210617T141500Z DTEND:20210617T160000Z DTSTAMP:20260422T033703Z UID:CJCS/21 DESCRIPTION:Title: On a Problem from Outer Space: Minimum Scan Covers\nby Linda Kleist (TU Braunschweig) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nA bstract\nIn this talk\, we investigate a natural geometric optimization pr oblem motivated by questions in the context of satellite communication and astrophysics. Given a graph embedded in Euclidean space\, the *Minimum S can Cover Problem* (MSC) asks for a schedule of minimum makespan that *sca ns* all edges. In order to scan an edge\, the incident vertices rotate at their positions such that they face each other. Thereby\, rotations take t ime proportional to the angular change. \n \nOur work reveals close conne ctions to both the graph coloring problem and the minimum cut cover proble m. In particular\, we show that the minimum scan time for instances in 1D and 2D lies in Θ(log χ(G))\, while it is not upper bounded by χ(G) in 3 D. Unless P = NP\, these insights imply that no constant-factor approximat ion exists even in 1D. Going to higher dimensions\, we discuss hardness an d approximation results for special graph classes. The talk is based on jo int work with Sándor Fekete and Dominik Krupke.\n LOCATION:https://researchseminars.org/talk/CJCS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Kwan (Stanford University) DTSTART:20210701T141500Z DTEND:20210701T160000Z DTSTAMP:20260422T033703Z UID:CJCS/22 DESCRIPTION:Title: Fr iendly bisections of random graphs\nby Matthew Kwan (Stanford Universi ty) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nR esolving a conjecture of Füredi\, we prove that almost every n-vertex gra ph admits a partition of its vertex set into two parts of equal size in wh ich almost all vertices have more neighbours on their own side than across . Our proof involves some new techniques for studying processes driven by degree information in random graphs\, which may be of general interest. Th is is joint work with Asaf Ferber\, Bhargav Narayanan\, Ashwin Sah and Meh taab Sawhney.\n LOCATION:https://researchseminars.org/talk/CJCS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Natan Rubin (Ben-Gurion University) DTSTART:20210708T141500Z DTEND:20210708T160000Z DTSTAMP:20260422T033703Z UID:CJCS/23 DESCRIPTION:Title: St ronger bounds for weak epsilon-nets in higher dimensions\nby Natan Rub in (Ben-Gurion University) as part of Copenhagen-Jerusalem Combinatorics S eminar\n\n\nAbstract\nGiven a finite point set $P$ in $R^d$\, and $\\varep silon>0$ we say that a point set $N$ in $R^d$ is a weak $\\varepsilon$-ne t if it pierces every convex set $K$ with $|K\\cap P|\\geq \\varepsilon |P |$.\n \nLet $d\\geq 3$. We show that for any finite point set in $R^d$\, a nd any $\\varepsilon>0$\, there exists a weak $\\varepsilon$-net of cardin ality $O(1/\\varepsilon^{d-1/2+\\delta})$\, where $\\delta>0$ is an arbitr ary small constant. \n\n\nThis is the first improvement of the bound of $O ^*(1/\\varepsilon^d)$ that was obtained in 1993 by Chazelle\, Edelsbrunner \, Grigni\, Guibas\, Sharir\, and Welzl for general point sets in dimensio n $d\\geq 3$.\n LOCATION:https://researchseminars.org/talk/CJCS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford University) DTSTART:20210715T141500Z DTEND:20210715T160000Z DTSTAMP:20260422T033703Z UID:CJCS/24 DESCRIPTION:Title: Ge ometric and o-minimal Littlewood-Offord problems\nby Hunter Spink (Sta nford University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\n(Joint with Jacob Fox and Matthew Kwan\, no o-minimal backgro und required!) The classical Erdős-Littlewood-Offord theorem says that fo r any n nonzero vectors in $\\mathbb{R}^d$\, a random signed sum concentra tes on any point with probability at most $O(n^{-1/2})$. Combining tools f rom probability theory\, additive combinatorics\, and o-minimality\, we ob tain an anti-concentration probability of $n^{-1/2+o(1)}$ for any o-minima l set $S$ in $\\mathbb{R}^d$ (such as a hypersurface defined by a polynomi al in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a restricted analytic fu nction) not containing a line segment. We do this by showing such o-minima l sets have no higher-order additive structure\, complementing work by Pil a on lower-order additive structure developed to count rational and algebr aic points of bounded height.\n LOCATION:https://researchseminars.org/talk/CJCS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Shoham Letzter (University College London) DTSTART:20210902T141500Z DTEND:20210902T160000Z DTSTAMP:20260422T033703Z UID:CJCS/25 DESCRIPTION:Title: Ti ght cycles in hypergraphs\nby Shoham Letzter (University College Londo n) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nHo w many edges can an r-uniform hypergraph on n vertices with no tight cycle s have? We determine the correct answer to this question up to a polylogar ithmic factor\, improving on a recent result by Sudakov and Tomon.\n LOCATION:https://researchseminars.org/talk/CJCS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Wesolek (Simon Fraser University) DTSTART:20210909T141500Z DTEND:20210909T160000Z DTSTAMP:20260422T033703Z UID:CJCS/26 DESCRIPTION:Title: Gr aph Drawings and Graph Limits\nby Alexandra Wesolek (Simon Fraser Univ ersity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstrac t\nIn this talk we will explain a setup which shows that the theory of gra ph limits introduced by Lovász et al. can be applied to intersection grap hs of graph drawings. In intersection graphs\, vertices correspond to edge s of the drawing\, with two vertices being connected in the intersection g raph if the corresponding edges cross. We consider models of random\, geod esic drawings on the unit sphere for which the intersection graphs form a convergent series (for n going to infinity). This talk is based on joint w ork with Marthe Bonamy and Bojan Mohar.\n LOCATION:https://researchseminars.org/talk/CJCS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgios Petridis (University of Georgia) DTSTART:20210923T141500Z DTEND:20210923T160000Z DTSTAMP:20260422T033703Z UID:CJCS/28 DESCRIPTION:Title: Th e q-analogue of almost orthogonal sets\nby Georgios Petridis (Universi ty of Georgia) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\n Abstract\nAn almost orthogonal set in $\\mathbb{R}^d$ is a collection of v ectors with the property that among any three distinct elements there is a n orthogonal pair. The maximum size of such sets was determined by Rosenfe ld\, who verified a belief of Erdos. The same question was studied by Ahma di and Mohammadian in $\\mathbb{F}_q^d$. We will present a proof of a conj ecture of Ahmadi and Mohammadian and also see how it implies an “almost ” analogue of a theorem of Berlekamp on eventowns. Joint work with Ali M ohammadi.\n LOCATION:https://researchseminars.org/talk/CJCS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Thang Pham (Vietnam National University) DTSTART:20211007T141500Z DTEND:20211007T160000Z DTSTAMP:20260422T033703Z UID:CJCS/29 DESCRIPTION:Title: Po int-sphere incidence bounds in finite spaces\nby Thang Pham (Vietnam N ational University) as part of Copenhagen-Jerusalem Combinatorics Seminar\ n\n\nAbstract\nIn this talk\, I present an approach to study the point-sph ere incidence problem in the vector spaces over finite fields by using res ults from restriction theory. This is joint work with Doowon Koh and Sujin Lee.\n LOCATION:https://researchseminars.org/talk/CJCS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Goaoc (École des Mines de Nancy) DTSTART:20211104T151500Z DTEND:20211104T170000Z DTSTAMP:20260422T033703Z UID:CJCS/30 DESCRIPTION:Title: Co ncentration in order types of random point sets\nby Xavier Goaoc (Éco le des Mines de Nancy) as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\n\nAbstract\nThe order type of a planar point set is a combinatorial structure that \nencodes many of its geometric properties\, for instance t he face lattice \nof its convex hull or the triangulations it supports. In a sense\, it is \na generalization of the permutation associated to a seq uence of real \nnumbers.\n\nThis talk will start with a quick introduction to order types. Then\, \nI'll discuss a concentration phenomenon that ari ses when taking order \ntypes of various natural models of random point se ts\, and that makes \norder types hard to sample efficiently. This will gi ve us an occasion to \n revisit Klein's celebrated proof of the classific ation of finite \nsubgroups of SO(3).\n\nThis is joint work with Emo Welzl (https://arxiv.org/abs/2003.08456).\n LOCATION:https://researchseminars.org/talk/CJCS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Simkin (Harvard University) DTSTART:20210930T141500Z DTEND:20210930T160000Z DTSTAMP:20260422T033703Z UID:CJCS/31 DESCRIPTION:Title: Th e number of $n$-queens configurations\nby Michael Simkin (Harvard Univ ersity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstrac t\nThe $n$-queens problem is to determine $\\mathcal{Q}(n)$\, the number o f ways to place $n$ mutually non-threatening queens on an $n \\times n$ bo ard. We show that there exists a constant $\\alpha = 1.942 \\pm 3 \\times 10^{-3}$ such that $\\mathcal{Q}(n) = ((1 \\pm o(1))ne^{-\\alpha})^n$. The constant $\\alpha$ is characterized as the solution to a convex optimizat ion problem in $\\mathcal{P}([-1/2\,1/2]^2)$\, the space of Borel probabil ity measures on the square.\n\nThe chief innovation is the introduction of limit objects for $n$-queens configurations\, which we call \\textit{quee nons}. These are a convex set in $\\mathcal{P}([-1/2\,1/2]^2)$. We define an entropy function that counts the number of $n$-queens configurations th at approximate a given queenon. The upper bound uses the entropy method. F or the lower bound we describe a randomized algorithm that constructs a co nfiguration near a prespecified queenon and whose entropy matches that fou nd in the upper bound. The enumeration of $n$-queens configurations is the n obtained by maximizing the (concave) entropy function in the space of qu eenons.\n\nBased on arXiv:2107.13460\n LOCATION:https://researchseminars.org/talk/CJCS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnau Padrol (Sorbonne Université) DTSTART:20211014T141500Z DTEND:20211014T160000Z DTSTAMP:20260422T033703Z UID:CJCS/32 DESCRIPTION:Title: Th e convex dimension of hypergraphs and the hypersimplicial Van Kampen-Flor es Theorem\nby Arnau Padrol (Sorbonne Université) as part of Copenhag en-Jerusalem Combinatorics Seminar\n\n\nAbstract\nI will present joint wor k with Leonardo Martínez-Sandoval on the \nhypersimplicial generalization of the linear van Kampen-Flores theorem: \nfor each n\, k and i we determ ine onto which dimensions can the \n(n\,k)-hypersimplex be linearly projec ted while preserving its \ni-skeleton. This is motivated by the study of t he convex dimensions of \nhypergraphs. The convex dimension of a k-uniform hypergraph is the \nsmallest dimension d for which there is an injective mapping of its \nvertices into R^d such that the set of k-barycenters of a ll hyperedges \nis in convex position. Our results completely determine th e convex \ndimension of complete k-uniform hypergraphs. This settles an op en \nquestion by Halman\, Onn and Rothblum\, who solved the problem for \n complete graphs. We also provide lower and upper bounds for the extremal \ nproblem of estimating the maximal number of hyperedges of k-uniform \nhyp ergraphs on n vertices with convex dimension d.\n LOCATION:https://researchseminars.org/talk/CJCS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Eur (Harvard University) DTSTART:20211021T141500Z DTEND:20211021T160000Z DTSTAMP:20260422T033703Z UID:CJCS/33 DESCRIPTION:Title: Ta utological classes of matroids\nby Christopher Eur (Harvard University ) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe introduce a new way of geometrically studying matroids that unifies\, reco vers\, and extends several recent developments in the interaction between matroid theory and algebraic geometry. Joint work with Andrew Berget\, Hu nter Spink\, and Dennis Tseng.\n LOCATION:https://researchseminars.org/talk/CJCS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Labbé (École de Technologie Supérieure Montreal) DTSTART:20211028T141500Z DTEND:20211028T160000Z DTSTAMP:20260422T033703Z UID:CJCS/34 DESCRIPTION:Title: Li neup polytopes and applications in quantum physics\nby Jean-Philippe L abbé (École de Technologie Supérieure Montreal) as part of Copenhagen-J erusalem Combinatorics Seminar\n\n\nAbstract\nThe set of all possible spec tra of 1-reduced density operators for systems of N\nparticles on a d-dime nsional Hilbert space is a polytope called hypersimplex. If\nthe spectrum of the original density operators is fixed\, the set of spectra (ordered\n decreasingly) of 1-reduced density operators is also a polytope. A theoret ical\ndescription of this polytope using inequalities was provided by Klya chko in the\nearly 2000’s.\nAdapting and enhancing tools from discrete g eometry and combinatorics (symmetric\npolytopes\, sweep polytopes\, and th e Gale order)\, we obtained such necessary\ninequalities explicitly\, that are furthermore valid for arbitrarily large N and d.\nThese may therefore be interpreted as generalizations of Pauli's exclusion principle\nfor fer mions. In particular\, this approach leads to a new class of polytopes cal led\nlineup polytopes.\n\nThis is joint work with physicists Julia Liebert \, Christian Schilling and mathematicians\nEva Philippe\, Federico Castill o and Arnau Padrol.\n LOCATION:https://researchseminars.org/talk/CJCS/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Mats Boij (KTH) DTSTART:20211111T151500Z DTEND:20211111T170000Z DTSTAMP:20260422T033703Z UID:CJCS/35 DESCRIPTION:Title: Le fschetz Properties\nby Mats Boij (KTH) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nLefschetz properties have been in fo cus in combinatorics and commutative algebra since Stanley’s proof of th e g-Theorem for simplicial polytopes. I will give some background and then I’ll present two projects that I have been working on recently. The fir st is related to symmetric polynomial and is joint work with Migliore\, Na gel and Miró-Roig. The second is related to powers of general linear form s and is joint work with Lundqvist.\n LOCATION:https://researchseminars.org/talk/CJCS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Adams (Colorado State University) DTSTART:20211202T151500Z DTEND:20211202T170000Z DTSTAMP:20260422T033703Z UID:CJCS/37 DESCRIPTION:Title: Bo unding Gromov-Hausdorff distances with Borsuk-Ulam theorems and Vietoris-R ips complexes\nby Henry Adams (Colorado State University) as part of C openhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe Gromov-Hausdo rff distance between two metric spaces is an important tool in geometry\, but it is difficult to compute. For example\, the Gromov-Hausdorff distanc e between unit spheres of different dimensions is unknown in nearly all ca ses. I will introduce recent work by Lim\, Mémoli\, and Okutan that lower bounds the Gromov-Hausdorff distance between spheres using Borsuk-Ulam th eorems. We improve these lower bounds by connecting this story to Vietoris -Rips complexes\, providing new generalizations of Borsuk-Ulam.\n LOCATION:https://researchseminars.org/talk/CJCS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Reiner (Univerity of Minnesota) DTSTART:20211118T151500Z DTEND:20211118T170000Z DTSTAMP:20260422T033703Z UID:CJCS/39 DESCRIPTION:Title: To pology of augmented Bergman complexes\nby Victor Reiner (Univerity of Minnesota) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst ract\n(based on arxiv:2108.13394\; joint with REU students E. Bullock\, A. Kelley\, K. Ren\, G. Shemy\, D. Shen\, B. Sun\, A. Tao\, Z. Zhang)\n\nThe augmented Bergman complex of a matroid is a simplicial complex introduced recently in work of Braden\, Huh\, Matherne\, Proudfoot and Wang. It may be viewed as a hybrid of two well-studied pure shellable simplicial comple xes associated to matroids: the independent set complex and the order comp lex of the lattice of flats.\n\nAfter recalling the relevance of the augme nted Bergman complex in the B-H-M-P-W work\, we show that it is shellable\ , via two different families of shelling orders. Both shellings determine the homotopy type\, and comparing the two answers re-interprets a known co nvolution formula counting bases of the matroid. One of the shellings lead s to a surprisingly simple description for how symmetries of the matroid a ct on the homology of the complex.\n LOCATION:https://researchseminars.org/talk/CJCS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Jozsef Solymosi (University of British Columbia) DTSTART:20211216T151500Z DTEND:20211216T170000Z DTSTAMP:20260422T033703Z UID:CJCS/41 DESCRIPTION:Title: Ra nk of matrices with entries from a multiplicative group\nby Jozsef Sol ymosi (University of British Columbia) as part of Copenhagen-Jerusalem Com binatorics Seminar\n\n\nAbstract\nWe establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative gr oup of small rank. Applying these bounds we show that the distance sets of finite pointsets in ℝ^d generate high rank multiplicative groups and th at multiplicative groups of small rank cannot contain large sumsets. (Join t work with Noga Alon)\n LOCATION:https://researchseminars.org/talk/CJCS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Giorgis Petridis (University of Georgia) DTSTART:20211215T151500Z DTEND:20211215T170000Z DTSTAMP:20260422T033703Z UID:CJCS/42 DESCRIPTION:Title: Sm all progress towards the Paley graph conjecture\nby Giorgis Petridis ( University of Georgia) as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\n\nAbstract\nThe question of determining the largest independent set in a Paley graph (a special kind of Cayley graph) is connected to the clas sical question of Vinogradov on determining the least quadratic non-residu e modulo a given prime. This connection will be discussed and small progre ss in the state-of-the-art will be presented.\n LOCATION:https://researchseminars.org/talk/CJCS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Pak (UCLA) DTSTART:20211104T170000Z DTEND:20211104T190000Z DTSTAMP:20260422T033703Z UID:CJCS/43 DESCRIPTION:Title: Lo g-concave poset inequalities\nby Igor Pak (UCLA) as part of Copenhagen -Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn the ocean of log-concav e inequalities\, there are two islands that are especially difficult. Fir st\, Mason's conjectures say that the number of forests in a graph with k edges is log-concave. More generally\, the number of independent sets of size k in a matroid is log-concave. Versions of these results were establ ished just recently\, in a remarkable series of papers inspired by algebra ic and geometric considerations. Second\, Stanley's inequality for the nu mbers of linear extensions of a poset with value k at a given poset elemen t\, is log-concave. This was originally conjectured by Chung\, Fishburn a nd Graham\, and proved by Stanley in 1981 using the Alexandrov–Fenchel i nequalities in convex geometry. In our recent paper\, we present a new fr amework of combinatorial atlas which allows one to give elementary proofs of both results\, and extend them in several directions. I will give an i ntroduction to the area and then outline our approach. Joint work with Sw ee Hong Chan.\n LOCATION:https://researchseminars.org/talk/CJCS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Nina Kamcev (University of Zagreb) DTSTART:20211125T151500Z DTEND:20211125T170000Z DTSTAMP:20260422T033703Z UID:CJCS/44 DESCRIPTION:Title: Co mmon systems of equations are rare\nby Nina Kamcev (University of Zagr eb) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nS everal classical results in Ramsey theory (including famous theorems of Sc hur\, van der Waerden\, Rado) deal with finding monochromatic linear patte rns in two-colourings of the integers. Our topic will be quantitative exte nsions of such results.\n \nA linear system $L$ over $\\mathcal{F}_q$ is \ \emph{common} if the number of monochromatic solutions to $L=0$ in any two -colouring of $\\mathcal{F}_q^n$ is asymptotically at least the expected n umber of monochromatic solutions in a random two-colouring of $\\mathcal{F }_q^n$. Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions)\, as well as extensive research on co mmon and Sidorenko graphs\, the systematic study of common systems of line ar equations was recently initiated by Saad and Wolf. Fox\, Pham and Zhao characterised common linear equations. \n \nI will talk about recent prog ress towards a classification of common systems of two or more linear equa tions. In particular\, any system containing a four-term arithmetic progre ssion is uncommon. This follows from a more general result which allows us to deduce the uncommonness of a general system from certain properties of one- or two-equation subsystems.\n \nJoint work with Anita Liebenau and N atasha Morrison.\n LOCATION:https://researchseminars.org/talk/CJCS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Baker (Georgia Tech) DTSTART:20211209T150000Z DTEND:20211209T160000Z DTSTAMP:20260422T033703Z UID:CJCS/45 DESCRIPTION:Title: Th e Foundation of a Matroid\nby Matt Baker (Georgia Tech) as part of Cop enhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMatroid theorists a re interested in questions concerning representability of matroids over fi elds. More generally\, one can ask about representability over partial fie lds in the sense of Semple and Whittle. Pendavingh and van Zwam introduced the universal partial field of a matroid\, which governs the representati ons of over all partial fields. Unfortunately\, most matroids are not rep resentable over any partial field\, and in this case\, the universal parti al field is not defined.\n\nOliver Lorscheid and I have introduced a gener alization of the universal partial field which we call the foundation of a matroid\; it is always well-defined. The foundation is a type of algebrai c object which we call a pasture\; pastures include both hyperfields and p artial fields. As a particular application of this point of view\, I will explain the classification of all possible foundations for matroids having no minor isomorphic to U(2\,5) or U(3\,5). Among other things\, this prov ides a short and conceptual proof of the 1997 theorem of Lee and Scobee wh ich says that a matroid is both ternary and orientable if and only if it i s dyadic.\n LOCATION:https://researchseminars.org/talk/CJCS/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Escobar (Washington University in St. Louis) DTSTART:20220203T151500Z DTEND:20220203T170000Z DTSTAMP:20260422T033703Z UID:CJCS/46 DESCRIPTION:Title: Th e harmonic polytope\nby Laura Escobar (Washington University in St. Lo uis) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\n This talk\, based on joint work with Federico Ardila\, is about the harmon ic polytope\, which arose in Ardila\, Denham\, and Huh’s work on the Lag rangian geometry of matroids. We show that the harmonic polytope is a (2n- 2)-dimensional polytope with (n!)^2(1+1/2+···+1/n) vertices and 3n-3 fa cets. Lastly\, we use the Bernstein-Khovanskii-Kushnirenko Theorem to give a formula for its volume.\n LOCATION:https://researchseminars.org/talk/CJCS/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Sheffer (City University of New York) DTSTART:20220310T151500Z DTEND:20220310T170000Z DTSTAMP:20260422T033703Z UID:CJCS/47 DESCRIPTION:Title: A structural Szemerédi–Trotter theorem for cartesian products\nby Ada m Sheffer (City University of New York) as part of Copenhagen-Jerusalem Co mbinatorics Seminar\n\n\nAbstract\nThe Szemerédi–Trotter theorem can be considered as the fundamental theorem of geometric incidences. This combi natorial theorem has an unusually wide variety of applications\, and is us ed in combinatorics\, theoretical computer science\, harmonic analysis\, n umber theory\, model theory\, and more. Surprisingly\, hardly anything is known about the structural question - characterizing the cases where the t heorem is tight. We present such structural results for the case of cartes ian products. This is a basic survey talk and does not require previous kn owledge of the field.\n \nJoint work with Olivine Silier. Also\, a shamele ss advertisement of the speaker's new book "Polynomial Methods and Inciden ce Theory."\n LOCATION:https://researchseminars.org/talk/CJCS/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Miloš Trujić (ETH Zürich) DTSTART:20220210T151500Z DTEND:20220210T170000Z DTSTAMP:20260422T033703Z UID:CJCS/48 DESCRIPTION:Title: Tw o problems in (size-)Ramsey theory\nby Miloš Trujić (ETH Zürich) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn 1978 \, Erdős\, Faudree\, Rousseau\, and Schelp introduced the study of the si ze-Ramsey\nnumber of a graph H\, defined as a minimum positive integer m f or which there exists a\ngraph G with m edges such that in every colouring of its edges by two colours there is a\nmonochromatic copy of H. I will d iscuss recent advances for two problems in this area when\nH is a large gr aph of bounded maximum degree. This is joint work with David Conlon and \n Rajko Nenadov.\n LOCATION:https://researchseminars.org/talk/CJCS/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Anschel Schaffer-Cohen (University of Pennsylvania) DTSTART:20220127T161500Z DTEND:20220127T170000Z DTSTAMP:20260422T033703Z UID:CJCS/49 DESCRIPTION:Title: Au tomorphisms of the loop and arc graph of an infinite-type surface\nby Anschel Schaffer-Cohen (University of Pennsylvania) as part of Copenhagen- Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe show that the extended b ased mapping class group of an infinite-type surface is naturally isomorph ic to the automorphism group of the loop graph of that surface. Additional ly\, we show that the extended mapping class group stabilizing a finite se t of punctures is isomorphic to the arc graph relative to that finite set of punctures. This extends a known result for sufficiently complex finite- type surfaces\, and provides a new angle from which to study the mapping c lass groups of infinite-type surfaces.\n LOCATION:https://researchseminars.org/talk/CJCS/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Chavez Caliz (Pennsylvania State University) DTSTART:20220106T161500Z DTEND:20220106T170000Z DTSTAMP:20260422T033703Z UID:CJCS/50 DESCRIPTION:Title: Pr ojective self-dual polygons\nby Ana Chavez Caliz (Pennsylvania State U niversity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst ract\nIn his book "Arnold's Problems\," Vladimir Arnold shares a collectio n of questions without answers formulated during seminars in Moscow and Pa ris for over 40 years. One of these problems\, stated in 1994\, goes as fo llows:\nFind all projective curves projectively equivalent to their duals. The answer seems to be unknown even in RP^2.\n\nMotivated by this questio n\, in their paper "Self-dual polygons and self-dual curves" from 2009\, D . Fuchs and S. Tabachnikov explore a discrete version of Arnold's question in 2-dimensions. If P is an n-gon with vertices A_1\, A_3\, ... A_{2n-1}\ , then its dual polygon P* has vertices B*_2\, B*_4\, ... B*_{2n}\, where B*_i is the line connecting the points A_{i-1}\, A_{i+1}. Given an integer m\, a polygon P is m-self-dual if there is a projective transformation f such that f(A_i) = B_{i+m}. \n\nIn this talk\, I will discuss how we can g eneralize Fuchs and Tabachnikov's work to polygons in higher dimensions. I will include some conjectures which are supported by computational result s.\n LOCATION:https://researchseminars.org/talk/CJCS/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Arina Voorhaar (University of Geneva) DTSTART:20220106T151500Z DTEND:20220106T160000Z DTSTAMP:20260422T033703Z UID:CJCS/51 DESCRIPTION:Title: On the Newton Polytope of the Morse Discriminant\nby Arina Voorhaar (Uni versity of Geneva) as part of Copenhagen-Jerusalem Combinatorics Seminar\n \n\nAbstract\nA famous classical result by Gelfand\, Kapranov and Zelevins ky provides a combinatorial description of the vertices of the Newton poly tope of the A-discriminant (the closure of the set of all non-smooth hyper surfaces defined by polynomials with the given support A). Namely\, it giv es a surjection from the set of all convex triangulations of the convex hu ll of the set A with vertices in A (or\, equivalently\, the set of all pos sible combinatorial types of smooth tropical hypersurfaces defined by trop ical polynomials with support A) onto the set of vertices of this Newton p olytope. In my talk\, I will discuss a similar problem for the Morse discr iminant — the closure of the set of all polynomials with the given suppo rt A which are non-Morse if viewed as polynomial maps. Namely\, for a 1-di mensional support set A\, there is a surjection from the set of all possib le combinatorial types of so-called Morse tropical polynomials onto the ve rtices of the Newton polytope of the Morse discriminant.\n LOCATION:https://researchseminars.org/talk/CJCS/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Spirkl (University of Waterloo) DTSTART:20220113T151500Z DTEND:20220113T170000Z DTSTAMP:20260422T033703Z UID:CJCS/52 DESCRIPTION:Title: Ne w results on polynomial $\\chi$-boundedness\nby Sophie Spirkl (Univers ity of Waterloo) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n \nAbstract\nThe number of colours required to colour a graph $G$ (the chro matic number $\\chi(G)$) is at least its clique number\, that is\, the max imum size of a set of pairwise adjacent vertices. A class of graphs is $\\ chi$-bounded if the converse is approximately true\, that is\, the chromat ic number is at most some function of the clique number. In this talk\, we are interested in when this function can be chosen as a polynomial. I wil l discuss some recent results\, mostly concerning the case of forbidding a single graph as an induced subgraph.\nJoint work with Maria Chudnovsky\, Alex Scott and Paul Seymour.\n LOCATION:https://researchseminars.org/talk/CJCS/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Shubhangi Saraf (Rutgers University) DTSTART:20220120T151500Z DTEND:20220120T170000Z DTSTAMP:20260422T033703Z UID:CJCS/53 DESCRIPTION:Title: Fa ctors of sparse polynomials: structural results and some algorithms\nb y Shubhangi Saraf (Rutgers University) as part of Copenhagen-Jerusalem Com binatorics Seminar\n\n\nAbstract\nAre factors of sparse polynomials sparse ? This is basic question\, and we are still quite far from understanding i t in general. In this talk\, I will show that this is in some sense true f or multivariate polynomials when the polynomial has each variable appearin g only with bounded degree. Our sparsity bound uses techniques from convex geometry\, such as the theory of Newton polytopes and an approximate vers ion of the classical Caratheodory's Theorem. \nUsing our sparsity bound\, we then show how to devise efficient deterministic factoring algorithms f or sparse polynomials of bounded individual degree.\nThe talk is based on joint work with Vishwas Bhargav and Ilya Volkovich.\n LOCATION:https://researchseminars.org/talk/CJCS/53/ END:VEVENT BEGIN:VEVENT SUMMARY:William Gustafson (University of Kentucky) DTSTART:20220127T151500Z DTEND:20220127T160000Z DTSTAMP:20260422T033703Z UID:CJCS/54 DESCRIPTION:Title: La ttice minors and Eulerian posets\nby William Gustafson (University of Kentucky) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr act\nWe introduce a notion of deletion and contraction on lattices enriche d with a generating set\, and from these operations a notion of minors. Wh en considering the lattice of flats of a graph the lattice minors are in b ijection with the simple minors of the graph when the vertices are labeled and the edges are unlabeled. We show how this correspondence generalizes to the setting of polymatroids. Then we introduce the minor poset of a giv en generator enriched lattice and show these posets are Eulerian and PL sp heres. Finally we discuss some inequalities between the cd-indices of mino r posets.\n LOCATION:https://researchseminars.org/talk/CJCS/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Clifton (Emory University) DTSTART:20220217T151500Z DTEND:20220217T160000Z DTSTAMP:20260422T033703Z UID:CJCS/55 DESCRIPTION:Title: Ra msey Theory for Diffsequences\nby Alexander Clifton (Emory University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nVan der Waerden's theorem states that any coloring of $\\mathbb{N}$ with a fin ite number of colors will contain arbitrarily long monochromatic arithmeti c progressions. This motivates the definition of the van der Waerden numbe r $W(r\,k)$ which is the smallest $n$ such that any $r$-coloring of $\\{1\ ,2\,\\cdots\,n\\}$ guarantees the presence of a monochromatic arithmetic p rogression of length $k$.\n\nIt is natural to ask what other arithmetic st ructures exhibit van der Waerden-type results. One notion\, introduced by Landman and Robertson\, is that of a $D$-diffsequence\, which is an increa sing sequence $a_1 < a_2 <\\cdots< a_k$ in which the consecutive differenc es $a_i-a_{i-1}$ all lie in some given set $D$. For each $D$ that exhibits a van der Waerden-type result\, we let $\\Delta(D\,k\;r)$ represent the a nalogue of the van der Waerden number $W(r\,k)$. One question of interest is to determine the possible behaviors of $\\Delta$ as a function of $k$. In this talk\, we will demonstrate that it is possible for $\\Delta(D\,k\; r)$ to grow faster than polynomial in $k$. Time permitting\, we will also discuss a class of $D$'s for which no van der Waerden-type result is possi ble.\n LOCATION:https://researchseminars.org/talk/CJCS/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Marija Jelić Milutinović (University of Belgrade) DTSTART:20220224T151500Z DTEND:20220224T170000Z DTSTAMP:20260422T033703Z UID:CJCS/56 DESCRIPTION:Title: Ma tching complexes of graphs\nby Marija Jelić Milutinović (University of Belgrade) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb stract\nThe matching complex M(G) of a graph G is the simplicial complex w ith the vertex set given by edges of G and faces given by subsets of pairw ise disjoint edges\, i.e.\, matchings of G. There is a long history of the study of matching complexes\, and there are many results on the topology of the matching complexes of interesting classes of graphs. We will discus s the reverse question: which simplicial complexes are matching complexes of graphs? In this talk we will answer this question for the homology mani folds\, with and without boundary. While in dimension 2 there are several interesting manifolds\, in dimension three and higher the only matching co mplexes are combinatorial spheres and combinatorial disks. Moreover\, the graphs that produce manifold matching complexes are all constructed from t he disjoint union of copies of a finite set of graphs. The talk is based o n joint work with M. Bayer and B. Goeckner.\n LOCATION:https://researchseminars.org/talk/CJCS/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Lei Xue (University of Washington) DTSTART:20220127T171500Z DTEND:20220127T180000Z DTSTAMP:20260422T033703Z UID:CJCS/57 DESCRIPTION:Title: A Proof of Grünbaum’s Lower Bound Conjecture for polytopes\, lattices\, a nd strongly regular pseudomanifolds.\nby Lei Xue (University of Washin gton) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\ nIn 1967\, Grünbaum conjectured that any $d$-dimensional polytope with $d + s \\leq 2d$ vertices has at least $\\phi_k (d + s\, d) = {d + 1 \\choos e k + 1} + { d \\choose k + 1} - { d + 1 - s \\choose k + 1}$ $k$-faces. I n the talk\, we will prove this conjecture and discuss equality cases. We will then extend our results to lattices with diamond property (the inequa lity part) and to strongly regular normal pseudomanifolds (the equality pa rt). We will also talk about recent results on $d$-dimensional polytopes w ith $2d + 1$ or $2d + 2$ vertices.\n LOCATION:https://researchseminars.org/talk/CJCS/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Lundqvist (Stockholm University) DTSTART:20220317T151500Z DTEND:20220317T170000Z DTSTAMP:20260422T033703Z UID:CJCS/58 DESCRIPTION:Title: Th e Fröberg conjecture and some questions on powers of general linear forms \nby Samuel Lundqvist (Stockholm University) as part of Copenhagen-Jer usalem Combinatorics Seminar\n\n\nAbstract\nThe longstanding Fröberg conj ecture states that there are no non-trivial relations between general homo geneous polynomials. But if we replace "general homogeneous polynomials" b y ”powers of general linear forms” it turns out that in some cases the re are in fact such non-trivial relations\, which may at first seem unnatu ral. I will present some results and some combinatorial questions related to these two classes of objects\, and will give brief connections to latti ce paths\, the Exterior algebra\, the Lefschetz properties\, and fat point schemes. No previous knowledge of the Fröberg conjecture is assumed.\n LOCATION:https://researchseminars.org/talk/CJCS/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Venturello (KTH Stockholm) DTSTART:20220331T141500Z DTEND:20220331T160000Z DTSTAMP:20260422T033703Z UID:CJCS/59 DESCRIPTION:Title: Go renstein algebras from simplicial complexes\nby Lorenzo Venturello (KT H Stockholm) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb stract\nGorenstein algebras form an intriguing class of objects which ofte n show up in combinatorics and geometry. In this talk I will present a con struction which associates to every pure simplicial complex a standard gra ded Gorenstein algebra. We describe a presentation of this algebra as a po lynomial ring modulo an ideal generated by monomials and pure binomials. W hen the simplicial complex is flag\, i.e.\, it is the clique complex of it s graph\, our main results establish equivalences between well studied pro perties of the complex (being S_2\, Cohen-Macaulay\, Shellable) with those of the algebra (being quadratic\, Koszul\, having a quadratic GB). Finall y\, we study the h-vector of the Gorenstein algebras in our construction a nd answer a question of Peeva and Stillman by showing that it is very ofte n not gamma-positive. This is joint work with Alessio D'Alì.\n LOCATION:https://researchseminars.org/talk/CJCS/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Suk (UC San Diego) DTSTART:20220428T141500Z DTEND:20220428T160000Z DTSTAMP:20260422T033703Z UID:CJCS/60 DESCRIPTION:Title: Un avoidable patterns in simple topological graphs\nby Andrew Suk (UC San Diego) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstrac t\nA simple topological graph is a graph drawn in the plane so that its ve rtices are represented by points\, and its edges are represented by non-se lf-intersecting arcs connecting the corresponding points\, with the proper ty that any two edges have at most one point in common. In 2003\, Pach-So lymosi-Toth showed that every n-vertex complete simple topological graph c ontains a topological subgraph on m = Omega(\\log^{1/8} n) vertices that i s weakly isomorphic to the complete convex geometric graph or to the compl ete twisted graph on m vertices. Here\, we improve this bound to (log n)^ {1/4 - o(1)}. I will also discuss other related problems as well.\nThis is joint work with Ji Zeng.\n LOCATION:https://researchseminars.org/talk/CJCS/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Machado (University of Cambridge) DTSTART:20220407T141500Z DTEND:20220407T160000Z DTSTAMP:20260422T033703Z UID:CJCS/61 DESCRIPTION:Title: Wh en are discrete subsets of Lie groups approximate subgroups ? Around a the orem of Lagarias.\nby Simon Machado (University of Cambridge) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMeyer sets ar e fascinating objects: they are aperiodic subsets of Euclidean spaces that nonetheless exhibit long-range aperiodic order. Sets of vertices of the P enrose tiling (P3) and Pisot—Vijarayaghavan numbers of a real number fie ld are some of the most well-known examples. In modern lingo\, they can be defined as the discrete and co-compact approximate subgroups of Euclidean spaces.\n\nLagarias found an elegant characterisation of Meyer sets: they are those subsets X of a Euclidean space E that are relatively dense (any point of E is within uniformly bounded distance of X) and whose Minkowski difference X - X is uniformly discrete (the distance between any two poin ts is uniformly bounded below). In essence\, his theorem provides a charac terisation of discrete approximate subgroups that is analogous to the Plun necke—Ruzsa theorem about sets of small doubling.\n\nI will discuss the general theory of Meyer sets and state Lagarias theorem. I will explain ho w additive combinatorics can be used to extend Lagarias result to discrete subsets of amenable groups. Going beyond the framework of amenable groups \, I will talk about how one can use simple ideas from additive combinator ics in combination with powerful tools from ergodic theory - such as Zimme r’s cocycle superrigidity - to generalise Lagarias theorem to discrete s ubsets of $SL_n(\\mathbb{R})$ for n > 2.\n LOCATION:https://researchseminars.org/talk/CJCS/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Lew (Technion) DTSTART:20220217T161500Z DTEND:20220217T170000Z DTSTAMP:20260422T033703Z UID:CJCS/62 DESCRIPTION:Title: Le ray numbers of tolerance complexes\nby Alan Lew (Technion) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn this talk we will discuss the Leray and collapsibility numbers of a simplic ial complex K\, and their role in Helly-type theorems in combinator ial geometry. The Leray number is\, roughly speaking\, the hereditary hom ological dimension of K\, while the collapsibility number captures the com plexity of dismantling K by sequentially removing free faces from K.\nFoll owing the formal definition of these parameters and their connection to th e combinatorics of convex sets\, we will introduce the construction of the “tolerance complex” of a complex K. We will explain its relation to a tolerant version of Helly’s theorem due to Montejano and Oliveros and present new results on the Leray numbers of these complexes.\nThe talk is based on joint work with Minki Kim.\n LOCATION:https://researchseminars.org/talk/CJCS/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Shubhangi Saraf (University of Toronto) DTSTART:20220303T151500Z DTEND:20220303T170000Z DTSTAMP:20260422T033703Z UID:CJCS/63 DESCRIPTION:Title: Fa ctors of sparse polynomials: structural results and some algorithms\nb y Shubhangi Saraf (University of Toronto) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nAre factors of sparse polynomials spa rse? This is basic question\, and we are still quite far from understandin g it in general. In this talk\, I will show that this is in some sense tru e for multivariate polynomials when the polynomial has each variable appea ring only with bounded degree. Our sparsity bound uses techniques from con vex geometry\, such as the theory of Newton polytopes and an approximate v ersion of the classical Caratheodory's Theorem. \nUsing our sparsity boun d\, we then show how to devise efficient deterministic factoring algorithm s for sparse polynomials of bounded individual degree.\nThe talk is based on joint work with Vishwas Bhargav and Ilya Volkovich.\n LOCATION:https://researchseminars.org/talk/CJCS/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Ashwin Sah (MIT) DTSTART:20220324T151500Z DTEND:20220324T170000Z DTSTAMP:20260422T033703Z UID:CJCS/64 DESCRIPTION:Title: Hi gh-Girth Steiner Triple Systems\nby Ashwin Sah (MIT) as part of Copenh agen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe prove a 1973 conjec ture due to Erdős on the existence of Steiner triple systems with arbitra rily high girth. Our proof builds on the method of iterative absorption fo r the existence of designs by Glock\, Kü​hn\, Lo\, and Osthus while inc orporating a "high girth triangle removal process". In particular\, we dev elop techniques to handle triangle-decompositions of polynomially sparse g raphs\, construct efficient high girth absorbers for Steiner triple system s\, and introduce a moments technique to understand the probability our ra ndom process includes certain configurations of triples. In this talk we w ill also give a high-level overview of iterative absorption. This work is joint with Matthew Kwan\, Mehtaab Sawhney\, and Michael Simkin.\n LOCATION:https://researchseminars.org/talk/CJCS/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Amita Malik (Max Planck Institute for Mathematics) DTSTART:20220421T141500Z DTEND:20220421T160000Z DTSTAMP:20260422T033703Z UID:CJCS/65 DESCRIPTION:Title: Pa rtitions into primes with a Chebotarev condition\nby Amita Malik (Max Planck Institute for Mathematics) as part of Copenhagen-Jerusalem Combinat orics Seminar\n\n\nAbstract\nIn this talk\, we discuss the asymptotic beha vior of the number of integer partitions into primes concerning a Chebotar ev condition. In special cases\, this reduces to the study of partitions i nto primes in arithmetic progressions. While the study for ordinary partit ions goes back to Hardy and Ramanujan\, partitions into primes were recent ly re-visited by Vaughan. Our error term is sharp and improves on previous known estimates in the special case of primes as parts of the partition. As an application\, monotonicity of this partition function is established explicitly via an asymptotic formula in connection to a result of Bateman and Erdõs.\n LOCATION:https://researchseminars.org/talk/CJCS/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Karasev DTSTART:20220505T141500Z DTEND:20220505T160000Z DTSTAMP:20260422T033703Z UID:CJCS/66 DESCRIPTION:Title: Co vering by planks and avoiding zeros of polynomials\nby Roman Karasev a s part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe not e that the recent polynomial proofs of (particular \ncases of) the spheric al and complex plank covering problems by Zhao and \nOrtega-Moreno give so me general information on zeros of real and complex \npolynomials restrict ed to the unit sphere. After that we establish \npolynomial analogs of the Bang theorem by explaining how to find a point \nin the unit ball suffici ently far from the zero set of a given \npolynomial. As a corollary of the se results\, we establish a conjecture \nof Jiang and Polyanskii about cov ering a sphere by spherical segments \ngeneralizing the zone conjecture of Fejes Tóth.\n\nJoint work with Alexey Glazyrin and Alexander Polyanskii. \n LOCATION:https://researchseminars.org/talk/CJCS/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Yelena Yuditsky (Université libre de Bruxelles) DTSTART:20220512T141500Z DTEND:20220512T160000Z DTSTAMP:20260422T033703Z UID:CJCS/67 DESCRIPTION:Title: We ak Coloring Numbers of Intersection Graphs\nby Yelena Yuditsky (Univer sité libre de Bruxelles) as part of Copenhagen-Jerusalem Combinatorics Se minar\n\n\nAbstract\nWeak and strong coloring numbers are generalizations of the degeneracy of a graph\, where for a positive integer $k$\,\nwe seek a vertex ordering such every vertex can (weakly respectively strongly) re ach in $k$ steps only few vertices that precede it in the ordering.\nBoth notions capture the sparsity of a graph or a graph class\, and have intere sting applications in the structural and algorithmic graph theory.\nRecent ly\, Dvoràk\, McCarty\, and Norin observed a natural volume-based upper b ound for the strong coloring numbers\nof intersection graphs of well-behav ed objects in $\\mathbb{R}^d$\, such as homothets of a compact convex obje ct\, or comparable axis-aligned boxes.\n \nWe prove upper and lower bounds for the $k$-th weak coloring numbers of these classes of intersection gra phs.\nAs a consequence\, we describe a natural graph class whose strong co loring numbers are polynomial in $k$\, but the weak coloring numbers\nare exponential. We also observe a surprising difference in terms of the depen dence of the weak coloring numbers on the dimension\nbetween touching grap hs of balls (single-exponential) and hypercubes (double-exponential).\n LOCATION:https://researchseminars.org/talk/CJCS/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Erika Roldan (TU München) DTSTART:20220519T141500Z DTEND:20220519T160000Z DTSTAMP:20260422T033703Z UID:CJCS/68 DESCRIPTION:Title: Pa rity Property of Hexagonal Sliding Puzzles\nby Erika Roldan (TU Münch en) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nW e study the puzzle graphs of hexagonal sliding puzzles of various shapes a nd with various numbers of holes. The puzzle graph is a combinatorial mode l which captures the solvability and the complexity of sequential mechanic al puzzles. Questions relating to the puzzle graph have been previously st udied and resolved for the 15 Puzzle which is the most famous\, and unsolv able\, square sliding puzzle of all times. The puzzle graph is also a disc rete model for the configuration space of hard tiles (hexagons or squares) moving on different tessellation-based domains. Understanding the combina torics of the puzzle graph leads to understanding some aspects of the topo logy of these configuration spaces.\n LOCATION:https://researchseminars.org/talk/CJCS/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathilde Bouvel (LORIA) DTSTART:20220602T141500Z DTEND:20220602T160000Z DTSTAMP:20260422T033703Z UID:CJCS/69 DESCRIPTION:Title: Li mits of permutations and graphs avoiding substructures\nby Mathilde Bo uvel (LORIA) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb stract\nIn this talk\, I would like to present a survey of a series of pap ers\, describing limits of random graphs or random permutations\, taken un iformly at random conditioned to avoid certain substructures. \nOur first results concern families of pattern-avoiding permutations. Our approach is to use the co-called substitution decomposition of permutations\, thus en coding permutations as trees. Using analytic combinatorics\, we are then a ble to compute the expected densities of patterns in our permutations. Thi s result can be interpreted in the framework of permutons\, thus providing limit shape results for random pattern-avoiding permutations.\nAnalogous results can be obtained for hereditary classes of graphs (defined by the a voidance of induced subgraphs)\, following a similar methodology. The obta ined results are limit shape results in the framework of graphons.\n LOCATION:https://researchseminars.org/talk/CJCS/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Karin Baur (University of Leeds) DTSTART:20221006T141500Z DTEND:20221006T160000Z DTSTAMP:20260422T033703Z UID:CJCS/70 DESCRIPTION:Title: Cl uster structures for Grassmannians\nby Karin Baur (University of Leeds ) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe category of Cohen Macaulay modules over a quotient of a preprojective alg ebra is a cluster category associated to the coordinate ring of the Grassm annian Gr(k\,n). We study this category and describe some of its indecompo sable modules. We also explain how one can associate frieze patterns to th em.\n LOCATION:https://researchseminars.org/talk/CJCS/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Tucker-Foltz (Harvard University) DTSTART:20220414T141500Z DTEND:20220414T160000Z DTSTAMP:20260422T033703Z UID:CJCS/71 DESCRIPTION:Title: Po litical Redistricting\, Graph Partition Sampling\, and Counting Spanning T rees\nby Jamie Tucker-Foltz (Harvard University) as part of Copenhagen -Jerusalem Combinatorics Seminar\n\n\nAbstract\nSay you are handed a 10 X 10 grid graph and are asked to "randomly" partition the vertices into 10 c onnected subgraphs of 10 vertices each. How do you do it? From a complexit y perspective\, the asymptotic version of this question is largely unanswe red\, and even for these small specific parameters there are some very bas ic things we don't know how to do efficiently.\n\nThe primary motivation f or these questions comes from an increasingly popular paradigm for fairnes s in political redistricting whereby electoral maps are judged in comparis on to ensembles of randomly generated maps. This is a truly amazing area w here mathematical theorems are actually having a positive societal impact\ , and the primary goal of this talk will be to inspire more interest in it . I'll focus on a recent paper of mine (https://arxiv.org/abs/2109.13394) that sheds light on one particular angle\, but I will also discuss several tantalizing questions I was unable to answer\, and are still very widely open.\n LOCATION:https://researchseminars.org/talk/CJCS/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Jesus de Loera (UC Davis) DTSTART:20220526T141500Z DTEND:20220526T160000Z DTSTAMP:20260422T033703Z UID:CJCS/72 DESCRIPTION:Title: On Polyhedra Parametrizing ALL pivot rules for the Simplex Method\nby Je sus de Loera (UC Davis) as part of Copenhagen-Jerusalem Combinatorics Semi nar\n\n\nAbstract\nThe simplex method is one of the most famous and popula r algorithms in optimization. The engine of any version of the simplex met hod is a pivot rule that selects the outgoing arc for a current vertex. Pi vot rules come in many forms and types\, but after 80 years we are still i gnorant whether there is one that can make the simplex method run in polyn omial time. This talk is about the polyhedral combinatorics of the simplex method. I will present two recent positive results: For 0/1 polytopes the re are explicit pivot rules for which the number of non-degenerate pivots is polynomial and even linear (joint work with A. Black\, S. Kafer\, L. Sa nita). I also present a parametric analysis for all pívot rules. We cons truct a polytope\, the pivot rule polytope\, that parametrizes all memoryl ess pívot rules of a given LP. Its construction is a generalization of th e Fiber polytope construction of Billera Sturmfels. This is an attempt to get a complete picture of the structure “ space of all pivot rules of an LP” (joint work with A. Black\, N. Lutjeharms\, and R. Sanyal). No pri or knowledge of the simplex method will be assume\, I will only assume the audience loves polytopes.\n LOCATION:https://researchseminars.org/talk/CJCS/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Shira Zerbib (Iowa State University) DTSTART:20220609T141500Z DTEND:20220609T160000Z DTSTAMP:20260422T033703Z UID:CJCS/73 DESCRIPTION:Title: KK M-type theorems and their applications\nby Shira Zerbib (Iowa State Un iversity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr act\nThe KKM theorem\, due to Knaster\, Kuratowski and Mazurkiewicz in 192 9\, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fi xed point theorem. It has numerous applications in combinatorics\, discret e geometry\, economics\, game theory and other areas. Generalizations of t his lemma in several different directions were proved over the years (e.g. \, by Shapley\, Gale\, Komiya\, Soberon) and have been widely applied as w ell. We will discuss a recent common generalization of all these theorems. We will also show two very different applications of KKM-type theorems: o ne is a proof of a conjecture of Eckhoff from 1994 on the line piercing nu mbers in certain families of convex sets in the plane\, and the other is a theorem on fair division of multiple cakes among players with subjective preferences.\n LOCATION:https://researchseminars.org/talk/CJCS/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Soohyun Park (University of Chicago) DTSTART:20220623T141500Z DTEND:20220623T160000Z DTSTAMP:20260422T033703Z UID:CJCS/74 DESCRIPTION:Title: An ti-Ramsey theory\, lattice points on polytopes\, and Hodge structures on t oric hypersurfaces\nby Soohyun Park (University of Chicago) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe relation be tween the topics in the title is obtained by combining combinatorial inter pretations of the simplicial chromatic polynomial. A reinterpretation of t he definition yields the connection to edge colorings of graphs avoiding m onochromatic colorings of specified subgraphs. As for lattice point counts on polytopes and Hodge structures on toric hypersurfaces\, we specialize an expression of the polynomial in terms of the h-vector of an auxiliary s implicial complex.\n LOCATION:https://researchseminars.org/talk/CJCS/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Cardinal (Université Libre de Bruxelles) DTSTART:20220630T141500Z DTEND:20220630T160000Z DTSTAMP:20260422T033703Z UID:CJCS/75 DESCRIPTION:Title: Di ameter estimates for graph associahedra\nby Jean Cardinal (Université Libre de Bruxelles) as part of Copenhagen-Jerusalem Combinatorics Seminar \n\n\nAbstract\nGraph associahedra are generalized permutohedra arising as special cases of nestohedra and hypergraphic polytopes. The graph associa hedron of a graph G encodes the combinatorics of search trees on G\, defin ed recursively by a root r together with search trees on each of the conne cted components of G−r. In particular\, the skeleton of the graph associ ahedron is the rotation graph of those search trees. We investigate the di ameter of graph associahedra as a function of some graph parameters such a s treedepth and treewidth\, and give tight estimates for specific families of graphs\, including trivially perfect\, complete split and complete bip artite graphs. This is a joint work with Lionel Pournin and Mario Valencia -Pabon from Université Sorbonne Paris Nord.\n LOCATION:https://researchseminars.org/talk/CJCS/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie-Charlotte Brandenburg (MPI MiS) DTSTART:20220811T141500Z DTEND:20220811T160000Z DTSTAMP:20260422T033703Z UID:CJCS/76 DESCRIPTION:Title: Tr opical Positivity and Determinantal varieties\nby Marie-Charlotte Bran denburg (MPI MiS) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\nA determinantal variety is the set of (d x n)-matrices of bou nded rank.\nWe study the tropicalization of the set of matrices with posit ive entries and bounded rank\, i.e. the positive part of determinant varie ties. Given such a (d x n)-matrix of fixed rank r\, we can interpret the c olumns of the tropicalization of this matrix as n points in d-dimensional space\, lying on a common r-dimensional tropical linear space. We consider such tropical point configurations\, and introduce a combinatorial criter ion to characterize configurations which can be obtained from the tropical ization of matrices with positive entries.\nNo prior knowledge of tropical geometry will be assumed for this talk. This is based on joint work with Georg Loho and Rainer Sinn.\n LOCATION:https://researchseminars.org/talk/CJCS/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehtaab Sawhney (MIT) DTSTART:20220818T141500Z DTEND:20220818T160000Z DTSTAMP:20260422T033703Z UID:CJCS/77 DESCRIPTION:Title: On low-degree dependencies for sparse random graphs\nby Mehtaab Sawhney (MIT) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\ nVery sparse random graphs are known to typically be singular (i.e.\, have singular adjacency matrix)\, due to the presence of "low-degree dependenc ies" such as isolated vertices and pairs of degree-1 vertices with the sam e neighborhood. We prove that these kinds of dependencies are in some sens e the only causes of singularity: for constants $k\\geq 3$ and $\\lambda>0 $\, an Erdős–Rényi random graph of $n$ vertices and edge probability $ \\lambda/n$ typically has the property that its $k$-core (largest subgraph with min-degree at least $k$) is nonsingular. This resolves a conjecture of Vu from the 2014 ICM\, and adds to a short list of known nonsingularity theorems for "extremely sparse" random matrices with density $O(1/n)$. In subsequent work\, we draw on related techniques to give a precise combina torial characterization of the co-rank of the Erdős–Rényi random graph with density $\\lambda/n$ coming from the Karp-Sipser core. A key aspect of our proof is a technique to extract high-degree vertices and use them t o "boost" the rank\, starting from approximate rank bounds obtainable from (non-quantitative) spectral convergence machinery due to Bordenave\, Lela rge and Salez.\n\nThis talk is based on joint works with Asaf Ferber\, Mar galit Glasgow\, Matthew Kwan\, and Ashwin Sah.\n LOCATION:https://researchseminars.org/talk/CJCS/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Radoslav Fulek (UC San Diego) DTSTART:20220825T141500Z DTEND:20220825T160000Z DTSTAMP:20260422T033703Z UID:CJCS/78 DESCRIPTION:Title: At omic Embeddability\, Clustered Planarity\, and Thickenability\nby Rado slav Fulek (UC San Diego) as part of Copenhagen-Jerusalem Combinatorics Se minar\n\n\nAbstract\nThe planarity testing problem is the algorithmic prob lem of testing whether a given input graph is planar\, that is\, whether i t can be drawn in the plane without edge crossings. C-planarity was introd uced in 1995 by Feng\, Cohen\, and Eades as a generalization of graph plan arity\, in which the vertex set of the input graph is endowed with a hiera rchical clustering and we seek an embedding (edge crossing-free drawing) o f the graph in the plane that respects the clustering in a certain natural sense.\n\nThe problem of thickenability for simplicial complexes emerged in the topology of manifolds in the 1960s. A 2-dimensional simplicial comp lex is thickenable if it embeds in some orientable 3 dimensional manifold. \n\nWe study the atomic embeddability testing problem\, which is a common generalization of clustered planarity (c-planarity\, for short) and thicke nability testing\, and present a polynomial time algorithm for this proble m\, thereby giving the first polynomial time algorithm for c-planarity.\n\ nBefore our work\, it has been an open problem whether c-planarity can be tested efficiently\, despite relentless efforts. Recently\, Carmesin annou nced that thickenability can be tested in polynomial time. Our algorithm f or atomic embeddability combines ideas from Carmesin's work with algorithm ic tools previously developed for so-called weak embeddability testing.\n\ nJoint work with Csaba Tóth.\n LOCATION:https://researchseminars.org/talk/CJCS/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Joachim Kock (KU) DTSTART:20220929T140000Z DTEND:20220929T160000Z DTSTAMP:20260422T033703Z UID:CJCS/79 DESCRIPTION:Title: Fr om Möbius inversion to renormalisation\nby Joachim Kock (KU) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nAlthough Möb ius inversion originates in number theory\, its standard formulation\, due to Rota\, is in the setting of posets\, where it is about splitting of in tervals. It has become a standard and widely used counting device in comb inatorics and application areas. The goal of the talk is to show how a sl ight generalisation of the Möbius inversion principle can also explain (t he algebraic aspect of) one of the main approaches to renormalisation of p erturbative quantum field theories\, the so-called BPHZ renormalisation (a fter Bogoliubov\, Parasiuk\, Hepp\, and Zimmerman)\, in the Hopf-algebraic formulation due to Kreimer. In the talk\, I will explain all the words a bove. (In particular\, no prior knowledge of physics is assumed.)\n\nDiet ary info: the talk does not contain category theory.\n LOCATION:https://researchseminars.org/talk/CJCS/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Zilin Jiang (Arizona State University) DTSTART:20220707T141500Z DTEND:20220707T160000Z DTSTAMP:20260422T033703Z UID:CJCS/80 DESCRIPTION:Title: Ra inbow structures via topological methods\nby Zilin Jiang (Arizona Stat e University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nA bstract\nGiven a family of structures\, is it possible to choose an elemen t from each structure to form a new structure of the same kind? This new s tructure is poetically called rainbow because we can think of each given s tructure in a different color. Some long standing combinatorial problems\, such as transversals in a Latin square and the Caccetta–Haggkvist conje cture\, are rainbow in nature. In this talk\, we will discuss a line of at tacks to related problems via algebraic topology.\n LOCATION:https://researchseminars.org/talk/CJCS/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Castillo (Universidad Católica de Chile) DTSTART:20220714T141500Z DTEND:20220714T160000Z DTSTAMP:20260422T033703Z UID:CJCS/81 DESCRIPTION:Title: Ta ngent hyperplanes to convex bodies\nby Federico Castillo (Universidad Católica de Chile) as part of Copenhagen-Jerusalem Combinatorics Seminar\ n\n\nAbstract\nThe Greeks two thousand years ago already knew that two dis joint circles have four tangent lines. We will explore this question when the circles are replaced by convex bodies in arbitrary dimensions. Bisztri czky (1990) proved that\, with the right generalization of disjointness\, d convex bodies in dimension d have 2^d tangent hyperplanes. In this talk we present a general description of the set of tangent hyperplanes to m co nvex bodies in dimension d (with mPu re-Circuit: Strong Inapproximability for PPAD\nby Alexandros Hollender (University of Oxford) as part of Copenhagen-Jerusalem Combinatorics Semi nar\n\n\nAbstract\nPPAD is a complexity class that contains search problem s that are guaranteed to always have a solution. Due to its close connecti on with topological tools such as Brouwer's fixed point theorem\, it has e merged as the class characterizing the complexity of many fundamental prob lems in game theory and economics. In this talk\, I will introduce the Pur e-Circuit problem: a new tool for proving hardness of approximation for pr oblems in the class PPAD. We will see how this new technique can be used t o show tight inapproximability results for various Nash equilibrium comput ation problems.\n\nBased on joint work with Argyrios Deligkas\, John Fearn ley\, and Themistoklis Melissourgos.\n LOCATION:https://researchseminars.org/talk/CJCS/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Lisa Sauermann (MIT) DTSTART:20220908T141500Z DTEND:20220908T160000Z DTSTAMP:20260422T033703Z UID:CJCS/83 DESCRIPTION:Title: An ticoncentration in Ramsey graphs and a proof of the Erdös-McKay Conjectur e\nby Lisa Sauermann (MIT) as part of Copenhagen-Jerusalem Combinatori cs Seminar\n\n\nAbstract\nThis talk will discuss recent joint work with Ma tthew Kwan\, Ashwin Sah\, and Mehtaab Sawhney\, proving an old conjecture of Erdös and McKay (for which Erdős offered $100). This conjecture conce rns Ramsey graphs\, which are (roughly speaking) graphs without large comp lete or empty subgraphs. In order to prove the conjecture\, we study edge- statistics in Ramsey graphs\, i.e. we study the distribution of the number of edges in a random vertex subset of a Ramsey graph. After discussing so me background on Ramsey graphs\, the talk will explain our results and giv e an overview of our proof approach.\n LOCATION:https://researchseminars.org/talk/CJCS/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Déborah Oliveros (UNAM) DTSTART:20220915T141500Z DTEND:20220915T160000Z DTSTAMP:20260422T033703Z UID:CJCS/84 DESCRIPTION:Title: In tersection Patterns and Tverberg type theorems\nby Déborah Oliveros ( UNAM) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\ nOne of the most beautiful and classic theorems in Discrete Geometry is Tv erberg’s theorem\, which says that any set with sufficiently many points in $R^d$ can always be partitioned into m parts so that their convex hull s intersect. In this talk we will give some generalizations of this theore m that are related to some interesting computing and graph theory problems as well as some cool applications.\n LOCATION:https://researchseminars.org/talk/CJCS/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruy Fabila Monroy (Cinvestav) DTSTART:20220922T141500Z DTEND:20220922T160000Z DTSTAMP:20260422T033703Z UID:CJCS/85 DESCRIPTION:Title: To ken graph reconstruction in Diamond and C_4 free graphs\nby Ruy Fabila Monroy (Cinvestav) as part of Copenhagen-Jerusalem Combinatorics Seminar\ n\n\nAbstract\nLet G be a graph on n vertices and 0< k Sw eep polytopes and sweep oriented matroids\nby Eva Philippe (IMJ-PRG) a s part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nConsid er a configuration of n labeled points in a Euclidean space. Any linear fu nctional gives an ordering of these points: an ordered partition that we c all a sweep\, because we can imagine its parts as the sets of points succe ssively hit by a sweeping hyperplane. The set of all such sweeps forms a p oset which is isomorphic to a polytope\, called the sweep polytope.\nI wil l present several constructions of the sweep polytope\, related to zonotop es\, projections of permutahedra and monotone path polytopes of zonotopes. \n\nThis structure can also be generalized in terms of oriented matroids. For oriented matroids that admit a sweep oriented matroid\, we gain precis ion on the topological description of their poset of cellular strings\, re fining a particular case of the Generalized Baues Problem.\n\nThis is join t work with Arnau Padrol.\n LOCATION:https://researchseminars.org/talk/CJCS/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Søren Eilers (KU) DTSTART:20221027T141500Z DTEND:20221027T160000Z DTSTAMP:20260422T033703Z UID:CJCS/87 DESCRIPTION:Title: Ch romatic numbers for contact graphs of mutually congruent cuboids\nby S øren Eilers (KU) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\nMotivated by a wireless channel assignment problem\, Reed & A llwright proved that there is no upper bound for the chromatic numbers of contact graphs for general cuboids in Euclidean space\, even when all corn ers fall in the integer lattice. If one dimension of the cuboids is restri cted to be 1\, the cuboids will be layered\, and consequently the four col or theorem shows that 8 colors suffice. This bound is tight by work of Bes sy\, Goncalves and Sereni.\n\nWe will study the situation when all cuboids must be mutually congruent\, with a particular interest in what happens i n cases when the rigid motion is required to preserve one or several of th e directions of the cuboids. We can provide non-trivial upper and lower bo unds for the maximally occuring chromatic numbers in many cases\, but only in a few instances we are able to determine these numbers fully. Our most satisfying result\, obtained recently with Rasmus Veber Weis Rasmussen\, is the fact that for 2x1x1 cuboids with the long side restricted to the XY plane\, the maximal chromatic number becomes exactly 5. We have only mana ged to show that 5 colors are necessary after a pointed computer search re sulting in a large cuboid structure requiring 5 colors. \n\nThis problem h as been used as a case study in a course "Experimental Mathematics” taug ht in Copenhagen for more than a decade\, and as I will detail\, much of w hat I know has been taught to me by students. My initial motivation came f rom outreach activities associated to LEGO bricks\, and I will say a few w ords about that too.\n LOCATION:https://researchseminars.org/talk/CJCS/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Boulos El Hilany (TU Braunschweig) DTSTART:20221117T151500Z DTEND:20221117T170000Z DTSTAMP:20260422T033703Z UID:CJCS/88 DESCRIPTION:Title: Co upler curves of moving graphs and counting realizations of rigid graphs\nby Boulos El Hilany (TU Braunschweig) as part of Copenhagen-Jerusalem C ombinatorics Seminar\n\n\nAbstract\nA calligraph is a graph that for almos t all edge length assignments moves with one degree of freedom in the plan e\, if we fix an edge and consider the vertices as revolute joints. \nThe trajectory of a distinguished vertex of the calligraph is called its coupl er curve. Each calligraph corresponds to an algebraic series of real curve s in the plane. I will present a description for the class of those curves in the Néron-Severi lattice of the plane blown-up at six complex conjuga te points. \n\nA graph is said to be minimally rigid if\, up to rotations and translations\, admits finitely many\,\nbut at least two\, realizations into the plane for almost all edge length assignments. \nA minimally rigi d graph can be expressed as a union of two calligraphs\, and the number of its \nrealizations is equal to the product of classes of those two callig raphs. I will show how one \ncan apply those observations to produce an im proved algorithm that counts the numbers of realizations. \nThis\, in turn \, allows one to characterize invariants of coupler curves.\n\nThis is a j oint work with Georg Grasegger and Niels Lubbes (Symbolic computation grou p\, RICAM\, Austria)\n LOCATION:https://researchseminars.org/talk/CJCS/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Haase (FU Berlin) DTSTART:20221013T141500Z DTEND:20221013T160000Z DTSTAMP:20260422T033703Z UID:CJCS/89 DESCRIPTION:Title: Ne wton-Okounkov Semigroups (are often not finitely generated)\nby Christ ian Haase (FU Berlin) as part of Copenhagen-Jerusalem Combinatorics Semina r\n\n\nAbstract\nI will start with a combinatorialist's crash course on to ric varieties which hopefully can be useful in its own right.\nAfter a sho rt break\, I will talk about Newton-Okounkov theory\, which is an attempt to play as much of the toric game as possible with non-toric varieties. Th e theory associates an affine semigroup with a projectively embedded varie ty and tries to draw conlclusions from the asymptotic convex geometry of t his semigroup. Many of these theorems assume that the semigroup is finitel y generated\, but checking finite generation seems to be hard. I will desc ribe a combinatorial criterion\, in a slightly non-toric situation (toric surface\, but non-toric valuation)\, characterizing finite generation. Thi s is joint work with Klaus Altmann\, Alex Küronya\, Karin Schaller & Lena Walter.\n LOCATION:https://researchseminars.org/talk/CJCS/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Vecchi (Università di Bologna) DTSTART:20221020T141500Z DTEND:20221020T160000Z DTSTAMP:20260422T033703Z UID:CJCS/90 DESCRIPTION:Title: Sk ew Young Tableaux for KL polynomials of matroids\nby Lorenzo Vecchi (U niversità di Bologna) as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\n\nAbstract\nKazhdan-Lusztig polynomials of matroids were first intro duced in 2016 in analogy with the classical ones for the Bruhat order in C oxeter groups.\nIn 2020 it was proved that their coefficients are always n on-negative\, by interpreting them as the Hilbert series of the local inte rsection cohomology of some modules associated to the matroid\; however\, since these polynomials can be completely characterized only using the lat tice of flats\, a combinatorialist wonders if any result about them can be reobtained exploiting no algebraic geometry results.\nAfter introducing t he operation of stressed hyperplane relaxation\, we show that we can compu te these coefficients by counting fillings of special skew tableaux shapes . We will also show how these results can be interpreted using representat ion theory on the group of automorphisms of the matroid.\nThis is joint wo rk with Luis Ferroni and George Nasr\, and Trevor Karn\, George Nasr and N icholas Proudfoot.\n LOCATION:https://researchseminars.org/talk/CJCS/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Nill (Otto-von-Guericke-Universität Magdeburg) DTSTART:20221124T151500Z DTEND:20221124T170000Z DTSTAMP:20260422T033703Z UID:CJCS/91 DESCRIPTION:Title: An update on Gorenstein polytopes : reducibility and local $h*$-polynomials< /a>\nby Benjamin Nill (Otto-von-Guericke-Universität Magdeburg) as part o f Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nReflexive poly topes and more generally Gorenstein polytopes are the key objects in the B atyrev-Borisov mirror-symmetry construction of Calabi-Yau manifolds in Gor enstein toric Fano varieties. Moreover\, they are beautiful combinatorial objects that appear prominently in the Ehrhart theory of lattice polytopes . In this talk I plan to present two recent combinatorial results regardin g Gorenstein polytopes. First I will discuss a conjecture of Batyrev-Juny on Gorenstein polytopes of small Ehrhart degree corresponding to Gorenstei n toric Fano varieties that have highly divisible anticanonical divisors. And second I will explain a characterization when Gorenstein polytopes are "thin"\, namely when their l*-polynomial vanishes. This polynomial is an Ehrhart-theoretic invariant that had been independently studied by Gelfand -Kapranov-Zelevinsky\, Stanley\, Karu\, Borisov-Mavlyutov and Katz-Stapled on among others. I will highlight how underlying both results is a natural notion of reducibility for Gorenstein polytopes. This is partly joint wor k with Christopher Borger\, Andreas Kretschmer\, and Jan Schepers.\n LOCATION:https://researchseminars.org/talk/CJCS/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonid Monin (MPI MiS) DTSTART:20221103T151500Z DTEND:20221103T170000Z DTSTAMP:20260422T033703Z UID:CJCS/92 DESCRIPTION:Title: K- Theory and polytopes\nby Leonid Monin (MPI MiS) as part of Copenhagen- Jerusalem Combinatorics Seminar\n\n\nAbstract\nOne can associate a commuta tive\, graded algebra which satisfies Poincare duality to a homogeneous po lynomial $f$ on a vector space $V$. One particularly interesting example o f this construction is when $f$ is the volume polynomial on a suitable spa ce of (virtual) polytopes. In this case the algebra $A_f$ recovers cohomol ogy rings of toric or flag varieties.\n\nIn my talk I will explain these r esults and present their recent generalizations. In particular\, I will ex plain how to associate an algebra with Gorenstein duality to any function $g$ on a lattice $L.$ In the case when $g$ is the Ehrhart function on a la ttice of integer (virtual) polytopes\, this construction recovers K-theory of toric and full flag varieties.\n LOCATION:https://researchseminars.org/talk/CJCS/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Ayah Almousa (University of Minnesota - Twin Cities) DTSTART:20221201T151500Z DTEND:20221201T170000Z DTSTAMP:20260422T033703Z UID:CJCS/93 DESCRIPTION:Title: Ro ot Polytopes\, Tropical Types\, and Toric Edge Ideals\nby Ayah Almousa (University of Minnesota - Twin Cities) as part of Copenhagen-Jerusalem C ombinatorics Seminar\n\n\nAbstract\nThis is joint work with Anton Dochterm ann (Texas State) and Ben Smith (Manchester). We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to infi nity in certain directions. Such an arrangement defines a decomposition of Euclidean space where a cell is determined by its `type' data\, analogous to the covectors of an oriented matroid. By work of Develin-Sturmfels and Fink-Rincón\, these `tropical complexes' are dual to (regular) subdivisi ons of root polytopes\, which in turn are in bijection with mixed subdivis ions of certain generalized permutohedra. Extending previous work with Jos wig-Sanyal\, we show how a natural monomial labeling of these complexes de scribes polynomial relations (syzygies) among `type ideals' which arise na turally from the combinatorial data of the arrangement. In particular\, we show that the cotype ideal is Alexander dual to a corresponding initial i deal of the lattice ideal of the underlying root polytope. This leads to n ovel ways of studying algebraic properties of various monomial and toric i deals\, as well as relating them to combinatorial and geometric properties . In particular\, our methods of studying the dimension of the tropical co mplex leads to new formulas for homological invariants of toric edge ideal s of bipartite graphs\, which have been extensively studied in the commuta tive algebra community.\n LOCATION:https://researchseminars.org/talk/CJCS/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Daria Poliakova (University of Southern Denmark) DTSTART:20221208T151500Z DTEND:20221208T170000Z DTSTAMP:20260422T033703Z UID:CJCS/94 DESCRIPTION:Title: 2- Associahedra and the velocity fan\nby Daria Poliakova (University of S outhern Denmark) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n Lecture held in Aud. 9 HCØ (KU).\n\nAbstract\nAssociahedra are polytopes that encode homotopy associativity and allow for the definition of A-infin ity categories. There are numerous polytopal realizations of associahedra\ , my favourite being due to Loday.\n\nNate Bottman introduced a family of abstract polytopes called 2-associahedra\, that should stand behind the th eory of (A-infinity\,2)-categories. While an associahedron K(n) compactif ies the moduli space of configurations of n points on a line\, a 2-associ ahedron K(n_1\, ... \, n_k) compactifies the moduli space of configuration s of k lines\, with n_i points on the line number i. The combinatorics of this object is rather intricate\, and the question of finding a polytopal realization is difficult.\n\nIn my talk\, I will define 2-associahedra and tell about our recent construction of complete fans realizing these abstr act polytopes. We are currently working to prove that these fans are proje ctive. Some cases are settled\, so there will be 3D pictures.\n LOCATION:https://researchseminars.org/talk/CJCS/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Early (MPI MiS) DTSTART:20221215T151500Z DTEND:20221215T170000Z DTSTAMP:20260422T033703Z UID:CJCS/95 DESCRIPTION:Title: Po lytopes in particle physics\, starting from associahedra\nby Nick Earl y (MPI MiS) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbs tract\nThe combinatorics of the associahedron provides a key to understand ing the behavior of scattering amplitudes in theoretical particle physics. In this talk\, we will explore a physics-inspired construction of a two- parameter family of polytopes -- and their curvy analogs -- which have pre scribed sets of $\\binom{n}{k}-n$ facet directions\; associahedra provide the base case when $k=2$.\n LOCATION:https://researchseminars.org/talk/CJCS/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Miruna-Ştefana Sorea (SISSA) DTSTART:20230112T151500Z DTEND:20230112T170000Z DTSTAMP:20260422T033703Z UID:CJCS/96 DESCRIPTION:Title: Po incaré-Reeb Graphs of Real Algebraic Domains\nby Miruna-Ştefana Sore a (SISSA) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr act\nConsider a real bivariate polynomial function that has a strict local minimum at the origin and that vanishes at this point. In a sufficiently small neighborhood of the origin\, the non-zero level curves of this funct ion are smooth Jordan curves. Whenever the origin is a Morse strict local minimum\, the small enough level curves become boundaries of convex topolo gical disks. Otherwise\, the levels may be non-convex\, as was proven by M . Coste. In order to measure this non-convexity\, we introduce a combinato rial object called the Poincaré-Reeb tree associated to a level curve and to a projection direction. Our goal is to characterize all topological ty pes of Poincaré-Reeb trees. I will explain how to construct a family of p olynomials that realizes a large class of these trees. Moreover\, in a joi nt work with Arnaud Bodin and Patrick Popescu-Pampu\, we extend the previo us method of study of non-convexity to real algebraic domains.\n LOCATION:https://researchseminars.org/talk/CJCS/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Damian Osajda (KU) DTSTART:20230105T151500Z DTEND:20230105T170000Z DTSTAMP:20260422T033703Z UID:CJCS/97 DESCRIPTION:Title: In jective spaces\, Helly graphs\, and their automorphism groups\nby Dami an Osajda (KU) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\nLe cture held in Aud. 5 HCØ (KU).\n\nAbstract\nInjective metric spaces are c lassical and important (injective) objects studied within metric geometry. Their combinatorial counterpart are Helly graphs.\nI will present basic f acts in the two settings and show how they relate to each other.\nThen I w ill focus on groups acting by automorphisms on Helly graphs. Recently\, \n it has been shown that many classical groups\, including Gromov hyperbolic \ngroups\, Garside groups\, CAT(0) cubical groups\, and braid groups act " nicely"\non Helly graphs. This allows one to obtain new results on these c lassical groups\,\nusing nonpositive-curvature-like behavior of Helly grap hs.\n LOCATION:https://researchseminars.org/talk/CJCS/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Cosmin Pohoata (IAS School of Math) DTSTART:20230209T151500Z DTEND:20230209T170000Z DTSTAMP:20260422T033703Z UID:CJCS/98 DESCRIPTION:Title: Co nvexity\, color avoidance\, and total domination\nby Cosmin Pohoata (I AS School of Math) as part of Copenhagen-Jerusalem Combinatorics Seminar\n \n\nAbstract\nIn this talk\, I will discuss a few old and new hypergraph c oloring questions which arise in the context of the Erdős-Szekeres proble m in three dimensions\, along with recent (partial) progress on some of th em and various speculations.\n LOCATION:https://researchseminars.org/talk/CJCS/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Khanh Nguyen Duc (State University of New York at Albany) DTSTART:20221222T151500Z DTEND:20221222T170000Z DTSTAMP:20260422T033703Z UID:CJCS/99 DESCRIPTION:Title: Ne wton polytope of good symmetric functions\nby Khanh Nguyen Duc (State University of New York at Albany) as part of Copenhagen-Jerusalem Combinat orics Seminar\n\n\nAbstract\nWe introduce a general class of symmetric fun ctions that has saturated Newton polytope and their Newton polytope has in teger decomposition property. The class covers numerous previously studied symmetric functions.\n LOCATION:https://researchseminars.org/talk/CJCS/99/ END:VEVENT BEGIN:VEVENT SUMMARY:James Maxwell (University of Bristol) DTSTART:20230126T151500Z DTEND:20230126T170000Z DTSTAMP:20260422T033703Z UID:CJCS/100 DESCRIPTION:Title: G eneralising Kapranov’s Theorem for hyperfields and RAC maps\nby Jame s Maxwell (University of Bristol) as part of Copenhagen-Jerusalem Combinat orics Seminar\n\n\nAbstract\nKapranov’s theorem is a foundational result in tropical geometry. In this talk\nwe will discuss developments towards understanding a generalised hyperfield\nversion of Kapranov’s Theorem. W e will establish the relevant building blocks\nfrom the algebraic setting of hyperfields\, which allow addition to be multival-\nued operation. We w ill then introduce Relatively Algebraically Closed (RAC)\nhyperfield homom orphisms. This property is the key tool leveraged to formulate\na generali sed version of Kapranov’s theorem. I will present examples of RAC\nmaps and describe the progress towards the classification of this property. \n\ nThis will contain joint work with Ben Smith (Manchester).\n LOCATION:https://researchseminars.org/talk/CJCS/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladislav Pokidkin DTSTART:20230202T151500Z DTEND:20230202T161500Z DTSTAMP:20260422T033703Z UID:CJCS/101 DESCRIPTION:Title: D iscriminants of polynomial systems\nby Vladislav Pokidkin as part of C openhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe space of all systems of polynomial equations with prescribed Newton polytopes contains the discriminant - the set of all systems with a degenerate root. The stud y of such discriminants (so called A-discriminants) was initiated by Gelfa nd\, Kapranov\, Zelevinsky and Sturmfels in 1990th. We make a review of ex isting results about the structure of discriminants and provide a conjectu re about its number of irreducible components and their codimensions for t uples of Newton polytopes with positive mixed volume.\n LOCATION:https://researchseminars.org/talk/CJCS/101/ END:VEVENT BEGIN:VEVENT SUMMARY:István Tomon (Umeå University) DTSTART:20230302T151500Z DTEND:20230302T170000Z DTSTAMP:20260422T033703Z UID:CJCS/102 DESCRIPTION:Title: C onfigurations of boxes\nby István Tomon (Umeå University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nConfigurations of axis-parallel boxes in $\\mathbb{R}^d$ are extensively studied in combi natorial and computational geometry. Despite their innocent appearance\, t here are many old problems involving their structure that are still not we ll understood. I will talk about a construction\, which addresses several of these problems\, and shows that configurations of boxes may be more com plex than people conjectured.\n LOCATION:https://researchseminars.org/talk/CJCS/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Janzer (Trinity College\, Cambridge) DTSTART:20230119T151500Z DTEND:20230119T170000Z DTSTAMP:20260422T033703Z UID:CJCS/103 DESCRIPTION:Title: S mall subgraphs with large average degree\nby Oliver Janzer (Trinity Co llege\, Cambridge) as part of Copenhagen-Jerusalem Combinatorics Seminar\n \n\nAbstract\nWe study the fundamental problem of finding small dense subg raphs in a given graph. For a real number s>2\, we prove that every graph on n vertices with average degree at least d contains a subgraph of averag e degree at least s on at most nd^{-s/(s-2)}(log d)^{O_s(1)} vertices. Thi s is optimal up to the polylogarithmic factor\, and resolves a conjecture of Feige and Wagner. In addition\, we show that every graph with n vertice s and average degree at least n^{1-2/s+eps} contains a subgraph of average degree at least s on O_{eps\,s}(1) vertices\, which is also optimal up to the constant hidden in the O(.) notation\, and resolves a conjecture of V erstraete.\n\nJoint work with Benny Sudakov and Istvan Tomon.\n LOCATION:https://researchseminars.org/talk/CJCS/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosna Paul (Graz University of Technology) DTSTART:20230316T151500Z DTEND:20230316T170000Z DTSTAMP:20260422T033703Z UID:CJCS/104 DESCRIPTION:Title: C ompatibility Graph of Spanning trees in Simple Drawings\nby Rosna Paul (Graz University of Technology) as part of Copenhagen-Jerusalem Combinato rics Seminar\n\n\nAbstract\nFor a simple drawing D of the complete graph K _n\, two\n(plane) subdrawings are compatible if their union is plane. Let T_D be\nthe set of all plane spanning trees on D and F(T_D) be the compati bility\ngraph that has a vertex for each element in T_D and two vertices a re\nadjacent if and only if the corresponding trees are compatible. In thi s\ntalk\, we will show that F(T_D) is connected if D is a 2-page book\,\nm onotone\, or strongly c-monotone drawing. On the other hand\, we also focu s on the\nsubgraph of F(T_D) induced by stars\, double stars\, and twin st ars and show\nthat this subgraph will also be connected. This is a joint w ork with Oswin\nAichholzer\, Kristin Knorr\, Wolfgang Mulzer\, Nicolas El Maalouly\, Johannes\nObenaus\, Meghana M. Reddy\, Birgit Vogtenhuber\, and Alexandra Weinberger.\n LOCATION:https://researchseminars.org/talk/CJCS/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Meghana M. Reddy (ETH Zürich) DTSTART:20230309T151500Z DTEND:20230309T170000Z DTSTAMP:20260422T033703Z UID:CJCS/105 DESCRIPTION:Title: O n the Number of Edges in Maximal 2-planar Graphs\nby Meghana M. Reddy (ETH Zürich) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nA bstract\nA graph is 2-planar if it has local crossing number two\, that is \, it can be drawn in the plane such that every edge has at most two cross ings. A graph is maximal 2-planar if no edge can be added such that the re sulting graph remains 2-planar. A 2-planar graph on n vertices has at most 5n-10 edges\, and some (maximal) 2-planar graphs---referred to as optimal 2-planar---achieve this bound. However\, in strong contrast to maximal pl anar graphs\, a maximal 2-planar graph may have fewer than the maximum pos sible number of edges. In this paper\, we determine the minimum edge densi ty of maximal 2-planar graphs by proving that every maximal 2-planar graph on n vertices has at least 2n edges. We also show that this bound is tigh t\, up to an additive constant. The lower bound is based on an analysis of the degree distribution in specific classes of drawings of the graph. The upper bound construction is verified by carefully exploring the space of admissible drawings using computer support. This is joint work with Michae l Hoffmann.\n LOCATION:https://researchseminars.org/talk/CJCS/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephanie Mui (NYU Courant) DTSTART:20230223T151500Z DTEND:20230223T170000Z DTSTAMP:20260422T033703Z UID:CJCS/106 DESCRIPTION:Title: O n the $L^p$ dual Minkowski problem for $−1 < p < 0$\nby Stephanie Mu i (NYU Courant) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\ nAbstract\nThe $L^p$ dual curvature measure was introduced by Lutwak\, Yan g\, and Zhang in 2018. The associated Minkowski problem\, known as the $L^ p$ dual Minkowski problem\, asks about existence of a convex body with pre scribed $L^p$ dual curvature measure. This question unifies the previously disjoint $L^p$ Minkowski problem with the dual Minkowski problem\, two op en questions in convex geometry. In this talk\, we will discuss the existe nce of a solution to the $L^p$ dual Minkowski problem for the case of $q < p + 1\,$ $−1 < p < 0\,$ and $p\\neq q$ for even measures.\n LOCATION:https://researchseminars.org/talk/CJCS/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Geunho Lim (University of California\, Santa Barbara) DTSTART:20230216T151500Z DTEND:20230216T170000Z DTSTAMP:20260422T033703Z UID:CJCS/107 DESCRIPTION:Title: B ounds on rho-invariants and simplicial complexity of triangulated manifold s\nby Geunho Lim (University of California\, Santa Barbara) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn this talk\, we show the existence of linear bounds on various rho-invariants. In parti cular\, we construct a desired cobordism over a group\, whose complexity i s linearly bounded by that of its boundary. Employing a combinatorial conc ept of G-colored polyhedra\, we give linear bounds on Atiyah-Singer invari ants of PL manifolds. Using relative hyperbolization\, we obtain linear bo unds on Cheeger-Gromov invariants of PL manifolds endowed with a faithful representation. As applications\, we give concrete examples in the complex ity theory of high-dimensional (homotopy) lens spaces. This is a joint wor k with Shmuel Weinberger.\n LOCATION:https://researchseminars.org/talk/CJCS/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Vadim Semenov (NYU Courant) DTSTART:20230202T162000Z DTEND:20230202T172000Z DTSTAMP:20260422T033703Z UID:CJCS/108 DESCRIPTION:Title: T he Discrete Gauss Image Problem\nby Vadim Semenov (NYU Courant) as par t of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe Gauss I mage problem is a generalization to the question originally posed by Aleks androv who studied the existence of the convex body with the prescribed Al eksandrov's integral curvature. A simple discrete case of the Gauss Image Problem can be formulated as follows: given a finite set of directions in Euclidian space and the same number of unit vectors\, does there exist a c onvex polytope in this space containing the origin in its interior with ve rtices at given directions such that each normal cone at the vertex contai ns exactly one of the given vectors. In this talk\, we are going to discus s the discrete Gauss Image Problem\, and its relation to other Minkowski-t ype problems. Two different proofs of the problem are going to be addresse d: A smooth proof based on transportation polytopes and a discrete proof b ased on Helly’s theorem. Time permitting\, we will also discuss the uniq ueness statement for the problem.\n LOCATION:https://researchseminars.org/talk/CJCS/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Jany (University of Kentucky) DTSTART:20230406T141500Z DTEND:20230406T160000Z DTSTAMP:20260422T033703Z UID:CJCS/109 DESCRIPTION:Title: T he direct sum of q-matroids and their decomposition into irreducible compo nents\nby Benjamin Jany (University of Kentucky) as part of Copenhagen -Jerusalem Combinatorics Seminar\n\n\nAbstract\n$q$-Matroids\, the $q$-ana logue of matroids\, have been intensively studied in recent years in codin g theory due to their close connection with rank metric codes. In fact\, i t was shown in 2018 by Jurrius and Pellikaan that a rank metric code induc es a $q$-matroid that captures many of the code's invariants. Many results from classical matroid theory were found to have natural $q$-analogues. O ne of the major differences between classical matroids and $q$-matroids\, however\, arose with the introduction of the direct sum of $q$-matroids. In this talk\, I will discuss several combinatorial and algebraic properti es of the direct sum of $q$-matroids and show how they differ from the pro perties established for classical matroids. I will first show that similar ly to matroids\, $q$-matroids can be decomposed uniquely (up to equivalen ce) into the direct sum of irreducible components. However\, we will see t hat this result cannot be achieved via a natural analogue of the matroid n otion of connected components. I will then discuss the representability o f the direct sum of $q$-matroids. A $q$-matroid is said to be representabl e if it is induced by a rank metric code. I will show that unlike classica l matroids\, the direct sum of $q$-matroids does not necessarily preserve representability.\n LOCATION:https://researchseminars.org/talk/CJCS/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Torsten Ueckerdt (Karlsruher Institut für Technologie) DTSTART:20230420T141500Z DTEND:20230420T160000Z DTSTAMP:20260422T033703Z UID:CJCS/110 DESCRIPTION:Title: W hen Surrounding is not Catching in Cops and Robber\nby Torsten Ueckerd t (Karlsruher Institut für Technologie) as part of Copenhagen-Jerusalem C ombinatorics Seminar\n\n\nAbstract\nAfter a short introduction of the clas sical game of Cops and Robber on graphs\, we shall discuss two recently in troduced variants in which the robber only loses when he is completely sur rounded by the cops. In the first variant the robber is surrounded when he sits at a vertex v and there is at least one cop on each neighbor of v. I n the second variant cops occupy edges of the graph and the robber (still moving on vertices) is surrounded if he sits at a vertex v and there is at least one cop on each incident edge at v. We shall compare these games wi th each other and also with the classical game in which the robber is alre ady caught when one cop sits on the same vertex as the robber.\n LOCATION:https://researchseminars.org/talk/CJCS/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Faust (Texas A&M University) DTSTART:20230330T141500Z DTEND:20230330T160000Z DTSTAMP:20260422T033703Z UID:CJCS/111 DESCRIPTION:Title: O n Irreducibility of the Bloch Variety\nby Matthew Faust (Texas A&M Uni versity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstra ct\nGiven a ZZ^2 periodic graph G\, the Schrodinger operator associated to G is a graph Laplacian with a potential. After a Fourier transform we can represent our operator as a finite matrix whose entries are Laurent polyn omials. The vanishing set of this characteristic polynomial is the Bloch v ariety. Questions regarding the algebraic properties of this object are of interest in mathematical physics. We will focus our attention on the irre ducibility of this variety. Understanding the irreducibility of the Bloch variety is important in the study of the spectrum of periodic operators\, providing insight into quantum ergodicity. In this talk we will present results on preserving irreducibility of the Bloch variety after changing the period lattice. This is joint work with Jordy Lopez.\n LOCATION:https://researchseminars.org/talk/CJCS/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Schröter (Goethe-Universität Frankfurt am Main) DTSTART:20230427T141500Z DTEND:20230427T160000Z DTSTAMP:20260422T033703Z UID:CJCS/112 DESCRIPTION:Title: V aluative invariants for large classes of matroids\nby Benjamin Schröt er (Goethe-Universität Frankfurt am Main) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nValuations on polytopes are maps tha t combine the geometry of polytopes with relations in a group. It turns ou t that many important invariants of matroids are valuative on the collecti on of matroid base polytopes\, e.g.\, the Tutte polynomial and its special izations or the Hilbert–Poincaré series of the Chow ring of a matroid.\ n\nIn this talk I will present a framework that allows us to compute such invariants on large classes of matroids\, e.g.\, (sparse) paving and eleme ntary split matroids\, explicitly. The concept of split matroids introduce d by Joswig and myself is relatively new and generalize the notion of (spa rse) paving matroids. These classes appear naturally in the context of val uations and proved to be useful in other cases\, too. other cases. I will demonstrate our framework by looking at Ehrhart polynomials and further ex amples.\n\nThis talk is based on the preprint `Valuative invariants for la rge classes of matroids'. On special request I will also mention the main result of `The Merino-Welsh conjecture for split matroids' which discusses a well known conjecture on values of the Tutte polynomial. Both of these articles are joint work with Luis Ferroni.\n LOCATION:https://researchseminars.org/talk/CJCS/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Debus (Otto-von-Guericke-University Magdeburg) DTSTART:20230413T141500Z DTEND:20230413T160000Z DTSTAMP:20260422T033703Z UID:CJCS/113 DESCRIPTION:Title: T he wonderful geometry of the Vandermonde map\nby Sebastian Debus (Otto -von-Guericke-University Magdeburg) as part of Copenhagen-Jerusalem Combin atorics Seminar\n\n\nAbstract\nIn this talk we consider the geometry of th e image of the Vandermonde map consisting of the first d power sums restri cted on the probability simplex. The images form an increasing chain in th e number of variables. We describe the image for finite n and at infinity\ , and prove that it has the combinatorial structure of a cyclic polytope.\ nWe relate the image to the study of copositive symmetric forms and prove undecidability of verifying nonnegativity of trace polynomials whose domai n are all symmetric matrices of all sizes.\n\nThis is joint work with Jose Acevedo\, Greg Blekherman and Cordian Riener.\n LOCATION:https://researchseminars.org/talk/CJCS/113/ END:VEVENT BEGIN:VEVENT SUMMARY:no seminar DTSTART:20230323T151500Z DTEND:20230323T170000Z DTSTAMP:20260422T033703Z UID:CJCS/114 DESCRIPTION:Title: - ---\nby no seminar as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CJCS/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Huiberts (Columbia University in NYC) DTSTART:20230504T141500Z DTEND:20230504T160000Z DTSTAMP:20260422T033703Z UID:CJCS/115 DESCRIPTION:Title: S moothed analysis of the simplex method\nby Sophie Huiberts (Columbia U niversity in NYC) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\nThe simplex method is a combinatorial algorithm for solving l inear optimization problems. The algorithm is very efficient in practice\, but theoretical explanations of this fact are lacking. In this talk\, I w ill describe one of the primary theoretical frameworks for analysing the s implex method\, smoothed analysis\, and present upper and lower bounds on the algorithm's running time.\n LOCATION:https://researchseminars.org/talk/CJCS/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Laplante-Anfossi (University of Melbourne) DTSTART:20230518T141500Z DTEND:20230518T160000Z DTSTAMP:20260422T033703Z UID:CJCS/116 DESCRIPTION:Title: T he combinatorics of the permutahedron diagonals\nby Guillaume Laplante -Anfossi (University of Melbourne) as part of Copenhagen-Jerusalem Combina torics Seminar\n\n\nAbstract\nThe Fulton—Sturmfels formula (introduced i n 1997) gives a combinatorial-geometric way of defining the cup product on the Chow ring of toric varieties: one perturbs the normal fan of the asso ciated polytope in a generic direction and counts intersections of the res ulting complex. Starting with the Losev—Manin toric varieties (introduce d in 2000)\, associated to the permutahedron\, one is led to study generic ally translated copies of the braid arrangement. The combinatorics of the resulting hyperplane arrangements are quite interesting: one can obtain cl osed formulas for the number of facets and vertices\, and in the case of s pecific choices of perturbation that we call « operadic »\, find explici t bijections with some planar labelled bipartite trees. This allows us to recover the algebraic diagonal of Saneblidze—Umble (introduced in 2004)\ , and moreover prove by combinatorial means some purely (higher) algebraic results: for instance\, that there is exactly four universal tensor produ cts of homotopy associative algebras and morphisms. This is joint work wit h Bérénice Delcroix-Oger\, Matthieu Josuat-Vergès\, Vincent Pilaud and Kurt Stoeckl.\n LOCATION:https://researchseminars.org/talk/CJCS/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford University) DTSTART:20230511T141500Z DTEND:20230511T160000Z DTSTAMP:20260422T033703Z UID:CJCS/117 DESCRIPTION:Title: A dditive combinatorics at infinity in the presence of a lattice\nby Hun ter Spink (Stanford University) as part of Copenhagen-Jerusalem Combinator ics Seminar\n\n\nAbstract\n(Joint with Spencer Dembner) If X is a closed a lgebraic subset of C^n\, the Ax-Lindemann-Weierstrass theorem describes th e Zariski-closure of the image of X under coordinate-wise exp in (C^*)^n a s a union of algebraic subgroup cosets. Answering a question of Gallinaro\ , we give a [necessarily more complicated] description of the topological closure.\n LOCATION:https://researchseminars.org/talk/CJCS/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Iván Rasskin (TU Graz) DTSTART:20230525T141500Z DTEND:20230525T160000Z DTSTAMP:20260422T033703Z UID:CJCS/118 DESCRIPTION:Title: C onnecting numbers with knots through polytopes and sphere packings\nby Iván Rasskin (TU Graz) as part of Copenhagen-Jerusalem Combinatorics Sem inar\n\n\nAbstract\nHow many spheres are needed to construct a closed knot ted necklace? Behind this question lies a deep connection between geometri c knot theory\, sphere packings\, polytopes and number theory. In this tal k\, we will see how these different theories are linked by describing a me thod for constructing sphere packings containing optimal knotted necklaces \, which at the same time produces solutions of certain Diophantine equati ons. \nBased on joint works with Jorge Ramírez Alfonsín.\n LOCATION:https://researchseminars.org/talk/CJCS/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Tianran Chen (Auburn University at Montgomery) DTSTART:20230608T141500Z DTEND:20230608T160000Z DTSTAMP:20260422T033703Z UID:CJCS/119 DESCRIPTION:Title: W hat lattice polytopes can tell us about network of oscillators?\nby Ti anran Chen (Auburn University at Montgomery) as part of Copenhagen-Jerusal em Combinatorics Seminar\n\n\nAbstract\nLattice polytopes have found many\ , often surprising\, applications in science and engineering. We begin thi s talk with a brief review of the connections\nbetween symmetric edge poly topes and the Kuramoto equations\, which are crucial in the study of netwo rks of coupled oscillators derived from biology\, chemistry\, and engineer ing. We highlight the important information about Kuramoto equations that are encoded in the symmetric edge polytopes. We also extend this connectio n to other families of equations. Finally\, we end with an exploration on what symmetric edge polytopes can tell us about the interesting phenomenon of "oscillator death".\n LOCATION:https://researchseminars.org/talk/CJCS/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Cohen (MIT) DTSTART:20230601T141500Z DTEND:20230601T160000Z DTSTAMP:20260422T033703Z UID:CJCS/120 DESCRIPTION:Title: I mproved bound for Heilbronn's triangle problem and connections to projecti on theory\nby Alex Cohen (MIT) as part of Copenhagen-Jerusalem Combina torics Seminar\n\n\nAbstract\nWe discuss a new upper bound for the Heilbro nn triangle problem\, showing that in any set of n points placed inside th e unit square there exists a triangle with area less than C n^{-8/7-ep}. I n the course of this talk we will establish three different connections be tween Heilbronn's problem and projection theory. All joint with Cosmin Poh oata and Dmitrii Zakharov.\n LOCATION:https://researchseminars.org/talk/CJCS/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Isaiah Osborne (Middle Tennessee State University) DTSTART:20230622T141500Z DTEND:20230622T160000Z DTSTAMP:20260422T033703Z UID:CJCS/121 DESCRIPTION:Title: S ign Invertibility of Graphs\nby Isaiah Osborne (Middle Tennessee State University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb stract\nA graph is considered invertible if its adjacency matrix represent ation is also invertible. While the process of finding invertible graphs i s fairly simple\, we can also study a subfamily of invertible graphs that are sign-invertible. For our research\, a graph is considered sign-inverti ble if its graph’s adjacency matrix is invertible and its inverse is a m atrix with each entry belonging to {−1\, 0\, 1}. While the idea of sign- invertibility was first introduced in the 1980s by Bucky\, Doty and Harary \, there has been little progress toward finding a complete categorization of sign invertible graphs since then\, until Kalita and Sarma studied a s ub-family of unicyclic graphs. We provided a complete categorization of bo th invertible and s-invertible graphs with at most two cycles and a partia l characterization of sign-invertible cactus graphs.\n LOCATION:https://researchseminars.org/talk/CJCS/121/ END:VEVENT BEGIN:VEVENT SUMMARY:no seminar DTSTART:20230615T141500Z DTEND:20230615T160000Z DTSTAMP:20260422T033703Z UID:CJCS/122 DESCRIPTION:Title: - ---\nby no seminar as part of Copenhagen-Jerusalem Combinatorics Semin ar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CJCS/122/ END:VEVENT END:VCALENDAR