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BEGIN:VEVENT
SUMMARY:Manfred Scheucher (TU Berlin)
DTSTART:20210121T150000Z
DTEND:20210121T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/1
DESCRIPTION:Title: Using SAT Solvers in Combinatorics and Geometry\nby Manfred Scheuc
her (TU Berlin) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai Cheung (Harvard University)
DTSTART:20210128T150000Z
DTEND:20210128T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/2
DESCRIPTION:Title: Compactifications of cluster varieties and convexity\nby Man-Wai C
heung (Harvard University) as part of Copenhagen-Jerusalem Combinatorics S
eminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Benedetti (U Miami)
DTSTART:20210204T150000Z
DTEND:20210204T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/3
DESCRIPTION:Title: A d-dimensional version of interval graphs\, of Hamiltonian paths\, an
d of binomial edge ideals\nby Bruno Benedetti (U Miami) as part of Co
penhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe study the d-dim
ensional generalization of three mutually-related\nnotions in graph theory
: (unit)-interval graphs\, Hamiltonian cycles\, and\nbinomial edge ideals.
\n\nThis is joint work with Matteo Varbaro and Lisa Seccia (arXiv:2101.092
43).\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Manecke (University of Frankfurt)
DTSTART:20210211T150000Z
DTEND:20210211T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/4
DESCRIPTION:Title: Inscribable fans\, zonotopes\, and reflection arrangements\nby Seb
astian Manecke (University of Frankfurt) as part of Copenhagen-Jerusalem C
ombinatorics Seminar\n\n\nAbstract\nSteiner posed the question if any 3-di
mensional polytope had a\nrealization with vertices on a sphere. Steinitz
constructed the first\ncounter example and Rivin gave a complete resolutio
n. In\ndimensions 4 and up\, universality theorems by Mnev/Richter-Gebert\
nrender the question for inscribable combinatorial types hopeless.\n\nHowe
ver\, for a given complete fan N\, we can decide in polynomial time\nif th
ere is an inscribed polytope with normal fan N. Linear\nhyperplane arrange
ments can be realized as normal fans via zonotopes.\nIt turns out that ins
cribed zonotopes are rare and in this talk I\nwill focus on the question o
f classifying the corresponding\narrangements. This relates to localizaton
s and restrictions of\nreflection arrangements and Grünbaum's quest for t
he classification of \nsimplicial arrangements. The talk is based on joint
work with Raman\nSanyal.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Tancer (Charles University Prague)
DTSTART:20210218T150000Z
DTEND:20210218T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/5
DESCRIPTION:Title: The unbearable hardness of unknotting\nby Martin Tancer (Charles U
niversity Prague) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\
n\nAbstract\nDuring the talk\, I will sketch a proof that deciding if a di
agram of the unknot can be untangled using at most k Riedemeister moves (w
here k is part of the input) is NP-hard. (This is not the same as the unkn
ot recognition but it reveals some difficulties.) Similar ideas can be als
o used for proving that several other similar invariants are NP-hard to re
cognize on links.\n\nJoint work with A. de Mesmay\, Y. Rieck and E. Sedgwi
ck.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasso Petrotou (University of Ioannina)
DTSTART:20210225T150000Z
DTEND:20210225T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/6
DESCRIPTION:Title: Tom & Jerry triples\nby Vasso Petrotou (University of Ioannina) as
part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nUnproje
ction is a theory due to Reid which constructs and analyses more complicat
ed rings from simpler ones. The talk will be about a new format of unproje
ction which we call Tom & Jerry triples. As an application we will constru
ct 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://stable.researchseminars.org/talk/CJCS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Parada (TU Eindhoven)
DTSTART:20210311T150000Z
DTEND:20210311T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/7
DESCRIPTION:Title: Inserting edges into simple drawings\nby Irene Parada (TU Eindhove
n) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nSi
mple drawings of graphs are those in which each pair of edges share at mos
t one point\, either a common endpoint or a proper crossing. Given a simpl
e drawing D of a graph G\, in this talk we consider the problem of inserti
ng a given set of missing edges (edges of the complement of G) into D such
that the result is again a simple drawing. We show that it is NP-complete
to decide whether one edge can be inserted into a simple drawing. On the
positive side\, we present a Fixed-Parameter Tractable (FPT) algorithm for
this problem parameterized by the number of crossings that the edge to be
inserted can have. This algorithm is tight under the Exponential Time Hyp
othesis. We also obtain an FPT algorithm for inserting a bounded number of
edges with a bounded number of crossings. In these FPT algorithms\, after
working in the drawing\, the problem boils down to finding an algorithm f
or a labeled abstract graph. To obtain these FPT algorithms we use differe
nt tools including the sunflower lemma\, representative families for matro
ids\, and Courcelle's theorem. These techniques\, useful in many parameter
ized algorithms\, will be briefly introduced during the talk.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pilar Cano (Université Libre de Bruxelles)
DTSTART:20210304T150000Z
DTEND:20210304T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/8
DESCRIPTION:Title: Flips in higher order Delaunay triangulations\nby Pilar Cano (Univ
ersité Libre de Bruxelles) as part of Copenhagen-Jerusalem Combinatorics
Seminar\n\n\nAbstract\nWe study the flip graph of higher order Delaunay tr
iangulations. A triangulation of a set S of n points in the plane is order
-k Delaunay if for every triangle its circumcircle encloses at most k poin
ts of S. The flip graph of S has one vertex for each possible triangulatio
n of S\, and an edge connecting two vertices when the two corresponding tr
iangulations can be transformed into each other by a flip (i.e.\, exchangi
ng the diagonal of a convex quadrilateral by the other one). The flip grap
h is an essential structure in the study of triangulations\, but until now
it had been barely studied for order-k Delaunay triangulations. In this w
ork we show that\, even though the order-k flip graph might be disconnecte
d for k ≥ 3\, any order-k triangulation can be transformed into some oth
er order-k triangulation by at most k − 1 flips\, such that the intermed
iate triangulations are of order 2k − 2\, in the following settings: (1)
for any k ≥ 0 when S is in convex position\, and (2) for any k ≤ 5 an
d any point set S. Our results imply that the flip distance between two or
der-k triangulations is O(kn)\, as well as an efficient enumeration algori
thm.\n
LOCATION:https://stable.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:20260404T110742Z
UID:CJCS/9
DESCRIPTION:Title: Investigating Terao's freeness conjecture with computer algebra\nb
y Lukas Kühne (Max Planck Institute of Mathematics in the Sciences) as pa
rt of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMotivated
by singularity theory\, Hiroaki Terao introduced a module of logarithmic d
erivations associated with a hyperplane arrangement. This talk is concerne
d with Terao’s freeness conjecture which asserts that the freeness of th
is derivation module is determined by the underlying combinatorics of the
arrangement.\n\nTo investigate this conjecture\, we have enumerated all ma
troids 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
package ZariskiFrames we have computed the moduli space and the free locu
s of the derivation module of each of these matroids as a quasi-affine set
. As the main result\, this yields a computational proof of Terao’s free
ness conjecture for rank 3 arrangements with up to 14 hyperplanes in arbit
rary characteristic.\n\nIn this talk\, I will explain the background of th
is conjecture without assuming prior knowledge and demonstrate the databas
e and highlights of the computations.\n\nThis talk is based on joint work
with Mohamed Barakat\, Reimer Behrends\, Christopher Jefferson\, and Marti
n Lerner.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberon (CUNY)
DTSTART:20210325T150000Z
DTEND:20210325T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/10
DESCRIPTION:Title: Tverberg's theorem beyond prime powers\nby Pablo Soberon (CUNY) a
s part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nTverbe
rg-type theory aims to establish sufficient conditions for a simplicial co
mplex $\\Sigma$ such that every continuous map $f:\\Sigma \\to \\mathbb{R}
^d$ maps $q$ points from pairwise disjoint faces to the same point in $\\m
athbb{R}^d$. Such results are plentiful for $q$ a prime power. However\,
for $q$ with at least two distinct prime divisors\, results that guarante
e the existence of $q$-fold points of coincidence are non-existent— asid
e from immediate corollaries of the prime power case. Here we present a g
eneral method that yields such results beyond the case of prime powers. J
oint work with Florian Frick.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Torsten Mütze (University of Warwick)
DTSTART:20210506T140000Z
DTEND:20210506T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/11
DESCRIPTION:Title: Combinatorial generation via permutation languages\nby Torsten M
ütze (University of Warwick) as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\n\nAbstract\nIn this talk I present a general and versatile al
gorithmic framework for exhaustively generating a large variety of differe
nt combinatorial 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
framework: (1) the generation of pattern-avoiding permutations\; (2) the g
eneration of various classes of rectangulations\; (3) the generation of la
ttice congruences of the weak order on the symmetric group and of graph as
sociahedra.\n\nThis talk is based on joint work with Liz Hartung\, Hung P.
Hoang\, and Aaron Williams (SODA 2020)\, and with Arturo Merino (SoCG 202
1) and Jean Cardinal.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton)
DTSTART:20210408T140000Z
DTEND:20210408T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/12
DESCRIPTION:Title: Modular zeros in the character table of the symmetric group\nby S
arah Peluse (Princeton) as part of Copenhagen-Jerusalem Combinatorics Semi
nar\n\n\nAbstract\nIn 2017\, Miller conjectured\, based on computational e
vidence\, that for any fixed prime $p$ the density of entries in the chara
cter table of $S_n$ that are divisible by $p$ goes to $1$ as $n$ goes to i
nfinity. I’ll describe a proof of this conjecture\, which is joint work
with K. Soundararajan. I will also discuss the (still open) problem of det
ermining 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://stable.researchseminars.org/talk/CJCS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Felsner (TU Berlin)
DTSTART:20210422T140000Z
DTEND:20210422T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/13
DESCRIPTION:Title: Combinatorics of Pseudocircle Arrangements\nby Stefan Felsner (TU
Berlin) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstra
ct\nIn this talk we survey results for pseudocircle arrangements. Along th
e way we present several open problems. Among others we plan to touch the
following topics:\n * The taxonomy of classes of pseudocircle arrangements
.\n * The facial structure with emphasis on triangles and digons.\n * Circ
ularizability.\n * Coloring problems for pseudocircle arrangements.\nThe t
alk includes work of Grünbaum\, Snoeyink\, Pinchasi\, Scheucher\, and oth
ers.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (University of Cambridge)
DTSTART:20210513T140000Z
DTEND:20210513T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/14
DESCRIPTION:by Sean Eberhard (University of Cambridge) as part of Copenhag
en-Jerusalem Combinatorics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yufei Zhao (MIT)
DTSTART:20210429T140000Z
DTEND:20210429T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/15
DESCRIPTION:Title: The geometry of transitive sets\, with applications to eigenbasis of
Cayley graphs\nby Yufei Zhao (MIT) as part of Copenhagen-Jerusalem Com
binatorics Seminar\n\n\nAbstract\nI will discuss some counterintuitive fac
ts and conjectures about the width of a finite transitive subset of a high
dimensional sphere (here "transitive" means transitive under the orthogon
al group). We were motivated by the question of whether Cayley graphs alwa
ys have a bounded eigenbasis. I will explain this connection\, and mention
several open problems.\n\nBased on joint work with Ashwin Sah and Mehtaab
Sawhney: https://arxiv.org/abs/2005.04502 and https://arxiv.org/abs/2101.
11207\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Lackenby (University of Oxford)
DTSTART:20210520T140000Z
DTEND:20210520T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/16
DESCRIPTION:Title: Unknot recognition in quasi-polynomial time\nby Marc Lackenby (Un
iversity of Oxford) as part of Copenhagen-Jerusalem Combinatorics Seminar\
n\n\nAbstract\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 cro
ssings\, and the running time is 2^{O((log n)^3)}. The algorithm uses a wi
de variety of tools from 3-manifold theory\, including normal surfaces\, h
ierarchies and Heegaard splittings. In my talk\, I will explain this backg
round theory\, as well as explain how it fits into the algorithm.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Batyrev (Universität Tübingen)
DTSTART:20210603T141500Z
DTEND:20210603T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/17
DESCRIPTION:Title: Combinatorics of lattice polytopes and MMP\nby Victor Batyrev (Un
iversität Tübingen) as part of Copenhagen-Jerusalem Combinatorics Semina
r\n\n\nAbstract\nThe Minimal Model Program (MMP) was born in 80-ties from
attempts to extend classical results on the birational classification of
algebraic surfaces to algebraic varieties of dimension >2. The problem of
birational classification of higher dimensional algebraic varieties is
so difficult that its complete solution is not even expected. However\,
a significant progress in understanding this \nproblem can be achieved if
one restricts attention to some special and simultaneously sufficiently
rich class of algebraic varieties under consideration.\n\nThe talk suggest
s to look at the class of algebraic varieties that are birational to non-d
egenerate hypersurfaces Z in an algebraic torus T. It turns out that thi
s class is sufficiently rich to illustrate \nmany important ideas of MMP
using combinatorial properties of the Newton polytope P of the defining eq
uation of Z. The purpose of the talk is to explain the interplay between
the combinatorics of lattice polytopes and MMP which benefits from studing
its “combinatorial shadows”.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oswin Aichholzer (TU Graz)
DTSTART:20210610T141500Z
DTEND:20210610T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/18
DESCRIPTION:Title: Order Types\, Rotation Systems\, and Crossing Numbers of $K_n$\nb
y Oswin Aichholzer (TU Graz) as part of Copenhagen-Jerusalem Combinatorics
Seminar\n\n\nAbstract\nIn the area of crossing numbers we ask for minimi
zing the number of edge intersections in a drawing of a graph.\nThere is a
rich variety of crossing number problems: Which graphs do we consider\, w
hat exactly is a drawing of a graph\, and how are intersections counted? \
nIn this talk we will concentrate on the crossing number of complete graph
s embedded in the plane as either geometric\nor simple drawing. We will ha
ve a closer look at two useful combinatorial concepts for these representa
tions: order types for the\ngeometric case\, and rotation systes for the t
opological case.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miloš Stojakovic (University of Novi Sad)
DTSTART:20210624T141500Z
DTEND:20210624T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/19
DESCRIPTION:Title: Dealing with bichromatic non-crossing matchings\nby Miloš Stojak
ovic (University of Novi Sad) as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\n\nAbstract\nGiven a set of n red and n blue points in the pla
ne\, we are interested in matching red points with blue points by straight
line segments so that the segments do not cross. We develop a range of to
ols for dealing with the non-crossing matchings of points in convex positi
on. It turns out that the points naturally partition into groups that we r
efer to as orbits\, with a number of properties that prove useful for stud
ying and efficiently processing the non-crossing matchings.\n\n\nBottlenec
k matching is such a matching that minimizes the length of the longest seg
ment. Illustrating the use of the developed tools\, we show how to solve t
he problem of finding bottleneck matchings of points in convex position fa
ster than before.\n\nJoint work with Marko Savić.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaya Keller (Ariel University)
DTSTART:20210527T140000Z
DTEND:20210527T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/20
DESCRIPTION:Title: On multicolor Ramsey numbers and subset-coloring of hypergraphs\n
by Chaya Keller (Ariel University) as part of Copenhagen-Jerusalem Combina
torics Seminar\n\n\nAbstract\nThe multicolor hypergraph Ramsey number R_k(
s\,r) is the minimal n\, such that in any k-coloring of all r-element subs
ets of [n]\, there is a subset of size s\, all whose r-subsets are monochr
omatic. We present a new "stepping-up lemma" for R_k(s\,r): If R_k(s\,r)>
n\, then R_{k+3}(s+1\,r+1)>2^n. Using the lemma\, we improve some known lo
wer bounds on multicolor hypergraph Ramsey numbers.\nFurthermore\, given a
hypergraph H=(V\,E)\, we consider the Ramsey-like problem of coloring all
r-subsets of V such that no hyperedge of size >r is monochromatic. We pro
vide upper and lower bounds on the number of colors necessary in terms of
the chromatic 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 logarith
m.\n\nJoint work with Bruno Jartoux\, Shakhar Smorodinsky\, and Yelena Yud
itsky.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linda Kleist (TU Braunschweig)
DTSTART:20210617T141500Z
DTEND:20210617T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/21
DESCRIPTION:Title: On a Problem from Outer Space: Minimum Scan Covers\nby Linda Klei
st (TU Braunschweig) as part of Copenhagen-Jerusalem Combinatorics Seminar
\n\n\nAbstract\nIn this talk\, we investigate a natural geometric optimiza
tion problem motivated by questions in the context of satellite communicat
ion and astrophysics. Given a graph embedded in Euclidean space\, the *Mi
nimum Scan Cover Problem* (MSC) asks for a schedule of minimum makespan th
at *scans* all edges. In order to scan an edge\, the incident vertices rot
ate at their positions such that they face each other. Thereby\, rotations
take time proportional to the angular change. \n \nOur work reveals clos
e connections to both the graph coloring problem and the minimum cut cover
problem. 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 3D. Unless P = NP\, these insights imply that no constant-factor app
roximation exists even in 1D. Going to higher dimensions\, we discuss hard
ness and approximation results for special graph classes. The talk is base
d on joint work with Sándor Fekete and Dominik Krupke.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kwan (Stanford University)
DTSTART:20210701T141500Z
DTEND:20210701T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/22
DESCRIPTION:Title: Friendly bisections of random graphs\nby Matthew Kwan (Stanford U
niversity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst
ract\nResolving a conjecture of Füredi\, we prove that almost every n-ver
tex graph admits a partition of its vertex set into two parts of equal siz
e in which almost all vertices have more neighbours on their own side than
across. Our proof involves some new techniques for studying processes dri
ven by degree information in random graphs\, which may be of general inter
est. This is joint work with Asaf Ferber\, Bhargav Narayanan\, Ashwin Sah
and Mehtaab Sawhney.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natan Rubin (Ben-Gurion University)
DTSTART:20210708T141500Z
DTEND:20210708T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/23
DESCRIPTION:Title: Stronger bounds for weak epsilon-nets in higher dimensions\nby Na
tan Rubin (Ben-Gurion University) as part of Copenhagen-Jerusalem Combinat
orics Seminar\n\n\nAbstract\nGiven a finite point set $P$ in $R^d$\, and $
\\varepsilon>0$ we say that a point set $N$ in $R^d$ is a weak $\\varepsi
lon$-net if it pierces every convex set $K$ with $|K\\cap P|\\geq \\vareps
ilon |P|$.\n \nLet $d\\geq 3$. We show that for any finite point set in $R
^d$\, and any $\\varepsilon>0$\, there exists a weak $\\varepsilon$-net of
cardinality $O(1/\\varepsilon^{d-1/2+\\delta})$\, where $\\delta>0$ is an
arbitrary small constant. \n\n\nThis is the first improvement of the boun
d of $O^*(1/\\varepsilon^d)$ that was obtained in 1993 by Chazelle\, Edels
brunner\, Grigni\, Guibas\, Sharir\, and Welzl for general point sets in d
imension $d\\geq 3$.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford University)
DTSTART:20210715T141500Z
DTEND:20210715T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/24
DESCRIPTION:Title: Geometric and o-minimal Littlewood-Offord problems\nby Hunter Spi
nk (Stanford University) as part of Copenhagen-Jerusalem Combinatorics Sem
inar\n\n\nAbstract\n(Joint with Jacob Fox and Matthew Kwan\, no o-minimal
background required!) The classical Erdős-Littlewood-Offord theorem says
that for any n nonzero vectors in $\\mathbb{R}^d$\, a random signed sum co
ncentrates on any point with probability at most $O(n^{-1/2})$. Combining
tools from probability theory\, additive combinatorics\, and o-minimality\
, we obtain an anti-concentration probability of $n^{-1/2+o(1)}$ for any o
-minimal set $S$ in $\\mathbb{R}^d$ (such as a hypersurface defined by a p
olynomial in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a restricted anal
ytic function) not containing a line segment. We do this by showing such o
-minimal sets have no higher-order additive structure\, complementing work
by Pila on lower-order additive structure developed to count rational and
algebraic points of bounded height.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoham Letzter (University College London)
DTSTART:20210902T141500Z
DTEND:20210902T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/25
DESCRIPTION:Title: Tight cycles in hypergraphs\nby Shoham Letzter (University Colleg
e London) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr
act\nHow many edges can an r-uniform hypergraph on n vertices with no tigh
t cycles have? We determine the correct answer to this question up to a po
lylogarithmic factor\, improving on a recent result by Sudakov and Tomon.\
n
LOCATION:https://stable.researchseminars.org/talk/CJCS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Wesolek (Simon Fraser University)
DTSTART:20210909T141500Z
DTEND:20210909T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/26
DESCRIPTION:Title: Graph Drawings and Graph Limits\nby Alexandra Wesolek (Simon Fras
er University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\n
Abstract\nIn this talk we will explain a setup which shows that the theory
of graph limits introduced by Lovász et al. can be applied to intersecti
on graphs of graph drawings. In intersection graphs\, vertices correspond
to edges of the drawing\, with two vertices being connected in the interse
ction graph if the corresponding edges cross. We consider models of random
\, geodesic 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 work with Marthe Bonamy and Bojan Mohar.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Petridis (University of Georgia)
DTSTART:20210923T141500Z
DTEND:20210923T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/28
DESCRIPTION:Title: The q-analogue of almost orthogonal sets\nby Georgios Petridis (U
niversity of Georgia) as part of Copenhagen-Jerusalem Combinatorics Semina
r\n\n\nAbstract\nAn almost orthogonal set in $\\mathbb{R}^d$ is a collecti
on of vectors with the property that among any three distinct elements the
re is an orthogonal pair. The maximum size of such sets was determined by
Rosenfeld\, who verified a belief of Erdos. The same question was studied
by Ahmadi and Mohammadian in $\\mathbb{F}_q^d$. We will present a proof of
a conjecture of Ahmadi and Mohammadian and also see how it implies an “
almost” analogue of a theorem of Berlekamp on eventowns. Joint work with
Ali Mohammadi.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thang Pham (Vietnam National University)
DTSTART:20211007T141500Z
DTEND:20211007T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/29
DESCRIPTION:Title: Point-sphere incidence bounds in finite spaces\nby Thang Pham (Vi
etnam National University) as part of Copenhagen-Jerusalem Combinatorics S
eminar\n\n\nAbstract\nIn this talk\, I present an approach to study the po
int-sphere incidence problem in the vector spaces over finite fields by us
ing results from restriction theory. This is joint work with Doowon Koh an
d Sujin Lee.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Goaoc (École des Mines de Nancy)
DTSTART:20211104T151500Z
DTEND:20211104T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/30
DESCRIPTION:Title: Concentration in order types of random point sets\nby Xavier Goao
c (École des Mines de Nancy) as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\n\nAbstract\nThe order type of a planar point set is a combina
torial structure that \nencodes many of its geometric properties\, for ins
tance the face lattice \nof its convex hull or the triangulations it suppo
rts. In a sense\, it is \na generalization of the permutation associated t
o a sequence of real \nnumbers.\n\nThis talk will start with a quick intro
duction to order types. Then\, \nI'll discuss a concentration phenomenon t
hat arises when taking order \ntypes of various natural models of random p
oint sets\, and that makes \norder types hard to sample efficiently. This
will give us an occasion to \n revisit Klein's celebrated proof of the cl
assification of finite \nsubgroups of SO(3).\n\nThis is joint work with Em
o Welzl (https://arxiv.org/abs/2003.08456).\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Simkin (Harvard University)
DTSTART:20210930T141500Z
DTEND:20210930T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/31
DESCRIPTION:Title: The number of $n$-queens configurations\nby Michael Simkin (Harva
rd University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\n
Abstract\nThe $n$-queens problem is to determine $\\mathcal{Q}(n)$\, the n
umber of ways to place $n$ mutually non-threatening queens on an $n \\time
s n$ board. 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 op
timization problem in $\\mathcal{P}([-1/2\,1/2]^2)$\, the space of Borel p
robability measures on the square.\n\nThe chief innovation is the introduc
tion of limit objects for $n$-queens configurations\, which we call \\text
it{queenons}. 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 configurat
ions that approximate a given queenon. The upper bound uses the entropy me
thod. For the lower bound we describe a randomized algorithm that construc
ts a configuration near a prespecified queenon and whose entropy matches t
hat found in the upper bound. The enumeration of $n$-queens configurations
is then obtained by maximizing the (concave) entropy function in the spac
e of queenons.\n\nBased on arXiv:2107.13460\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnau Padrol (Sorbonne Université)
DTSTART:20211014T141500Z
DTEND:20211014T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/32
DESCRIPTION:Title: The convex dimension of hypergraphs and the hypersimplicial Van Kamp
en-Flores Theorem\nby Arnau Padrol (Sorbonne Université) as part of C
openhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nI will present jo
int work with Leonardo Martínez-Sandoval on the \nhypersimplicial general
ization of the linear van Kampen-Flores theorem: \nfor each n\, k and i we
determine onto which dimensions can the \n(n\,k)-hypersimplex be linearly
projected while preserving its \ni-skeleton. This is motivated by the stu
dy of the convex dimensions of \nhypergraphs. The convex dimension of a k-
uniform hypergraph is the \nsmallest dimension d for which there is an inj
ective mapping of its \nvertices into R^d such that the set of k-barycente
rs of all hyperedges \nis in convex position. Our results completely deter
mine the convex \ndimension of complete k-uniform hypergraphs. This settle
s an open \nquestion by Halman\, Onn and Rothblum\, who solved the problem
for \ncomplete graphs. We also provide lower and upper bounds for the ext
remal \nproblem of estimating the maximal number of hyperedges of k-unifor
m \nhypergraphs on n vertices with convex dimension d.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Eur (Harvard University)
DTSTART:20211021T141500Z
DTEND:20211021T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/33
DESCRIPTION:Title: Tautological classes of matroids\nby Christopher Eur (Harvard Uni
versity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstra
ct\nWe introduce a new way of geometrically studying matroids that unifies
\, recovers\, and extends several recent developments in the interaction b
etween matroid theory and algebraic geometry. Joint work with Andrew Berg
et\, Hunter Spink\, and Dennis Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Labbé (École de Technologie Supérieure Montreal)
DTSTART:20211028T141500Z
DTEND:20211028T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/34
DESCRIPTION:Title: Lineup polytopes and applications in quantum physics\nby Jean-Phi
lippe Labbé (École de Technologie Supérieure Montreal) as part of Copen
hagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe set of all possib
le spectra of 1-reduced density operators for systems of N\nparticles on a
d-dimensional Hilbert space is a polytope called hypersimplex. If\nthe sp
ectrum of the original density operators is fixed\, the set of spectra (or
dered\ndecreasingly) of 1-reduced density operators is also a polytope. A
theoretical\ndescription of this polytope using inequalities was provided
by Klyachko in the\nearly 2000’s.\nAdapting and enhancing tools from dis
crete geometry and combinatorics (symmetric\npolytopes\, sweep polytopes\,
and the Gale order)\, we obtained such necessary\ninequalities explicitly
\, that are furthermore valid for arbitrarily large N and d.\nThese may th
erefore be interpreted as generalizations of Pauli's exclusion principle\n
for fermions. In particular\, this approach leads to a new class of polyto
pes called\nlineup polytopes.\n\nThis is joint work with physicists Julia
Liebert\, Christian Schilling and mathematicians\nEva Philippe\, Federico
Castillo and Arnau Padrol.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mats Boij (KTH)
DTSTART:20211111T151500Z
DTEND:20211111T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/35
DESCRIPTION:Title: Lefschetz Properties\nby Mats Boij (KTH) as part of Copenhagen-Je
rusalem Combinatorics Seminar\n\n\nAbstract\nLefschetz properties have bee
n in focus in combinatorics and commutative algebra since Stanley’s proo
f of the g-Theorem for simplicial polytopes. I will give some background a
nd then I’ll present two projects that I have been working on recently.
The first is related to symmetric polynomial and is joint work with Miglio
re\, Nagel and Miró-Roig. The second is related to powers of general line
ar forms and is joint work with Lundqvist.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART:20211202T151500Z
DTEND:20211202T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/37
DESCRIPTION:Title: Bounding Gromov-Hausdorff distances with Borsuk-Ulam theorems and Vie
toris-Rips complexes\nby Henry Adams (Colorado State University) as pa
rt of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe Gromov
-Hausdorff distance between two metric spaces is an important tool in geom
etry\, but it is difficult to compute. For example\, the Gromov-Hausdorff
distance between unit spheres of different dimensions is unknown in nearly
all cases. I will introduce recent work by Lim\, Mémoli\, and Okutan tha
t lower bounds the Gromov-Hausdorff distance between spheres using Borsuk-
Ulam theorems. We improve these lower bounds by connecting this story to V
ietoris-Rips complexes\, providing new generalizations of Borsuk-Ulam.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Reiner (Univerity of Minnesota)
DTSTART:20211118T151500Z
DTEND:20211118T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/39
DESCRIPTION:Title: Topology of augmented Bergman complexes\nby Victor Reiner (Univer
ity of Minnesota) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\
n\nAbstract\n(based on arxiv:2108.13394\; joint with REU students E. Bullo
ck\, 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 int
roduced recently in work of Braden\, Huh\, Matherne\, Proudfoot and Wang.
It may be viewed as a hybrid of two well-studied pure shellable simplicial
complexes associated to matroids: the independent set complex and the ord
er complex of the lattice of flats.\n\nAfter recalling the relevance of th
e augmented Bergman complex in the B-H-M-P-W work\, we show that it is she
llable\, via two different families of shelling orders. Both shellings det
ermine the homotopy type\, and comparing the two answers re-interprets a k
nown convolution formula counting bases of the matroid. One of the shellin
gs leads to a surprisingly simple description for how symmetries of the ma
troid act on the homology of the complex.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jozsef Solymosi (University of British Columbia)
DTSTART:20211216T151500Z
DTEND:20211216T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/41
DESCRIPTION:Title: Rank of matrices with entries from a multiplicative group\nby Joz
sef Solymosi (University of British Columbia) as part of Copenhagen-Jerusa
lem Combinatorics Seminar\n\n\nAbstract\nWe establish lower bounds on the
rank of matrices in which all but the diagonal entries lie in a multiplica
tive group of small rank. Applying these bounds we show that the distance
sets of finite pointsets in ℝ^d generate high rank multiplicative groups
and that multiplicative groups of small rank cannot contain large sumsets
. (Joint work with Noga Alon)\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgis Petridis (University of Georgia)
DTSTART:20211215T151500Z
DTEND:20211215T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/42
DESCRIPTION:Title: Small progress towards the Paley graph conjecture\nby Giorgis Pet
ridis (University of Georgia) as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\n\nAbstract\nThe question of determining the largest independe
nt set in a Paley graph (a special kind of Cayley graph) is connected to t
he classical question of Vinogradov on determining the least quadratic non
-residue modulo a given prime. This connection will be discussed and small
progress in the state-of-the-art will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Pak (UCLA)
DTSTART:20211104T170000Z
DTEND:20211104T190000Z
DTSTAMP:20260404T110742Z
UID:CJCS/43
DESCRIPTION:Title: Log-concave poset inequalities\nby Igor Pak (UCLA) as part of Cop
enhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn the ocean of log
-concave inequalities\, there are two islands that are especially difficul
t. First\, Mason's conjectures say that the number of forests in a graph
with k edges is log-concave. More generally\, the number of independent s
ets of size k in a matroid is log-concave. Versions of these results were
established just recently\, in a remarkable series of papers inspired by
algebraic and geometric considerations. Second\, Stanley's inequality for
the numbers of linear extensions of a poset with value k at a given poset
element\, is log-concave. This was originally conjectured by Chung\, Fis
hburn and Graham\, and proved by Stanley in 1981 using the Alexandrov–Fe
nchel inequalities in convex geometry. In our recent paper\, we present a
new framework of combinatorial atlas which allows one to give elementary
proofs of both results\, and extend them in several directions. I will gi
ve an introduction to the area and then outline our approach. Joint work
with Swee Hong Chan.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Kamcev (University of Zagreb)
DTSTART:20211125T151500Z
DTEND:20211125T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/44
DESCRIPTION:Title: Common systems of equations are rare\nby Nina Kamcev (University
of Zagreb) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst
ract\nSeveral classical results in Ramsey theory (including famous theorem
s of Schur\, van der Waerden\, Rado) deal with finding monochromatic linea
r patterns in two-colourings of the integers. Our topic will be quantitati
ve extensions 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 exp
ected number of monochromatic solutions in a random two-colouring of $\\ma
thcal{F}_q^n$. Motivated by existing results for specific systems (such as
Schur triples and arithmetic progressions)\, as well as extensive researc
h on common and Sidorenko graphs\, the systematic study of common systems
of linear equations was recently initiated by Saad and Wolf. Fox\, Pham an
d Zhao characterised common linear equations. \n \nI will talk about rece
nt progress towards a classification of common systems of two or more line
ar equations. In particular\, any system containing a four-term arithmetic
progression is uncommon. This follows from a more general result which al
lows us to deduce the uncommonness of a general system from certain proper
ties of one- or two-equation subsystems.\n \nJoint work with Anita Liebena
u and Natasha Morrison.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Tech)
DTSTART:20211209T150000Z
DTEND:20211209T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/45
DESCRIPTION:Title: The Foundation of a Matroid\nby Matt Baker (Georgia Tech) as part
of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMatroid theo
rists are interested in questions concerning representability of matroids
over fields. More generally\, one can ask about representability over part
ial fields in the sense of Semple and Whittle. Pendavingh and van Zwam int
roduced the universal partial field of a matroid\, which governs the repre
sentations of over all partial fields. Unfortunately\, most matroids are n
ot representable over any partial field\, and in this case\, the universa
l partial field is not defined.\n\nOliver Lorscheid and I have introduced
a generalization of the universal partial field which we call the foundati
on of a matroid\; it is always well-defined. The foundation is a type of a
lgebraic object which we call a pasture\; pastures include both hyperfield
s and partial 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\, th
is provides a short and conceptual proof of the 1997 theorem of Lee and Sc
obee which says that a matroid is both ternary and orientable if and only
if it is dyadic.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20220203T151500Z
DTEND:20220203T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/46
DESCRIPTION:Title: The harmonic polytope\nby Laura Escobar (Washington University in
St. Louis) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbs
tract\nThis talk\, based on joint work with Federico Ardila\, is about the
harmonic polytope\, which arose in Ardila\, Denham\, and Huh’s work on
the Lagrangian 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 facets. Lastly\, we use the Bernstein-Khovanskii-Kushnirenko Theorem
to give a formula for its volume.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Sheffer (City University of New York)
DTSTART:20220310T151500Z
DTEND:20220310T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/47
DESCRIPTION:Title: A structural Szemerédi–Trotter theorem for cartesian products\
nby Adam Sheffer (City University of New York) as part of Copenhagen-Jerus
alem Combinatorics Seminar\n\n\nAbstract\nThe Szemerédi–Trotter theorem
can be considered as the fundamental theorem of geometric incidences. Thi
s combinatorial theorem has an unusually wide variety of applications\, an
d is used in combinatorics\, theoretical computer science\, harmonic analy
sis\, number theory\, model theory\, and more. Surprisingly\, hardly anyth
ing is known about the structural question - characterizing the cases wher
e the theorem is tight. We present such structural results for the case of
cartesian products. This is a basic survey talk and does not require prev
ious knowledge of the field.\n \nJoint work with Olivine Silier. Also\, a
shameless advertisement of the speaker's new book "Polynomial Methods and
Incidence Theory."\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miloš Trujić (ETH Zürich)
DTSTART:20220210T151500Z
DTEND:20220210T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/48
DESCRIPTION:Title: Two problems in (size-)Ramsey theory\nby Miloš Trujić (ETH Zür
ich) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\n
In 1978\, Erdős\, Faudree\, Rousseau\, and Schelp introduced the study of
the size-Ramsey\nnumber of a graph H\, defined as a minimum positive inte
ger m for which there exists a\ngraph G with m edges such that in every co
louring of its edges by two colours there is a\nmonochromatic copy of H. I
will discuss recent advances for two problems in this area when\nH is a l
arge graph of bounded maximum degree. This is joint work with David Conlon
and \nRajko Nenadov.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anschel Schaffer-Cohen (University of Pennsylvania)
DTSTART:20220127T161500Z
DTEND:20220127T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/49
DESCRIPTION:Title: Automorphisms of the loop and arc graph of an infinite-type surface\nby Anschel Schaffer-Cohen (University of Pennsylvania) as part of Cope
nhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe show that the ext
ended based mapping class group of an infinite-type surface is naturally i
somorphic to the automorphism group of the loop graph of that surface. Add
itionally\, we show that the extended mapping class group stabilizing a fi
nite set of punctures is isomorphic to the arc graph relative to that fini
te set of punctures. This extends a known result for sufficiently complex
finite-type surfaces\, and provides a new angle from which to study the ma
pping class groups of infinite-type surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Chavez Caliz (Pennsylvania State University)
DTSTART:20220106T161500Z
DTEND:20220106T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/50
DESCRIPTION:Title: Projective self-dual polygons\nby Ana Chavez Caliz (Pennsylvania
State University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\
n\nAbstract\nIn his book "Arnold's Problems\," Vladimir Arnold shares a co
llection of questions without answers formulated during seminars in Moscow
and Paris for over 40 years. One of these problems\, stated in 1994\, goe
s as follows:\nFind all projective curves projectively equivalent to their
duals. The answer seems to be unknown even in RP^2.\n\nMotivated by this
question\, in their paper "Self-dual polygons and self-dual curves" from 2
009\, D. Fuchs and S. Tabachnikov explore a discrete version of Arnold's q
uestion 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 transforma
tion f such that f(A_i) = B_{i+m}. \n\nIn this talk\, I will discuss how w
e can generalize Fuchs and Tabachnikov's work to polygons in higher dimens
ions. I will include some conjectures which are supported by computational
results.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arina Voorhaar (University of Geneva)
DTSTART:20220106T151500Z
DTEND:20220106T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/51
DESCRIPTION:Title: On the Newton Polytope of the Morse Discriminant\nby Arina Voorha
ar (University of Geneva) as part of Copenhagen-Jerusalem Combinatorics Se
minar\n\n\nAbstract\nA famous classical result by Gelfand\, Kapranov and Z
elevinsky provides a combinatorial description of the vertices of the Newt
on polytope of the A-discriminant (the closure of the set of all non-smoot
h hypersurfaces defined by polynomials with the given support A). Namely\,
it gives a surjection from the set of all convex triangulations of the co
nvex hull of the set A with vertices in A (or\, equivalently\, the set of
all possible combinatorial types of smooth tropical hypersurfaces defined
by tropical polynomials with support A) onto the set of vertices of this N
ewton polytope. In my talk\, I will discuss a similar problem for the Mors
e discriminant — the closure of the set of all polynomials with the give
n support A which are non-Morse if viewed as polynomial maps. Namely\, for
a 1-dimensional support set A\, there is a surjection from the set of all
possible combinatorial types of so-called Morse tropical polynomials onto
the vertices of the Newton polytope of the Morse discriminant.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Spirkl (University of Waterloo)
DTSTART:20220113T151500Z
DTEND:20220113T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/52
DESCRIPTION:Title: New results on polynomial $\\chi$-boundedness\nby Sophie Spirkl (
University of Waterloo) as part of Copenhagen-Jerusalem Combinatorics Semi
nar\n\n\nAbstract\nThe number of colours required to colour a graph $G$ (t
he chromatic number $\\chi(G)$) is at least its clique number\, that is\,
the maximum size of a set of pairwise adjacent vertices. A class of graphs
is $\\chi$-bounded if the converse is approximately true\, that is\, the
chromatic number is at most some function of the clique number. In this ta
lk\, we are interested in when this function can be chosen as a polynomial
. I will discuss some recent results\, mostly concerning the case of forbi
dding a single graph as an induced subgraph.\nJoint work with Maria Chudno
vsky\, Alex Scott and Paul Seymour.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubhangi Saraf (Rutgers University)
DTSTART:20220120T151500Z
DTEND:20220120T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/53
DESCRIPTION:Title: Factors of sparse polynomials: structural results and some algorithms
\nby Shubhangi Saraf (Rutgers University) as part of Copenhagen-Jerusa
lem Combinatorics Seminar\n\n\nAbstract\nAre factors of sparse polynomials
sparse? This is basic question\, and we are still quite far from understa
nding it in general. In this talk\, I will show that this is in some sense
true for multivariate polynomials when the polynomial has each variable a
ppearing only with bounded degree. Our sparsity bound uses techniques from
convex geometry\, such as the theory of Newton polytopes and an approxima
te version of the classical Caratheodory's Theorem. \nUsing our sparsity
bound\, we then show how to devise efficient deterministic factoring algor
ithms for sparse polynomials of bounded individual degree.\nThe talk is ba
sed on joint work with Vishwas Bhargav and Ilya Volkovich.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Gustafson (University of Kentucky)
DTSTART:20220127T151500Z
DTEND:20220127T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/54
DESCRIPTION:Title: Lattice minors and Eulerian posets\nby William Gustafson (Univers
ity of Kentucky) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n
\nAbstract\nWe introduce a notion of deletion and contraction on lattices
enriched with a generating set\, and from these operations a notion of min
ors. When considering the lattice of flats of a graph the lattice minors a
re in bijection with the simple minors of the graph when the vertices are
labeled and the edges are unlabeled. We show how this correspondence gener
alizes to the setting of polymatroids. Then we introduce the minor poset o
f a given generator enriched lattice and show these posets are Eulerian an
d PL spheres. Finally we discuss some inequalities between the cd-indices
of minor posets.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Clifton (Emory University)
DTSTART:20220217T151500Z
DTEND:20220217T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/55
DESCRIPTION:Title: Ramsey Theory for Diffsequences\nby Alexander Clifton (Emory Univ
ersity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstrac
t\nVan der Waerden's theorem states that any coloring of $\\mathbb{N}$ wit
h a finite number of colors will contain arbitrarily long monochromatic ar
ithmetic progressions. This motivates the definition of the van der Waerde
n number $W(r\,k)$ which is the smallest $n$ such that any $r$-coloring of
$\\{1\,2\,\\cdots\,n\\}$ guarantees the presence of a monochromatic arith
metic progression of length $k$.\n\nIt is natural to ask what other arithm
etic structures exhibit van der Waerden-type results. One notion\, introdu
ced by Landman and Robertson\, is that of a $D$-diffsequence\, which is an
increasing sequence $a_1 < a_2 <\\cdots< a_k$ in which the consecutive di
fferences $a_i-a_{i-1}$ all lie in some given set $D$. For each $D$ that e
xhibits a van der Waerden-type result\, we let $\\Delta(D\,k\;r)$ represen
t the analogue of the van der Waerden number $W(r\,k)$. One question of in
terest is to determine the possible behaviors of $\\Delta$ as a function o
f $k$. 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 wil
l also discuss a class of $D$'s for which no van der Waerden-type result i
s possible.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marija Jelić Milutinović (University of Belgrade)
DTSTART:20220224T151500Z
DTEND:20220224T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/56
DESCRIPTION:Title: Matching complexes of graphs\nby Marija Jelić Milutinović (Univ
ersity of Belgrade) as part of Copenhagen-Jerusalem Combinatorics Seminar\
n\n\nAbstract\nThe matching complex M(G) of a graph G is the simplicial co
mplex with the vertex set given by edges of G and faces given by subsets o
f pairwise 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 to
pology of the matching complexes of interesting classes of graphs. We will
discuss the reverse question: which simplicial complexes are matching com
plexes of graphs? In this talk we will answer this question for the homolo
gy manifolds\, with and without boundary. While in dimension 2 there are s
everal interesting manifolds\, in dimension three and higher the only matc
hing complexes are combinatorial spheres and combinatorial disks. Moreover
\, the graphs that produce manifold matching complexes are all constructed
from the disjoint union of copies of a finite set of graphs. The talk is
based on joint work with M. Bayer and B. Goeckner.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Xue (University of Washington)
DTSTART:20220127T171500Z
DTEND:20220127T180000Z
DTSTAMP:20260404T110742Z
UID:CJCS/57
DESCRIPTION:Title: A Proof of Grünbaum’s Lower Bound Conjecture for polytopes\, latti
ces\, and strongly regular pseudomanifolds.\nby Lei Xue (University of
Washington) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb
stract\nIn 1967\, Grünbaum conjectured that any $d$-dimensional polytope
with $d + s \\leq 2d$ vertices has at least $\\phi_k (d + s\, d) = {d + 1
\\choose k + 1} + { d \\choose k + 1} - { d + 1 - s \\choose k + 1}$ $k$-f
aces. In the talk\, we will prove this conjecture and discuss equality cas
es. We will then extend our results to lattices with diamond property (the
inequality part) and to strongly regular normal pseudomanifolds (the equa
lity part). We will also talk about recent results on $d$-dimensional poly
topes with $2d + 1$ or $2d + 2$ vertices.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lundqvist (Stockholm University)
DTSTART:20220317T151500Z
DTEND:20220317T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/58
DESCRIPTION:Title: The Fröberg conjecture and some questions on powers of general linea
r forms\nby Samuel Lundqvist (Stockholm University) as part of Copenha
gen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe longstanding Fröbe
rg conjecture states that there are no non-trivial relations between gener
al homogeneous polynomials. But if we replace "general homogeneous polynom
ials" by ”powers of general linear forms” it turns out that in some ca
ses there are in fact such non-trivial relations\, which may at first seem
unnatural. I will present some results and some combinatorial questions r
elated to these two classes of objects\, and will give brief connections t
o lattice paths\, the Exterior algebra\, the Lefschetz properties\, and fa
t point schemes. No previous knowledge of the Fröberg conjecture is assum
ed.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Venturello (KTH Stockholm)
DTSTART:20220331T141500Z
DTEND:20220331T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/59
DESCRIPTION:Title: Gorenstein algebras from simplicial complexes\nby Lorenzo Venture
llo (KTH Stockholm) as part of Copenhagen-Jerusalem Combinatorics Seminar\
n\n\nAbstract\nGorenstein algebras form an intriguing class of objects whi
ch often show up in combinatorics and geometry. In this talk I will presen
t a construction which associates to every pure simplicial complex a stand
ard graded Gorenstein algebra. We describe a presentation of this algebra
as a polynomial ring modulo an ideal generated by monomials and pure binom
ials. When the simplicial complex is flag\, i.e.\, it is the clique comple
x of its graph\, our main results establish equivalences between well stud
ied properties of the complex (being S_2\, Cohen-Macaulay\, Shellable) wit
h those of the algebra (being quadratic\, Koszul\, having a quadratic GB).
Finally\, we study the h-vector of the Gorenstein algebras in our constru
ction and answer a question of Peeva and Stillman by showing that it is ve
ry often not gamma-positive. This is joint work with Alessio D'Alì.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Suk (UC San Diego)
DTSTART:20220428T141500Z
DTEND:20220428T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/60
DESCRIPTION:Title: Unavoidable patterns in simple topological graphs\nby Andrew Suk
(UC San Diego) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\n
Abstract\nA simple topological graph is a graph drawn in the plane so that
its vertices are represented by points\, and its edges are represented by
non-self-intersecting arcs connecting the corresponding points\, with the
property that any two edges have at most one point in common. In 2003\,
Pach-Solymosi-Toth showed that every n-vertex complete simple topological
graph contains a topological subgraph on m = Omega(\\log^{1/8} n) vertices
that is weakly isomorphic to the complete convex geometric graph or to th
e complete 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://stable.researchseminars.org/talk/CJCS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Machado (University of Cambridge)
DTSTART:20220407T141500Z
DTEND:20220407T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/61
DESCRIPTION:Title: When are discrete subsets of Lie groups approximate subgroups ? Aroun
d a theorem of Lagarias.\nby Simon Machado (University of Cambridge) a
s part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMeyer
sets are fascinating objects: they are aperiodic subsets of Euclidean spac
es that nonetheless exhibit long-range aperiodic order. Sets of vertices o
f the Penrose tiling (P3) and Pisot—Vijarayaghavan numbers of a real num
ber field are some of the most well-known examples. In modern lingo\, they
can be defined as the discrete and co-compact approximate subgroups of Eu
clidean spaces.\n\nLagarias found an elegant characterisation of Meyer set
s: they are those subsets X of a Euclidean space E that are relatively den
se (any point of E is within uniformly bounded distance of X) and whose Mi
nkowski difference X - X is uniformly discrete (the distance between any t
wo points is uniformly bounded below). In essence\, his theorem provides a
characterisation of discrete approximate subgroups that is analogous to t
he Plunnecke—Ruzsa theorem about sets of small doubling.\n\nI will discu
ss the general theory of Meyer sets and state Lagarias theorem. I will exp
lain how additive combinatorics can be used to extend Lagarias result to d
iscrete subsets of amenable groups. Going beyond the framework of amenable
groups\, I will talk about how one can use simple ideas from additive com
binatorics in combination with powerful tools from ergodic theory - such a
s Zimmer’s cocycle superrigidity - to generalise Lagarias theorem to dis
crete subsets of $SL_n(\\mathbb{R})$ for n > 2.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Lew (Technion)
DTSTART:20220217T161500Z
DTEND:20220217T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/62
DESCRIPTION:Title: Leray numbers of tolerance complexes\nby Alan Lew (Technion) as p
art of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn this
talk we will discuss the Leray and collapsibility numbers of a
simplicial complex K\, and their role in Helly-type theorems in com
binatorial geometry. The Leray number is\, roughly speaking\, the heredit
ary homological dimension of K\, while the collapsibility number captures
the complexity of dismantling K by sequentially removing free faces from K
.\nFollowing the formal definition of these parameters and their connectio
n to the combinatorics of convex sets\, we will introduce the construction
of the “tolerance complex” of a complex K. We will explain its relat
ion to a tolerant version of Helly’s theorem due to Montejano and Oliver
os and present new results on the Leray numbers of these complexes.\nThe t
alk is based on joint work with Minki Kim.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubhangi Saraf (University of Toronto)
DTSTART:20220303T151500Z
DTEND:20220303T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/63
DESCRIPTION:Title: Factors of sparse polynomials: structural results and some algorithms
\nby Shubhangi Saraf (University of Toronto) as part of Copenhagen-Jer
usalem Combinatorics Seminar\n\n\nAbstract\nAre factors of sparse polynomi
als sparse? This is basic question\, and we are still quite far from under
standing it in general. In this talk\, I will show that this is in some se
nse true for multivariate polynomials when the polynomial has each variabl
e appearing only with bounded degree. Our sparsity bound uses techniques f
rom convex geometry\, such as the theory of Newton polytopes and an approx
imate version of the classical Caratheodory's Theorem. \nUsing our sparsi
ty bound\, we then show how to devise efficient deterministic factoring al
gorithms for sparse polynomials of bounded individual degree.\nThe talk is
based on joint work with Vishwas Bhargav and Ilya Volkovich.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashwin Sah (MIT)
DTSTART:20220324T151500Z
DTEND:20220324T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/64
DESCRIPTION:Title: High-Girth Steiner Triple Systems\nby Ashwin Sah (MIT) as part of
Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe prove a 1973
conjecture due to Erdős on the existence of Steiner triple systems with
arbitrarily high girth. Our proof builds on the method of iterative absorp
tion for the existence of designs by Glock\, Kühn\, Lo\, and Osthus wh
ile incorporating a "high girth triangle removal process". In particular\,
we develop techniques to handle triangle-decompositions of polynomially s
parse graphs\, construct efficient high girth absorbers for Steiner triple
systems\, and introduce a moments technique to understand the probability
our random process includes certain configurations of triples. In this ta
lk we will also give a high-level overview of iterative absorption. This w
ork is joint with Matthew Kwan\, Mehtaab Sawhney\, and Michael Simkin.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amita Malik (Max Planck Institute for Mathematics)
DTSTART:20220421T141500Z
DTEND:20220421T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/65
DESCRIPTION:Title: Partitions into primes with a Chebotarev condition\nby Amita Mali
k (Max Planck Institute for Mathematics) as part of Copenhagen-Jerusalem C
ombinatorics Seminar\n\n\nAbstract\nIn this talk\, we discuss the asymptot
ic behavior of the number of integer partitions into primes concerning a C
hebotarev condition. In special cases\, this reduces to the study of parti
tions into primes in arithmetic progressions. While the study for ordinary
partitions goes back to Hardy and Ramanujan\, partitions into primes were
recently re-visited by Vaughan. Our error term is sharp and improves on p
revious known estimates in the special case of primes as parts of the part
ition. As an application\, monotonicity of this partition function is esta
blished explicitly via an asymptotic formula in connection to a result of
Bateman and Erdõs.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Karasev
DTSTART:20220505T141500Z
DTEND:20220505T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/66
DESCRIPTION:Title: Covering by planks and avoiding zeros of polynomials\nby Roman Ka
rasev as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\
nWe note that the recent polynomial proofs of (particular \ncases of) the
spherical and complex plank covering problems by Zhao and \nOrtega-Moreno
give some general information on zeros of real and complex \npolynomials r
estricted 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
sufficiently far from the zero set of a given \npolynomial. As a corollary
of these results\, we establish a conjecture \nof Jiang and Polyanskii ab
out covering a sphere by spherical segments \ngeneralizing the zone conjec
ture of Fejes Tóth.\n\nJoint work with Alexey Glazyrin and Alexander Poly
anskii.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Yuditsky (Université libre de Bruxelles)
DTSTART:20220512T141500Z
DTEND:20220512T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/67
DESCRIPTION:Title: Weak Coloring Numbers of Intersection Graphs\nby Yelena Yuditsky
(Université libre de Bruxelles) as part of Copenhagen-Jerusalem Combinato
rics Seminar\n\n\nAbstract\nWeak and strong coloring numbers are generaliz
ations of the degeneracy of a graph\, where for a positive integer $k$\,\n
we seek a vertex ordering such every vertex can (weakly respectively stron
gly) reach 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
interesting applications in the structural and algorithmic graph theory.\
nRecently\, Dvoràk\, McCarty\, and Norin observed a natural volume-based
upper bound for the strong coloring numbers\nof intersection graphs of wel
l-behaved objects in $\\mathbb{R}^d$\, such as homothets of a compact conv
ex object\, or comparable axis-aligned boxes.\n \nWe prove upper and lower
bounds for the $k$-th weak coloring numbers of these classes of intersect
ion graphs.\nAs a consequence\, we describe a natural graph class whose st
rong coloring numbers are polynomial in $k$\, but the weak coloring number
s\nare exponential. We also observe a surprising difference in terms of th
e dependence of the weak coloring numbers on the dimension\nbetween touchi
ng graphs of balls (single-exponential) and hypercubes (double-exponential
).\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erika Roldan (TU München)
DTSTART:20220519T141500Z
DTEND:20220519T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/68
DESCRIPTION:Title: Parity Property of Hexagonal Sliding Puzzles\nby Erika Roldan (TU
München) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst
ract\nWe study the puzzle graphs of hexagonal sliding puzzles of various s
hapes and with various numbers of holes. The puzzle graph is a combinatori
al model which captures the solvability and the complexity of sequential m
echanical puzzles. Questions relating to the puzzle graph have been previo
usly studied and resolved for the 15 Puzzle which is the most famous\, and
unsolvable\, square sliding puzzle of all times. The puzzle graph is also
a discrete model for the configuration space of hard tiles (hexagons or s
quares) moving on different tessellation-based domains. Understanding the
combinatorics of the puzzle graph leads to understanding some aspects of t
he topology of these configuration spaces.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Bouvel (LORIA)
DTSTART:20220602T141500Z
DTEND:20220602T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/69
DESCRIPTION:Title: Limits of permutations and graphs avoiding substructures\nby Math
ilde Bouvel (LORIA) as part of Copenhagen-Jerusalem Combinatorics Seminar\
n\n\nAbstract\nIn this talk\, I would like to present a survey of a series
of papers\, describing limits of random graphs or random permutations\, t
aken uniformly at random conditioned to avoid certain substructures. \nOur
first results concern families of pattern-avoiding permutations. Our appr
oach is to use the co-called substitution decomposition of permutations\,
thus encoding permutations as trees. Using analytic combinatorics\, we are
then able to compute the expected densities of patterns in our permutatio
ns. This result can be interpreted in the framework of permutons\, thus pr
oviding limit shape results for random pattern-avoiding permutations.\nAna
logous results can be obtained for hereditary classes of graphs (defined b
y the avoidance of induced subgraphs)\, following a similar methodology. T
he obtained results are limit shape results in the framework of graphons.\
n
LOCATION:https://stable.researchseminars.org/talk/CJCS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds)
DTSTART:20221006T141500Z
DTEND:20221006T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/70
DESCRIPTION:Title: Cluster structures for Grassmannians\nby Karin Baur (University o
f Leeds) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstra
ct\nThe category of Cohen Macaulay modules over a quotient of a preproject
ive algebra is a cluster category associated to the coordinate ring of the
Grassmannian Gr(k\,n). We study this category and describe some of its in
decomposable modules. We also explain how one can associate frieze pattern
s to them.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jamie Tucker-Foltz (Harvard University)
DTSTART:20220414T141500Z
DTEND:20220414T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/71
DESCRIPTION:Title: Political Redistricting\, Graph Partition Sampling\, and Counting Spa
nning Trees\nby Jamie Tucker-Foltz (Harvard University) as part of Cop
enhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nSay you are handed
a 10 X 10 grid graph and are asked to "randomly" partition the vertices in
to 10 connected subgraphs of 10 vertices each. How do you do it? From a co
mplexity perspective\, the asymptotic version of this question is largely
unanswered\, and even for these small specific parameters there are some v
ery basic things we don't know how to do efficiently.\n\nThe primary motiv
ation for these questions comes from an increasingly popular paradigm for
fairness in political redistricting whereby electoral maps are judged in c
omparison to ensembles of randomly generated maps. This is a truly amazing
area where mathematical theorems are actually having a positive societal
impact\, and the primary goal of this talk will be to inspire more interes
t 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://stable.researchseminars.org/talk/CJCS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesus de Loera (UC Davis)
DTSTART:20220526T141500Z
DTEND:20220526T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/72
DESCRIPTION:Title: On Polyhedra Parametrizing ALL pivot rules for the Simplex Method
\nby Jesus de Loera (UC Davis) as part of Copenhagen-Jerusalem Combinatori
cs Seminar\n\n\nAbstract\nThe simplex method is one of the most famous and
popular algorithms in optimization. The engine of any version of the simp
lex method is a pivot rule that selects the outgoing arc for a current ver
tex. Pivot rules come in many forms and types\, but after 80 years we are
still ignorant whether there is one that can make the simplex method run i
n polynomial time. This talk is about the polyhedral combinatorics of the
simplex method. I will present two recent positive results: For 0/1 polyto
pes there 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. Sanita). I also present a parametric analysis for all pívot rules.
We construct a polytope\, the pivot rule polytope\, that parametrizes all
memoryless pívot rules of a given LP. Its construction is a generalizatio
n of the Fiber polytope construction of Billera Sturmfels. This is an atte
mpt to get a complete picture of the structure “ space of all pivot rule
s of an LP” (joint work with A. Black\, N. Lutjeharms\, and R. Sanyal).
No prior knowledge of the simplex method will be assume\, I will only ass
ume the audience loves polytopes.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shira Zerbib (Iowa State University)
DTSTART:20220609T141500Z
DTEND:20220609T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/73
DESCRIPTION:Title: KKM-type theorems and their applications\nby Shira Zerbib (Iowa S
tate University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n
\nAbstract\nThe KKM theorem\, due to Knaster\, Kuratowski and Mazurkiewicz
in 1929\, is a topological lemma reminiscent of Sperner's lemma and Brouw
er's fixed point theorem. It has numerous applications in combinatorics\,
discrete geometry\, economics\, game theory and other areas. Generalizatio
ns of this lemma in several different directions were proved over the year
s (e.g.\, by Shapley\, Gale\, Komiya\, Soberon) and have been widely appli
ed as well. We will discuss a recent common generalization of all these th
eorems. We will also show two very different applications of KKM-type theo
rems: one is a proof of a conjecture of Eckhoff from 1994 on the line pier
cing numbers in certain families of convex sets in the plane\, and the oth
er is a theorem on fair division of multiple cakes among players with subj
ective preferences.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soohyun Park (University of Chicago)
DTSTART:20220623T141500Z
DTEND:20220623T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/74
DESCRIPTION:Title: Anti-Ramsey theory\, lattice points on polytopes\, and Hodge structur
es on toric hypersurfaces\nby Soohyun Park (University of Chicago) as
part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe rela
tion between the topics in the title is obtained by combining combinatoria
l interpretations of the simplicial chromatic polynomial. A reinterpretati
on of the definition yields the connection to edge colorings of graphs avo
iding monochromatic colorings of specified subgraphs. As for lattice point
counts on polytopes and Hodge structures on toric hypersurfaces\, we spec
ialize an expression of the polynomial in terms of the h-vector of an auxi
liary simplicial complex.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Cardinal (Université Libre de Bruxelles)
DTSTART:20220630T141500Z
DTEND:20220630T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/75
DESCRIPTION:Title: Diameter estimates for graph associahedra\nby Jean Cardinal (Univ
ersité Libre de Bruxelles) as part of Copenhagen-Jerusalem Combinatorics
Seminar\n\n\nAbstract\nGraph associahedra are generalized permutohedra ari
sing as special cases of nestohedra and hypergraphic polytopes. The graph
associahedron of a graph G encodes the combinatorics of search trees on G\
, defined recursively by a root r together with search trees on each of th
e connected components of G−r. In particular\, the skeleton of the graph
associahedron is the rotation graph of those search trees. We investigate
the diameter of graph associahedra as a function of some graph parameters
such as treedepth and treewidth\, and give tight estimates for specific f
amilies of graphs\, including trivially perfect\, complete split and compl
ete bipartite graphs. This is a joint work with Lionel Pournin and Mario V
alencia-Pabon from Université Sorbonne Paris Nord.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-Charlotte Brandenburg (MPI MiS)
DTSTART:20220811T141500Z
DTEND:20220811T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/76
DESCRIPTION:Title: Tropical Positivity and Determinantal varieties\nby Marie-Charlot
te Brandenburg (MPI MiS) as part of Copenhagen-Jerusalem Combinatorics Sem
inar\n\n\nAbstract\nA determinantal variety is the set of (d x n)-matrices
of bounded rank.\nWe study the tropicalization of the set of matrices wit
h positive entries and bounded rank\, i.e. the positive part of determinan
t varieties. Given such a (d x n)-matrix of fixed rank r\, we can interpre
t the columns of the tropicalization of this matrix as n points in d-dimen
sional space\, lying on a common r-dimensional tropical linear space. We c
onsider such tropical point configurations\, and introduce a combinatorial
criterion to characterize configurations which can be obtained from the t
ropicalization of matrices with positive entries.\nNo prior knowledge of t
ropical geometry will be assumed for this talk. This is based on joint wor
k with Georg Loho and Rainer Sinn.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehtaab Sawhney (MIT)
DTSTART:20220818T141500Z
DTEND:20220818T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/77
DESCRIPTION:Title: On low-degree dependencies for sparse random graphs\nby Mehtaab S
awhney (MIT) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb
stract\nVery sparse random graphs are known to typically be singular (i.e.
\, have singular adjacency matrix)\, due to the presence of "low-degree de
pendencies" such as isolated vertices and pairs of degree-1 vertices with
the same neighborhood. We prove that these kinds of dependencies are in so
me sense the only causes of singularity: for constants $k\\geq 3$ and $\\l
ambda>0$\, an Erdős–Rényi random graph of $n$ vertices and edge probab
ility $\\lambda/n$ typically has the property that its $k$-core (largest s
ubgraph with min-degree at least $k$) is nonsingular. This resolves a conj
ecture of Vu from the 2014 ICM\, and adds to a short list of known nonsing
ularity theorems for "extremely sparse" random matrices with density $O(1/
n)$. In subsequent work\, we draw on related techniques to give a precise
combinatorial characterization of the co-rank of the Erdős–Rényi rando
m 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 to "boost" the rank\, starting from approximate rank bounds obtainab
le from (non-quantitative) spectral convergence machinery due to Bordenave
\, Lelarge and Salez.\n\nThis talk is based on joint works with Asaf Ferbe
r\, Margalit Glasgow\, Matthew Kwan\, and Ashwin Sah.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radoslav Fulek (UC San Diego)
DTSTART:20220825T141500Z
DTEND:20220825T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/78
DESCRIPTION:Title: Atomic Embeddability\, Clustered Planarity\, and Thickenability\n
by Radoslav Fulek (UC San Diego) as part of Copenhagen-Jerusalem Combinato
rics Seminar\n\n\nAbstract\nThe planarity testing problem is the algorithm
ic problem of testing whether a given input graph is planar\, that is\, wh
ether it can be drawn in the plane without edge crossings. C-planarity was
introduced in 1995 by Feng\, Cohen\, and Eades as a generalization of gra
ph planarity\, in which the vertex set of the input graph is endowed with
a hierarchical clustering and we seek an embedding (edge crossing-free dra
wing) of the graph in the plane that respects the clustering in a certain
natural sense.\n\nThe problem of thickenability for simplicial complexes e
merged in the topology of manifolds in the 1960s. A 2-dimensional simplici
al complex is thickenable if it embeds in some orientable 3 dimensional ma
nifold.\n\nWe study the atomic embeddability testing problem\, which is a
common generalization of clustered planarity (c-planarity\, for short) and
thickenability testing\, and present a polynomial time algorithm for this
problem\, thereby giving the first polynomial time algorithm for c-planar
ity.\n\nBefore our work\, it has been an open problem whether c-planarity
can be tested efficiently\, despite relentless efforts. Recently\, Carmesi
n announced that thickenability can be tested in polynomial time. Our algo
rithm for atomic embeddability combines ideas from Carmesin's work with al
gorithmic tools previously developed for so-called weak embeddability test
ing.\n\nJoint work with Csaba Tóth.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Kock (KU)
DTSTART:20220929T140000Z
DTEND:20220929T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/79
DESCRIPTION:Title: From Möbius inversion to renormalisation\nby Joachim Kock (KU) a
s part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nAlthou
gh Möbius inversion originates in number theory\, its standard formulatio
n\, due to Rota\, is in the setting of posets\, where it is about splittin
g of intervals. It has become a standard and widely used counting device
in combinatorics and application areas. The goal of the talk is to show h
ow a slight generalisation of the Möbius inversion principle can also exp
lain (the algebraic aspect of) one of the main approaches to renormalisati
on of perturbative quantum field theories\, the so-called BPHZ renormalisa
tion (after Bogoliubov\, Parasiuk\, Hepp\, and Zimmerman)\, in the Hopf-al
gebraic formulation due to Kreimer. In the talk\, I will explain all the
words above. (In particular\, no prior knowledge of physics is assumed.)\
n\nDietary info: the talk does not contain category theory.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zilin Jiang (Arizona State University)
DTSTART:20220707T141500Z
DTEND:20220707T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/80
DESCRIPTION:Title: Rainbow structures via topological methods\nby Zilin Jiang (Arizo
na State University) as part of Copenhagen-Jerusalem Combinatorics Seminar
\n\n\nAbstract\nGiven a family of structures\, is it possible to choose an
element from each structure to form a new structure of the same kind? Thi
s new structure is poetically called rainbow because we can think of each
given structure in a different color. Some long standing combinatorial pro
blems\, such as transversals in a Latin square and the Caccetta–Haggkvis
t conjecture\, are rainbow in nature. In this talk\, we will discuss a lin
e of attacks to related problems via algebraic topology.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Castillo (Universidad Católica de Chile)
DTSTART:20220714T141500Z
DTEND:20220714T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/81
DESCRIPTION:Title: Tangent hyperplanes to convex bodies\nby Federico Castillo (Unive
rsidad Católica de Chile) as part of Copenhagen-Jerusalem Combinatorics S
eminar\n\n\nAbstract\nThe Greeks two thousand years ago already knew that
two disjoint circles have four tangent lines. We will explore this questio
n when the circles are replaced by convex bodies in arbitrary dimensions.
Bisztriczky (1990) proved that\, with the right generalization of disjoint
ness\, d convex bodies in dimension d have 2^d tangent hyperplanes. In thi
s talk we present a general description of the set of tangent hyperplanes
to m convex bodies in dimension d (with mPure-Circuit: Strong Inapproximability for PPAD\nby Alexandros Ho
llender (University of Oxford) as part of Copenhagen-Jerusalem Combinatori
cs Seminar\n\n\nAbstract\nPPAD is a complexity class that contains search
problems that are guaranteed to always have a solution. Due to its close c
onnection with topological tools such as Brouwer's fixed point theorem\, i
t has emerged as the class characterizing the complexity of many fundament
al problems in game theory and economics. In this talk\, I will introduce
the Pure-Circuit problem: a new tool for proving hardness of approximation
for problems in the class PPAD. We will see how this new technique can be
used to show tight inapproximability results for various Nash equilibrium
computation problems.\n\nBased on joint work with Argyrios Deligkas\, Joh
n Fearnley\, and Themistoklis Melissourgos.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Sauermann (MIT)
DTSTART:20220908T141500Z
DTEND:20220908T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/83
DESCRIPTION:Title: Anticoncentration in Ramsey graphs and a proof of the Erdös-McKay Co
njecture\nby Lisa Sauermann (MIT) as part of Copenhagen-Jerusalem Comb
inatorics Seminar\n\n\nAbstract\nThis talk will discuss recent joint work
with Matthew Kwan\, Ashwin Sah\, and Mehtaab Sawhney\, proving an old conj
ecture of Erdös and McKay (for which Erdős offered $100). This conjectur
e concerns Ramsey graphs\, which are (roughly speaking) graphs without lar
ge complete or empty subgraphs. In order to prove the conjecture\, we stud
y 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 discus
sing some background on Ramsey graphs\, the talk will explain our results
and give an overview of our proof approach.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Déborah Oliveros (UNAM)
DTSTART:20220915T141500Z
DTEND:20220915T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/84
DESCRIPTION:Title: Intersection Patterns and Tverberg type theorems\nby Déborah Oli
veros (UNAM) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb
stract\nOne of the most beautiful and classic theorems in Discrete Geometr
y is Tverberg’s theorem\, which says that any set with sufficiently many
points in $R^d$ can always be partitioned into m parts so that their conv
ex hulls intersect. In this talk we will give some generalizations of this
theorem that are related to some interesting computing and graph theory p
roblems as well as some cool applications.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruy Fabila Monroy (Cinvestav)
DTSTART:20220922T141500Z
DTEND:20220922T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/85
DESCRIPTION:Title: Token graph reconstruction in Diamond and C_4 free graphs\nby Ruy
Fabila Monroy (Cinvestav) as part of Copenhagen-Jerusalem Combinatorics S
eminar\n\n\nAbstract\nLet G be a graph on n vertices and 0< k Sweep polytopes and sweep oriented matroids\nby Eva Philippe (IMJ
-PRG) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\
nConsider a configuration of n labeled points in a Euclidean space. Any li
near functional gives an ordering of these points: an ordered partition th
at we call a sweep\, because we can imagine its parts as the sets of point
s successively hit by a sweeping hyperplane. The set of all such sweeps fo
rms a poset which is isomorphic to a polytope\, called the sweep polytope.
\nI will present several constructions of the sweep polytope\, related to
zonotopes\, projections of permutahedra and monotone path polytopes of zon
otopes.\n\nThis structure can also be generalized in terms of oriented mat
roids. For oriented matroids that admit a sweep oriented matroid\, we gain
precision on the topological description of their poset of cellular strin
gs\, refining a particular case of the Generalized Baues Problem.\n\nThis
is joint work with Arnau Padrol.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Søren Eilers (KU)
DTSTART:20221027T141500Z
DTEND:20221027T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/87
DESCRIPTION:Title: Chromatic numbers for contact graphs of mutually congruent cuboids\nby Søren Eilers (KU) as part of Copenhagen-Jerusalem Combinatorics Sem
inar\n\n\nAbstract\nMotivated by a wireless channel assignment problem\, R
eed & Allwright proved that there is no upper bound for the chromatic numb
ers of contact graphs for general cuboids in Euclidean space\, even when a
ll corners fall in the integer lattice. If one dimension of the cuboids is
restricted to be 1\, the cuboids will be layered\, and consequently the f
our color theorem shows that 8 colors suffice. This bound is tight by work
of Bessy\, Goncalves and Sereni.\n\nWe will study the situation when all
cuboids must be mutually congruent\, with a particular interest in what ha
ppens in cases when the rigid motion is required to preserve one or severa
l of the directions of the cuboids. We can provide non-trivial upper and l
ower bounds for the maximally occuring chromatic numbers in many cases\, b
ut only in a few instances we are able to determine these numbers fully. O
ur most satisfying result\, obtained recently with Rasmus Veber Weis Rasmu
ssen\, 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 on
ly managed to show that 5 colors are necessary after a pointed computer se
arch resulting in a large cuboid structure requiring 5 colors. \n\nThis pr
oblem has been used as a case study in a course "Experimental Mathematics
” taught in Copenhagen for more than a decade\, and as I will detail\, m
uch of what I know has been taught to me by students. My initial motivatio
n came from outreach activities associated to LEGO bricks\, and I will say
a few words about that too.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (TU Braunschweig)
DTSTART:20221117T151500Z
DTEND:20221117T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/88
DESCRIPTION:Title: Coupler curves of moving graphs and counting realizations of rigid gr
aphs\nby Boulos El Hilany (TU Braunschweig) as part of Copenhagen-Jeru
salem Combinatorics Seminar\n\n\nAbstract\nA calligraph is a graph that fo
r almost all edge length assignments moves with one degree of freedom in t
he plane\, if we fix an edge and consider the vertices as revolute joints.
\nThe trajectory of a distinguished vertex of the calligraph is called it
s coupler curve. Each calligraph corresponds to an algebraic series of rea
l curves 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
conjugate points. \n\nA graph is said to be minimally rigid if\, up to rot
ations and translations\, admits finitely many\,\nbut at least two\, reali
zations into the plane for almost all edge length assignments. \nA minimal
ly rigid graph can be expressed as a union of two calligraphs\, and the nu
mber of its \nrealizations is equal to the product of classes of those two
calligraphs. I will show how one \ncan apply those observations to produc
e an improved algorithm that counts the numbers of realizations. \nThis\,
in turn\, allows one to characterize invariants of coupler curves.\n\nThis
is a joint work with Georg Grasegger and Niels Lubbes (Symbolic computati
on group\, RICAM\, Austria)\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Haase (FU Berlin)
DTSTART:20221013T141500Z
DTEND:20221013T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/89
DESCRIPTION:Title: Newton-Okounkov Semigroups (are often not finitely generated)\nby
Christian Haase (FU Berlin) as part of Copenhagen-Jerusalem Combinatorics
Seminar\n\n\nAbstract\nI will start with a combinatorialist's crash cours
e on toric varieties which hopefully can be useful in its own right.\nAfte
r a short break\, I will talk about Newton-Okounkov theory\, which is an a
ttempt to play as much of the toric game as possible with non-toric variet
ies. The theory associates an affine semigroup with a projectively embedde
d variety and tries to draw conlclusions from the asymptotic convex geomet
ry of this semigroup. Many of these theorems assume that the semigroup is
finitely generated\, but checking finite generation seems to be hard. I wi
ll describe a combinatorial criterion\, in a slightly non-toric situation
(toric surface\, but non-toric valuation)\, characterizing finite generati
on. This is joint work with Klaus Altmann\, Alex Küronya\, Karin Schaller
& Lena Walter.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Vecchi (Università di Bologna)
DTSTART:20221020T141500Z
DTEND:20221020T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/90
DESCRIPTION:Title: Skew Young Tableaux for KL polynomials of matroids\nby Lorenzo Ve
cchi (Università di Bologna) as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\n\nAbstract\nKazhdan-Lusztig polynomials of matroids were firs
t introduced in 2016 in analogy with the classical ones for the Bruhat ord
er in Coxeter groups.\nIn 2020 it was proved that their coefficients are a
lways non-negative\, by interpreting them as the Hilbert series of the loc
al intersection cohomology of some modules associated to the matroid\; how
ever\, since these polynomials can be completely characterized only using
the lattice of flats\, a combinatorialist wonders if any result about them
can be reobtained exploiting no algebraic geometry results.\nAfter introd
ucing the operation of stressed hyperplane relaxation\, we show that we ca
n compute these coefficients by counting fillings of special skew tableaux
shapes. We will also show how these results can be interpreted using repr
esentation theory on the group of automorphisms of the matroid.\nThis is j
oint work with Luis Ferroni and George Nasr\, and Trevor Karn\, George Nas
r and Nicholas Proudfoot.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Nill (Otto-von-Guericke-Universität Magdeburg)
DTSTART:20221124T151500Z
DTEND:20221124T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/91
DESCRIPTION:Title: An update on Gorenstein polytopes : reducibility and local $h*$-polyn
omials\nby Benjamin Nill (Otto-von-Guericke-Universität Magdeburg) as
part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nReflexi
ve polytopes and more generally Gorenstein polytopes are the key objects i
n the Batyrev-Borisov mirror-symmetry construction of Calabi-Yau manifolds
in Gorenstein toric Fano varieties. Moreover\, they are beautiful combina
torial objects that appear prominently in the Ehrhart theory of lattice po
lytopes. In this talk I plan to present two recent combinatorial results r
egarding Gorenstein polytopes. First I will discuss a conjecture of Batyre
v-Juny on Gorenstein polytopes of small Ehrhart degree corresponding to Go
renstein toric Fano varieties that have highly divisible anticanonical div
isors. And second I will explain a characterization when Gorenstein polyto
pes 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-
Stapledon among others. I will highlight how underlying both results is a
natural notion of reducibility for Gorenstein polytopes. This is partly jo
int work with Christopher Borger\, Andreas Kretschmer\, and Jan Schepers.\
n
LOCATION:https://stable.researchseminars.org/talk/CJCS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Monin (MPI MiS)
DTSTART:20221103T151500Z
DTEND:20221103T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/92
DESCRIPTION:Title: K-Theory and polytopes\nby Leonid Monin (MPI MiS) as part of Cope
nhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nOne can associate a
commutative\, graded algebra which satisfies Poincare duality to a homogen
eous polynomial $f$ on a vector space $V$. One particularly interesting ex
ample of this construction is when $f$ is the volume polynomial on a suita
ble space of (virtual) polytopes. In this case the algebra $A_f$ recovers
cohomology rings of toric or flag varieties.\n\nIn my talk I will explain
these results and present their recent generalizations. In particular\, I
will explain how to associate an algebra with Gorenstein duality to any fu
nction $g$ on a lattice $L.$ In the case when $g$ is the Ehrhart function
on a lattice of integer (virtual) polytopes\, this construction recovers K
-theory of toric and full flag varieties.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayah Almousa (University of Minnesota - Twin Cities)
DTSTART:20221201T151500Z
DTEND:20221201T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/93
DESCRIPTION:Title: Root Polytopes\, Tropical Types\, and Toric Edge Ideals\nby Ayah
Almousa (University of Minnesota - Twin Cities) as part of Copenhagen-Jeru
salem Combinatorics Seminar\n\n\nAbstract\nThis is joint work with Anton D
ochtermann (Texas State) and Ben Smith (Manchester). We consider arrangeme
nts of tropical hyperplanes where the apices of the hyperplanes are taken
to infinity in certain directions. Such an arrangement defines a decomposi
tion of Euclidean space where a cell is determined by its `type' data\, an
alogous to the covectors of an oriented matroid. By work of Develin-Sturmf
els and Fink-Rincón\, these `tropical complexes' are dual to (regular) su
bdivisions of root polytopes\, which in turn are in bijection with mixed s
ubdivisions of certain generalized permutohedra. Extending previous work w
ith Joswig-Sanyal\, we show how a natural monomial labeling of these compl
exes describes polynomial relations (syzygies) among `type ideals' which a
rise naturally from the combinatorial data of the arrangement. In particul
ar\, we show that the cotype ideal is Alexander dual to a corresponding in
itial ideal of the lattice ideal of the underlying root polytope. This lea
ds to novel ways of studying algebraic properties of various monomial and
toric ideals\, as well as relating them to combinatorial and geometric pro
perties. In particular\, our methods of studying the dimension of the trop
ical complex leads to new formulas for homological invariants of toric edg
e ideals of bipartite graphs\, which have been extensively studied in the
commutative algebra community.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daria Poliakova (University of Southern Denmark)
DTSTART:20221208T151500Z
DTEND:20221208T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/94
DESCRIPTION:Title: 2-Associahedra and the velocity fan\nby Daria Poliakova (Universi
ty of Southern Denmark) as part of Copenhagen-Jerusalem Combinatorics Semi
nar\n\nLecture held in Aud. 9 HCØ (KU).\n\nAbstract\nAssociahedra are pol
ytopes that encode homotopy associativity and allow for the definition of
A-infinity categories. There are numerous polytopal realizations of associ
ahedra\, my favourite being due to Loday.\n\nNate Bottman introduced a fam
ily of abstract polytopes called 2-associahedra\, that should stand behind
the theory of (A-infinity\,2)-categories. While an associahedron K(n) co
mpactifies the moduli space of configurations of n points on a line\, a 2
-associahedron K(n_1\, ... \, n_k) compactifies the moduli space of config
urations of k lines\, with n_i points on the line number i. The combinator
ics of this object is rather intricate\, and the question of finding a pol
ytopal realization is difficult.\n\nIn my talk\, I will define 2-associahe
dra and tell about our recent construction of complete fans realizing thes
e abstract polytopes. We are currently working to prove that these fans ar
e projective. Some cases are settled\, so there will be 3D pictures.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Early (MPI MiS)
DTSTART:20221215T151500Z
DTEND:20221215T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/95
DESCRIPTION:Title: Polytopes in particle physics\, starting from associahedra\nby Ni
ck Early (MPI MiS) as part of Copenhagen-Jerusalem Combinatorics Seminar\n
\n\nAbstract\nThe combinatorics of the associahedron provides a key to und
erstanding the behavior of scattering amplitudes in theoretical particle p
hysics. In this talk\, we will explore a physics-inspired construction of
a two-parameter family of polytopes -- and their curvy analogs -- which h
ave prescribed sets of $\\binom{n}{k}-n$ facet directions\; associahedra p
rovide the base case when $k=2$.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Ştefana Sorea (SISSA)
DTSTART:20230112T151500Z
DTEND:20230112T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/96
DESCRIPTION:Title: Poincaré-Reeb Graphs of Real Algebraic Domains\nby Miruna-Ştefa
na Sorea (SISSA) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n
\nAbstract\nConsider a real bivariate polynomial function that has a stric
t local minimum at the origin and that vanishes at this point. In a suffic
iently small neighborhood of the origin\, the non-zero level curves of thi
s function are smooth Jordan curves. Whenever the origin is a Morse strict
local minimum\, the small enough level curves become boundaries of convex
topological disks. Otherwise\, the levels may be non-convex\, as was prov
en by M. Coste. In order to measure this non-convexity\, we introduce a co
mbinatorial object called the Poincaré-Reeb tree associated to a level cu
rve and to a projection direction. Our goal is to characterize all topolog
ical types of Poincaré-Reeb trees. I will explain how to construct a fami
ly of polynomials that realizes a large class of these trees. Moreover\, i
n a joint work with Arnaud Bodin and Patrick Popescu-Pampu\, we extend the
previous method of study of non-convexity to real algebraic domains.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damian Osajda (KU)
DTSTART:20230105T151500Z
DTEND:20230105T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/97
DESCRIPTION:Title: Injective spaces\, Helly graphs\, and their automorphism groups\n
by Damian Osajda (KU) as part of Copenhagen-Jerusalem Combinatorics Semina
r\n\nLecture held in Aud. 5 HCØ (KU).\n\nAbstract\nInjective metric space
s are classical and important (injective) objects studied within metric ge
ometry. Their combinatorial counterpart are Helly graphs.\nI will present
basic facts in the two settings and show how they relate to each other.\nT
hen I will focus on groups acting by automorphisms on Helly graphs. Recent
ly\, \nit has been shown that many classical groups\, including Gromov hyp
erbolic\ngroups\, Garside groups\, CAT(0) cubical groups\, and braid group
s act "nicely"\non Helly graphs. This allows one to obtain new results on
these classical groups\,\nusing nonpositive-curvature-like behavior of Hel
ly graphs.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (IAS School of Math)
DTSTART:20230209T151500Z
DTEND:20230209T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/98
DESCRIPTION:Title: Convexity\, color avoidance\, and total domination\nby Cosmin Poh
oata (IAS School of Math) as part of Copenhagen-Jerusalem Combinatorics Se
minar\n\n\nAbstract\nIn this talk\, I will discuss a few old and new hyper
graph coloring questions which arise in the context of the Erdős-Szekeres
problem in three dimensions\, along with recent (partial) progress on som
e of them and various speculations.\n
LOCATION:https://stable.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:20260404T110742Z
UID:CJCS/99
DESCRIPTION:Title: Newton polytope of good symmetric functions\nby Khanh Nguyen Duc
(State University of New York at Albany) as part of Copenhagen-Jerusalem C
ombinatorics Seminar\n\n\nAbstract\nWe introduce a general class of symmet
ric functions that has saturated Newton polytope and their Newton polytope
has integer decomposition property. The class covers numerous previously
studied symmetric functions.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maxwell (University of Bristol)
DTSTART:20230126T151500Z
DTEND:20230126T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/100
DESCRIPTION:Title: Generalising Kapranov’s Theorem for hyperfields and RAC maps\n
by James Maxwell (University of Bristol) as part of Copenhagen-Jerusalem C
ombinatorics Seminar\n\n\nAbstract\nKapranov’s theorem is a foundational
result in tropical geometry. In this talk\nwe will discuss developments t
owards understanding a generalised hyperfield\nversion of Kapranov’s The
orem. We will establish the relevant building blocks\nfrom the algebraic s
etting of hyperfields\, which allow addition to be multival-\nued operatio
n. We will then introduce Relatively Algebraically Closed (RAC)\nhyperfiel
d homomorphisms. This property is the key tool leveraged to formulate\na g
eneralised version of Kapranov’s theorem. I will present examples of RAC
\nmaps and describe the progress towards the classification of this proper
ty. \n\nThis will contain joint work with Ben Smith (Manchester).\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladislav Pokidkin
DTSTART:20230202T151500Z
DTEND:20230202T161500Z
DTSTAMP:20260404T110742Z
UID:CJCS/101
DESCRIPTION:Title: Discriminants of polynomial systems\nby Vladislav Pokidkin as pa
rt of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe space
of all systems of polynomial equations with prescribed Newton polytopes co
ntains the discriminant - the set of all systems with a degenerate root. T
he study of such discriminants (so called A-discriminants) was initiated b
y Gelfand\, Kapranov\, Zelevinsky and Sturmfels in 1990th. We make a revie
w of existing results about the structure of discriminants and provide a c
onjecture about its number of irreducible components and their codimension
s for tuples of Newton polytopes with positive mixed volume.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:István Tomon (Umeå University)
DTSTART:20230302T151500Z
DTEND:20230302T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/102
DESCRIPTION:Title: Configurations of boxes\nby István Tomon (Umeå University) as
part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nConfigur
ations of axis-parallel boxes in $\\mathbb{R}^d$ are extensively studied i
n combinatorial and computational geometry. Despite their innocent appeara
nce\, there are many old problems involving their structure that are still
not well understood. I will talk about a construction\, which addresses s
everal of these problems\, and shows that configurations of boxes may be m
ore complex than people conjectured.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Janzer (Trinity College\, Cambridge)
DTSTART:20230119T151500Z
DTEND:20230119T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/103
DESCRIPTION:Title: Small subgraphs with large average degree\nby Oliver Janzer (Tri
nity College\, Cambridge) as part of Copenhagen-Jerusalem Combinatorics Se
minar\n\n\nAbstract\nWe study the fundamental problem of finding small den
se subgraphs 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
average degree at least s on at most nd^{-s/(s-2)}(log d)^{O_s(1)} vertic
es. This is optimal up to the polylogarithmic factor\, and resolves a conj
ecture of Feige and Wagner. In addition\, we show that every graph with n
vertices 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 optima
l up to the constant hidden in the O(.) notation\, and resolves a conjectu
re of Verstraete.\n\nJoint work with Benny Sudakov and Istvan Tomon.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosna Paul (Graz University of Technology)
DTSTART:20230316T151500Z
DTEND:20230316T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/104
DESCRIPTION:Title: Compatibility Graph of Spanning trees in Simple Drawings\nby Ros
na Paul (Graz University of Technology) as part of Copenhagen-Jerusalem Co
mbinatorics 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 plan
e. Let T_D be\nthe set of all plane spanning trees on D and F(T_D) be the
compatibility\ngraph that has a vertex for each element in T_D and two ver
tices are\nadjacent if and only if the corresponding trees are compatible.
In this\ntalk\, we will show that F(T_D) is connected if D is a 2-page bo
ok\,\nmonotone\, or strongly c-monotone drawing. On the other hand\, we al
so focus on the\nsubgraph of F(T_D) induced by stars\, double stars\, and
twin stars and show\nthat this subgraph will also be connected. This is a
joint work with Oswin\nAichholzer\, Kristin Knorr\, Wolfgang Mulzer\, Nico
las El Maalouly\, Johannes\nObenaus\, Meghana M. Reddy\, Birgit Vogtenhube
r\, and Alexandra Weinberger.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meghana M. Reddy (ETH Zürich)
DTSTART:20230309T151500Z
DTEND:20230309T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/105
DESCRIPTION:Title: On the Number of Edges in Maximal 2-planar Graphs\nby Meghana M.
Reddy (ETH Zürich) as part of Copenhagen-Jerusalem Combinatorics Seminar
\n\n\nAbstract\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 tw
o crossings. A graph is maximal 2-planar if no edge can be added such that
the resulting 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 max
imal planar graphs\, a maximal 2-planar graph may have fewer than the maxi
mum possible number of edges. In this paper\, we determine the minimum edg
e density of maximal 2-planar graphs by proving that every maximal 2-plana
r graph on n vertices has at least 2n edges. We also show that this bound
is tight\, up to an additive constant. The lower bound is based on an anal
ysis of the degree distribution in specific classes of drawings of the gra
ph. The upper bound construction is verified by carefully exploring the sp
ace of admissible drawings using computer support. This is joint work with
Michael Hoffmann.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephanie Mui (NYU Courant)
DTSTART:20230223T151500Z
DTEND:20230223T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/106
DESCRIPTION:Title: On the $L^p$ dual Minkowski problem for $−1 < p < 0$\nby Steph
anie Mui (NYU Courant) as part of Copenhagen-Jerusalem Combinatorics Semin
ar\n\n\nAbstract\nThe $L^p$ dual curvature measure was introduced by Lutwa
k\, Yang\, and Zhang in 2018. The associated Minkowski problem\, known as
the $L^p$ dual Minkowski problem\, asks about existence of a convex body w
ith prescribed $L^p$ dual curvature measure. This question unifies the pre
viously disjoint $L^p$ Minkowski problem with the dual Minkowski problem\,
two open questions in convex geometry. In this talk\, we will discuss the
existence 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://stable.researchseminars.org/talk/CJCS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geunho Lim (University of California\, Santa Barbara)
DTSTART:20230216T151500Z
DTEND:20230216T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/107
DESCRIPTION:Title: Bounds on rho-invariants and simplicial complexity of triangulated m
anifolds\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. I
n particular\, we construct a desired cobordism over a group\, whose compl
exity is linearly bounded by that of its boundary. Employing a combinatori
al concept of G-colored polyhedra\, we give linear bounds on Atiyah-Singer
invariants of PL manifolds. Using relative hyperbolization\, we obtain li
near bounds on Cheeger-Gromov invariants of PL manifolds endowed with a fa
ithful representation. As applications\, we give concrete examples in the
complexity theory of high-dimensional (homotopy) lens spaces. This is a jo
int work with Shmuel Weinberger.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Semenov (NYU Courant)
DTSTART:20230202T162000Z
DTEND:20230202T172000Z
DTSTAMP:20260404T110742Z
UID:CJCS/108
DESCRIPTION:Title: The Discrete Gauss Image Problem\nby Vadim Semenov (NYU Courant)
as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe
Gauss Image problem is a generalization to the question originally posed b
y Aleksandrov who studied the existence of the convex body with the prescr
ibed Aleksandrov's integral curvature. A simple discrete case of the Gauss
Image Problem can be formulated as follows: given a finite set of directi
ons in Euclidian space and the same number of unit vectors\, does there ex
ist a convex polytope in this space containing the origin in its interior
with vertices at given directions such that each normal cone at the vertex
contains exactly one of the given vectors. In this talk\, we are going to
discuss the discrete Gauss Image Problem\, and its relation to other Mink
owski-type problems. Two different proofs of the problem are going to be a
ddressed: A smooth proof based on transportation polytopes and a discrete
proof based on Helly’s theorem. Time permitting\, we will also discuss t
he uniqueness statement for the problem.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Jany (University of Kentucky)
DTSTART:20230406T141500Z
DTEND:20230406T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/109
DESCRIPTION:Title: The direct sum of q-matroids and their decomposition into irreducibl
e components\nby Benjamin Jany (University of Kentucky) as part of Cop
enhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\n$q$-Matroids\, the
$q$-analogue of matroids\, have been intensively studied in recent years i
n coding theory due to their close connection with rank metric codes. In f
act\, it was shown in 2018 by Jurrius and Pellikaan that a rank metric cod
e induces a $q$-matroid that captures many of the code's invariants. Many
results from classical matroid theory were found to have natural $q$-analo
gues. One of the major differences between classical matroids and $q$-matr
oids\, however\, arose with the introduction of the direct sum of $q$-mat
roids. In this talk\, I will discuss several combinatorial and algebraic p
roperties of the direct sum of $q$-matroids and show how they differ from
the properties established for classical matroids. I will first show that
similarly to matroids\, $q$-matroids can be decomposed uniquely (up to eq
uivalence) into the direct sum of irreducible components. However\, we wil
l see that this result cannot be achieved via a natural analogue of the ma
troid notion of connected components. I will then discuss the representab
ility of the direct sum of $q$-matroids. A $q$-matroid is said to be repre
sentable if it is induced by a rank metric code. I will show that unlike c
lassical matroids\, the direct sum of $q$-matroids does not necessarily pr
eserve representability.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Torsten Ueckerdt (Karlsruher Institut für Technologie)
DTSTART:20230420T141500Z
DTEND:20230420T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/110
DESCRIPTION:Title: When Surrounding is not Catching in Cops and Robber\nby Torsten
Ueckerdt (Karlsruher Institut für Technologie) as part of Copenhagen-Jeru
salem Combinatorics Seminar\n\n\nAbstract\nAfter a short introduction of t
he classical game of Cops and Robber on graphs\, we shall discuss two rece
ntly introduced variants in which the robber only loses when he is complet
ely surrounded 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. In 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 ther
e is at least one cop on each incident edge at v. We shall compare these g
ames with each other and also with the classical game in which the robber
is already caught when one cop sits on the same vertex as the robber.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Faust (Texas A&M University)
DTSTART:20230330T141500Z
DTEND:20230330T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/111
DESCRIPTION:Title: On Irreducibility of the Bloch Variety\nby Matthew Faust (Texas
A&M University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\
nAbstract\nGiven a ZZ^2 periodic graph G\, the Schrodinger operator associ
ated 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 Lauren
t polynomials. The vanishing set of this characteristic polynomial is the
Bloch variety. Questions regarding the algebraic properties of this object
are of interest in mathematical physics. We will focus our attention on t
he irreducibility of this variety. Understanding the irreducibility of th
e Bloch variety is important in the study of the spectrum of periodic oper
ators\, providing insight into quantum ergodicity. In this talk we will
present results on preserving irreducibility of the Bloch variety after ch
anging the period lattice. This is joint work with Jordy Lopez.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schröter (Goethe-Universität Frankfurt am Main)
DTSTART:20230427T141500Z
DTEND:20230427T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/112
DESCRIPTION:Title: Valuative invariants for large classes of matroids\nby Benjamin
Schröter (Goethe-Universität Frankfurt am Main) as part of Copenhagen-Je
rusalem Combinatorics Seminar\n\n\nAbstract\nValuations on polytopes are m
aps that combine the geometry of polytopes with relations in a group. It t
urns out that many important invariants of matroids are valuative on the c
ollection of matroid base polytopes\, e.g.\, the Tutte polynomial and its
specializations or the Hilbert–Poincaré series of the Chow ring of a ma
troid.\n\nIn this talk I will present a framework that allows us to comput
e such invariants on large classes of matroids\, e.g.\, (sparse) paving an
d elementary split matroids\, explicitly. The concept of split matroids in
troduced by Joswig and myself is relatively new and generalize the notion
of (sparse) paving matroids. These classes appear naturally in the context
of valuations and proved to be useful in other cases\, too. other cases.
I will demonstrate our framework by looking at Ehrhart polynomials and fur
ther examples.\n\nThis talk is based on the preprint `Valuative invariants
for large classes of matroids'. On special request I will also mention th
e main result of `The Merino-Welsh conjecture for split matroids' which di
scusses a well known conjecture on values of the Tutte polynomial. Both of
these articles are joint work with Luis Ferroni.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Debus (Otto-von-Guericke-University Magdeburg)
DTSTART:20230413T141500Z
DTEND:20230413T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/113
DESCRIPTION:Title: The wonderful geometry of the Vandermonde map\nby Sebastian Debu
s (Otto-von-Guericke-University Magdeburg) as part of Copenhagen-Jerusalem
Combinatorics Seminar\n\n\nAbstract\nIn this talk we consider the geometr
y of the image of the Vandermonde map consisting of the first d power sums
restricted on the probability simplex. The images form an increasing chai
n in the number of variables. We describe the image for finite n and at in
finity\, and prove that it has the combinatorial structure of a cyclic pol
ytope.\nWe relate the image to the study of copositive symmetric forms and
prove undecidability of verifying nonnegativity of trace polynomials whos
e domain are all symmetric matrices of all sizes.\n\nThis is joint work wi
th Jose Acevedo\, Greg Blekherman and Cordian Riener.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20230323T151500Z
DTEND:20230323T170000Z
DTSTAMP:20260404T110742Z
UID:CJCS/114
DESCRIPTION:Title: ----\nby no seminar as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Huiberts (Columbia University in NYC)
DTSTART:20230504T141500Z
DTEND:20230504T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/115
DESCRIPTION:Title: Smoothed analysis of the simplex method\nby Sophie Huiberts (Col
umbia University in NYC) as part of Copenhagen-Jerusalem Combinatorics Sem
inar\n\n\nAbstract\nThe simplex method is a combinatorial algorithm for so
lving linear optimization problems. The algorithm is very efficient in pra
ctice\, but theoretical explanations of this fact are lacking. In this tal
k\, I will describe one of the primary theoretical frameworks for analysin
g the simplex method\, smoothed analysis\, and present upper and lower bou
nds on the algorithm's running time.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Laplante-Anfossi (University of Melbourne)
DTSTART:20230518T141500Z
DTEND:20230518T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/116
DESCRIPTION:Title: The combinatorics of the permutahedron diagonals\nby Guillaume L
aplante-Anfossi (University of Melbourne) as part of Copenhagen-Jerusalem
Combinatorics Seminar\n\n\nAbstract\nThe Fulton—Sturmfels formula (intro
duced in 1997) gives a combinatorial-geometric way of defining the cup pro
duct on the Chow ring of toric varieties: one perturbs the normal fan of t
he associated polytope in a generic direction and counts intersections of
the resulting complex. Starting with the Losev—Manin toric varieties (in
troduced in 2000)\, associated to the permutahedron\, one is led to study
generically translated copies of the braid arrangement. The combinatorics
of the resulting hyperplane arrangements are quite interesting: one can ob
tain closed formulas for the number of facets and vertices\, and in the ca
se of specific choices of perturbation that we call « operadic »\, find
explicit 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) al
gebraic results: for instance\, that there is exactly four universal tenso
r products of homotopy associative algebras and morphisms. This is joint w
ork with Bérénice Delcroix-Oger\, Matthieu Josuat-Vergès\, Vincent Pila
ud and Kurt Stoeckl.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford University)
DTSTART:20230511T141500Z
DTEND:20230511T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/117
DESCRIPTION:Title: Additive combinatorics at infinity in the presence of a lattice\
nby Hunter Spink (Stanford University) as part of Copenhagen-Jerusalem Com
binatorics Seminar\n\n\nAbstract\n(Joint with Spencer Dembner) If X is a c
losed algebraic subset of C^n\, the Ax-Lindemann-Weierstrass theorem descr
ibes the Zariski-closure of the image of X under coordinate-wise exp in (C
^*)^n as a union of algebraic subgroup cosets. Answering a question of Gal
linaro\, we give a [necessarily more complicated] description of the topol
ogical closure.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Rasskin (TU Graz)
DTSTART:20230525T141500Z
DTEND:20230525T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/118
DESCRIPTION:Title: Connecting numbers with knots through polytopes and sphere packings<
/a>\nby Iván Rasskin (TU Graz) as part of Copenhagen-Jerusalem Combinator
ics Seminar\n\n\nAbstract\nHow many spheres are needed to construct a clos
ed knotted necklace? Behind this question lies a deep connection between g
eometric knot theory\, sphere packings\, polytopes and number theory. In t
his talk\, we will see how these different theories are linked by describi
ng a method for constructing sphere packings containing optimal knotted ne
cklaces\, which at the same time produces solutions of certain Diophantine
equations. \nBased on joint works with Jorge Ramírez Alfonsín.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianran Chen (Auburn University at Montgomery)
DTSTART:20230608T141500Z
DTEND:20230608T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/119
DESCRIPTION:Title: What lattice polytopes can tell us about network of oscillators?
\nby Tianran Chen (Auburn University at Montgomery) as part of Copenhagen-
Jerusalem Combinatorics Seminar\n\n\nAbstract\nLattice polytopes have foun
d many\, often surprising\, applications in science and engineering. We be
gin this talk with a brief review of the connections\nbetween symmetric ed
ge polytopes and the Kuramoto equations\, which are crucial in the study o
f networks of coupled oscillators derived from biology\, chemistry\, and e
ngineering. We highlight the important information about Kuramoto equation
s that are encoded in the symmetric edge polytopes. We also extend this co
nnection to other families of equations. Finally\, we end with an explorat
ion on what symmetric edge polytopes can tell us about the interesting phe
nomenon of "oscillator death".\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Cohen (MIT)
DTSTART:20230601T141500Z
DTEND:20230601T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/120
DESCRIPTION:Title: Improved bound for Heilbronn's triangle problem and connections to p
rojection theory\nby Alex Cohen (MIT) as part of Copenhagen-Jerusalem
Combinatorics Seminar\n\n\nAbstract\nWe discuss a new upper bound for the
Heilbronn triangle problem\, showing that in any set of n points placed in
side the unit square there exists a triangle with area less than C n^{-8/7
-ep}. In the course of this talk we will establish three different connect
ions between Heilbronn's problem and projection theory. All joint with Cos
min Pohoata and Dmitrii Zakharov.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaiah Osborne (Middle Tennessee State University)
DTSTART:20230622T141500Z
DTEND:20230622T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/121
DESCRIPTION:Title: Sign Invertibility of Graphs\nby Isaiah Osborne (Middle Tennesse
e State University) as part of Copenhagen-Jerusalem Combinatorics Seminar\
n\n\nAbstract\nA graph is considered invertible if its adjacency matrix re
presentation is also invertible. While the process of finding invertible g
raphs is fairly simple\, we can also study a subfamily of invertible graph
s that are sign-invertible. For our research\, a graph is considered sign-
invertible if its graph’s adjacency matrix is invertible and its inverse
is a matrix with each entry belonging to {−1\, 0\, 1}. While the idea o
f sign-invertibility was first introduced in the 1980s by Bucky\, Doty and
Harary\, there has been little progress toward finding a complete categor
ization of sign invertible graphs since then\, until Kalita and Sarma stud
ied a sub-family of unicyclic graphs. We provided a complete categorizatio
n of both invertible and s-invertible graphs with at most two cycles and a
partial characterization of sign-invertible cactus graphs.\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar
DTSTART:20230615T141500Z
DTEND:20230615T160000Z
DTSTAMP:20260404T110742Z
UID:CJCS/122
DESCRIPTION:Title: ----\nby no seminar as part of Copenhagen-Jerusalem Combinatoric
s Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CJCS/122/
END:VEVENT
END:VCALENDAR