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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Sergey Avvakumov (University of Copenhagen\, Denmark)
DTSTART:20201202T131000Z
DTEND:20201202T135000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/1
DESCRIPTION:Title: A subexponential size $\\mathbb{R}P^N$\nby Sergey Avvakumov
(University of Copenhagen\, Denmark) as part of Combinatorics and Geometr
y Days III\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberon (Baruch College\, City University of New York\, US)
DTSTART:20201202T135500Z
DTEND:20201202T143500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/2
DESCRIPTION:by Pablo Soberon (Baruch College\, City University of New York
\, US) as part of Combinatorics and Geometry Days III\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Garber (University of Texas Rio Grande Valley\, US)
DTSTART:20201202T144000Z
DTEND:20201202T152000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/3
DESCRIPTION:Title: Helly numbers for crystals and cut-and-project sets\nby Ale
xey Garber (University of Texas Rio Grande Valley\, US) as part of Combina
torics and Geometry Days III\n\n\nAbstract\nIn this talk I'll introduce He
lly numbers for (discrete) point sets and explain why finite Helly numbers
exist for periodic and certain quasiperiodic sets in Euclidean space of a
ny dimension though the bounds in the latter case seem to be extremely non
-optimal. I'll also show that for a wider class of Meyer sets Helly number
s could be infinite.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Attila Jung (Institute of Mathematics\, ELTE Eötvös Loránd Univ
ersity\, Hungary)
DTSTART:20201202T160000Z
DTEND:20201202T164000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/4
DESCRIPTION:Title: Quantitative Fractional Helly and (p\,q)-Theorems\nby Attil
a Jung (Institute of Mathematics\, ELTE Eötvös Loránd University\, Hung
ary) as part of Combinatorics and Geometry Days III\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:József Solymosi (University of British Columbia\, Canada)
DTSTART:20201203T130000Z
DTEND:20201203T134500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/5
DESCRIPTION:Title: Planar point sets with many similar triangles\nby József S
olymosi (University of British Columbia\, Canada) as part of Combinatorics
and Geometry Days III\n\n\nAbstract\nElekes and Erdős proved that for an
y triangle $T$\, there are $n$-element planar point sets with $\\Omega(n^2
)$ triangles similar to $T$. It was proved shortly after that if the numbe
r of equilateral triangles is at least $(1/6 + \\epsilon)n^2$ then the poi
ntset should contain large parts of a triangular lattice. On the other han
d\, no lattice is guaranteed for $cn^2$ similar copies if $c < 1/6$. We wi
ll show that one can still expect some structural results for triangles\,
even if the number of similar copies is as low as $n^{11/6 + \\epsilon}$.\
n\n\nJoint work with Dhruv Mubayi.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivér Janzer (ETH Zürich\, Switzerland)
DTSTART:20201203T135000Z
DTEND:20201203T143500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/6
DESCRIPTION:Title: On the Zarankiewicz problem for graphs with bounded VC-dimensio
n\nby Olivér Janzer (ETH Zürich\, Switzerland) as part of Combinator
ics and Geometry Days III\n\n\nAbstract\nThe problem of Zarankiewicz asks
for the maximum number of edges in a bipartite graph on $n$ vertices which
does not contain the complete bipartite graph $K_{k\,k}$ as a subgraph. A
classical theorem due to Kővári\, Sós and Turán says that this number
of edges is $O(n^{2 - 1/k})$. An important variant of this problem is the
analogous question in bipartite graphs with VC-dimension at most $d$\, wh
ere $d$ is a fixed integer such that $k\\ge d\\ge 1$. A remarkable result
of Fox\, Pach\, Sheffer\, Suk and Zahl with multiple applications in incid
ence geometry shows that\, under this additional hypothesis\, the number o
f edges in a bipartite graph on $n$ vertices and with no copy of $K_{k\,k}
$ as a subgraph must be $O(n^{2 - 1/d})$. This theorem is sharp when $d=2$
\, because any $K_{2\,2}$-free graph has VC-dimension at most $2$\, and th
ere are well-known examples of such graphs with $\\Omega(n^{3/2})$ edges.
However\, it turns out this phenomenon no longer carries through for any l
arger $d$.\n\n\nWe show the following improved result: the maximum number
of edges in bipartite graphs with no copies of $K_{k\, k}$\nand VC-dimensi
on at most $d$ is $o(n^{2 - 1/d})$\, for every $k \\ge~d~\\ge~3.$ \n\n\nJo
int work with Cosmin Pohoata.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Géza Tóth (Rényi Institute of Mathematics\, Hungary)
DTSTART:20201203T144500Z
DTEND:20201203T153000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/7
DESCRIPTION:Title: Crossings between non-homotopic edges\nby Géza Tóth (Rén
yi Institute of Mathematics\, Hungary) as part of Combinatorics and Geomet
ry Days III\n\n\nAbstract\nWe call a multigraph non-homotopic if it can be
drawn in the plane in such a way that no two edges connecting the same pa
ir of vertices can be continuously transformed into each other without pas
sing through a vertex\, and no loop can be shrunk to its end-vertex in the
same way. It is easy to see that a non-homotopic multigraph on $n > 1$ ve
rtices can have arbitrarily many edges. We prove that the number of crossi
ngs between the edges of a non-homotopic multigraph with $n$ vertices and
$m > 4n$ edges is larger than $c \\frac{m^2}{n}$\nfor some constant $C > 0
$\, and that this bound is tight up to a polylogarithmic factor. We also s
how that the lower bound is not asymptotically sharp as $n$ is fixed and $
m \\rightarrow \\infty$.\n\n\nJoint work with János Pach and Gábor Tardo
s.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Tsiutsiurupa (MIPT\, Russia)
DTSTART:20201202T164500Z
DTEND:20201202T172500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/8
DESCRIPTION:Title: Functional Lowner Ellipsoid\nby Igor Tsiutsiurupa (MIPT\, R
ussia) as part of Combinatorics and Geometry Days III\n\n\nAbstract\nWe ex
tend the notion of the smallest volume ellipsoid containing a convex body
in to the setting of logarithmically concave functions. We consider a vast
class of logarithmically concave functions whose superlevel sets are conc
entric ellipsoids. For a fixed function from this class\, we consider the
set of all its "affine" positions. For any log-concave function f on R^d\,
we consider functions belonging to this set of "affine" positions\, and f
ind the one with the smallest integral under the condition that it is poin
twise greater than or equal to f. We study the properties of existence and
uniqueness of the solution to this problem. Finally\, extending the notio
n of the outer volume ratio\, we define the outer integral ratio of a log-
concave function and give an asymptotically tight bound on it. \n\nJoint w
ork with Grigory Ivanov.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisabeth Werner (Case Western Reserve University\, US)
DTSTART:20201202T173000Z
DTEND:20201202T181000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/9
DESCRIPTION:Title: Convex Floating Bodies of Equilibrium\nby Elisabeth Werner
(Case Western Reserve University\, US) as part of Combinatorics and Geomet
ry Days III\n\n\nAbstract\nWe study a long standing open problem by Ulam\,
which is whether the Euclidean ball is the unique body of uniform density
which will float in equilibrium in any direction. We answer this problem
in the class of origin symmetric n-dimensional convex bodies whose relativ
e density to water is 1/2. For n=3\, this result is due to Falconer.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rom Pinchasi (Technion\, Israel)
DTSTART:20201203T153500Z
DTEND:20201203T162000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/10
DESCRIPTION:Title: Conics and Small Number of Distinct Directions\nby Rom Pin
chasi (Technion\, Israel) as part of Combinatorics and Geometry Days III\n
\n\nAbstract\nGiven a set $P$ of $n$ points in general position in the pla
ne\, Jamison conjectured in 1986 that if $P$ determines at most $m \\le 2n
- C$ distinct directions\, then $P$ is contained in the set of vertices o
f a regular $m$-gon. Jamison verified his conjecture for $m = n$ and recen
tly the case $m = n + 1$ was proved by Pilatte. We will discuss this conje
cture and prove it in the case $m \\le n + O(\\sqrt{n})$. \n\n\nBased on j
oint works with Mehdi Makhul and with Alexandr Polyanskii.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Litvak (University of Alberta\, Canada)
DTSTART:20201203T163000Z
DTEND:20201203T171000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/11
DESCRIPTION:Title: A remark on the minimal dispersion\nby Alexander Litvak (U
niversity of Alberta\, Canada) as part of Combinatorics and Geometry Days
III\n\n\nAbstract\nWe improve known upper bounds for the minimal dispersio
n of a point set in the unit cube and its inverse. Some of our bounds are
sharp up to logarithmic factors.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Moustrou (UiT – The Arctic University of Norway)
DTSTART:20201204T120000Z
DTEND:20201204T124000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/12
DESCRIPTION:Title: Exact semidefinite programming bounds for packing problems
\nby Philippe Moustrou (UiT – The Arctic University of Norway) as part o
f Combinatorics and Geometry Days III\n\n\nAbstract\nIn the first part of
the talk\, we present how semidefinite programming methods can provide upp
er bounds for various geometric packing problems\, such as kissing numbers
\, spherical codes\, or packings of spheres into a larger sphere. When the
se bounds are sharp\, they give additional information on optimal configur
ations\, that may lead to prove the uniqueness of such packings. For examp
le\, we show that the lattice E8 is the unique solution for the kissing nu
mber problem on the hemisphere in dimension 8.\n\nHowever\, semidefinite p
rogramming solvers provide approximate solutions\, and some additional wor
k is required to turn them into an exact solution\, giving a certificate t
hat the bound is sharp. In the second part of the talk\, we explain how\,
via our rounding procedure\, we can obtain an exact rational solution of s
emidefinite program from an approximate solution in floating point given b
y the solver.\n\n\nJoint work with Maria Dostert and David de Laat.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Dostert (KTH Royal Institute of Technology\, Stockholm)
DTSTART:20201204T124500Z
DTEND:20201204T132500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/13
DESCRIPTION:Title: Semidefinite programming bounds for the average kissing number
\nby Maria Dostert (KTH Royal Institute of Technology\, Stockholm) as
part of Combinatorics and Geometry Days III\n\n\nAbstract\nThe average kis
sing number of $\\mathbb{R}^n$ is the supremum of the average degrees of c
ontact graphs of packings of finitely many balls (of any radii) in $\\math
bb{R}^n$. In this talk I will provide an upper bound for the average kissi
ng number based on semidefinite programming that improves previous bounds
in dimensions 3\, ...\, 9. A very simple upper bound for the average kissi
ng number is twice the kissing number\; in dimensions 6\, ...\, 9 our new
bound is the first to improve on this simple upper bound. \n\n\nJoint work
with Alexander Kolpakov and Fernando Mário de Oliveira Filho.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Krupp (University of Cologne\, Germany)
DTSTART:20201204T133000Z
DTEND:20201204T141000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/14
DESCRIPTION:Title: Calculating the EHZ Capacity of Polytopes\nby Stefan Krupp
(University of Cologne\, Germany) as part of Combinatorics and Geometry D
ays III\n\n\nAbstract\nConsider the Euclidean space $R^n$ with an even dim
ension n. Equipped with a nondegenerate and alternating (sometimes called
skew-symmetric) bilinear form this is referred to as a symplectic space. S
ymplectic spaces appear for instance if we express classical mechanics in
a general way. The interest in the study of symplectic spaces arose in the
1980s due to the celebrated non-squeezing theorem by Gromov. In particula
r\, Gromov's result required the existence of symplectic invariants\, so c
alled symplectic capacities. A symplectic capacity maps a nonnegative numb
er to each subset of $R^n$ while fulfilling certain properties. By now\, s
everal families of such invariants have been found. However\, they are not
oriously hard to compute. In my talk I will introduce a specific symplecti
c capacity\, i.e. the Ekeland-Hofer-Zehnder (EHZ) capacity\, restricted to
polytopes. More precisely\, I will state a result by Abbondandolo and Maj
er which formulates the EHZ capacity as an optimization problem. Afterward
s\, I will discuss this optimization problem in more detail as well as str
ategies to solve it. \n\n\nJoint work with Daniel Rudolf (Ruhr-University
Bochum).\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kolpakov (University of Neuchâtel\, Switzerland)
DTSTART:20201204T141500Z
DTEND:20201204T145500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/15
DESCRIPTION:Title: Space vectors forming rational angles: on a question of J.H. C
onway\nby Alexander Kolpakov (University of Neuchâtel\, Switzerland)
as part of Combinatorics and Geometry Days III\n\n\nAbstract\nWe classify
all sets of nonzero vectors in $\\mathbb{R}^3$ such that the angle formed
by each pair is a rational multiple of $\\pi$. The special case of four-el
ement subsets lets us classify all tetrahedra whose dihedral angles are mu
ltiples of $\\pi$\, solving a 1976 problem of Conway and Jones: there are
$2$ one-parameter families and $59$ sporadic tetrahedra\, all but three of
which are related to either the icosidodecahedron or the $B_3$ root latti
ce. The proof requires the solution in roots of unity of a $W(D_6)$-symmet
ric polynomial equation with $105$ monomials (the previous record was only
$12$ monomials).\n\n\nJoint work with Kiran Kedlaya\, Bjorn Poonen\, and
Michael Rubinstein.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dragnev (Purdue University Fort Wayne\, US)
DTSTART:20201204T153000Z
DTEND:20201204T161000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/16
DESCRIPTION:Title: Mastodon Theorem - 20 Years in the Making\nby Peter Dragne
v (Purdue University Fort Wayne\, US) as part of Combinatorics and Geometr
y Days III\n\n\nAbstract\nThe Mastodon theorem (PD.\, D. Legg\, D. Townsen
d\, 2002)\, establishes that the regular bi-pyramid (North and South poles
\, and an equilateral triangle on the Equator) is the unique up to rotatio
n five-point configuration on the sphere that maximizes the product of all
mutual (Euclidean) distances.\n\nIn a joint work with Oleg Musin we gener
alize the Mastodon Theorem to $n+2$\npoints on $S^{n-1}$\, namely we chara
cterize all stationary configurations\, and show that all local minima occ
ur when a configuration splits in two orthogonal simplexes of $k$ and $l$
vertices\, $k+l=n+2$ \, with global minimum attained when $k = l$ or $k =
l + 1$ depending on the parity of $n$.\n\n\nJoint work with Oleg Musin.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Musin (University of Texas Rio Grande Valley\, US)
DTSTART:20201204T161500Z
DTEND:20201204T165500Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/17
DESCRIPTION:Title: Optimal spherical configurations\, majorization and f-designs<
/a>\nby Oleg Musin (University of Texas Rio Grande Valley\, US) as part of
Combinatorics and Geometry Days III\n\n\nAbstract\nWe consider the majori
zation (Karamata) inequality and minimums of the majorization (M-sets) for
f-energy potentials of m-point configurations in a sphere. In particular\
, we discuss the optimality of regular simplexes\, describe M-sets with a
small number of points\, define and discuss spherical f-designs.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Glazyrin (University of Texas Rio Grande Valley\, US)
DTSTART:20201204T170000Z
DTEND:20201204T174000Z
DTSTAMP:20260422T212937Z
UID:combgeo_days_three/18
DESCRIPTION:Title: Domes over curves\nby Alexey Glazyrin (University of Texas
Rio Grande Valley\, US) as part of Combinatorics and Geometry Days III\n\
n\nAbstract\nA closed polygonal curve is called integral if it is composed
of unit segments. Kenyon's problem asks whether for every integral curve\
, there is a dome over this curve\, i.e. whether the curve is a boundary o
f a polyhedral surface whose faces are equilateral triangles with unit edg
e lengths. In this talk\, we will give a necessary algebraic condition whe
n the curve is a quadrilateral\, thus giving a negative solution to Kenyon
's problem in full generality. We will then explain why domes exist over a
dense set of integral curves and give an explicit construction of domes o
ver all regular polygons. Finally\, we will formulate several open questio
ns related to the initial problem of Kenyon.\n
LOCATION:https://researchseminars.org/talk/combgeo_days_three/18/
END:VEVENT
END:VCALENDAR