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BEGIN:VEVENT
SUMMARY:Matthew Baker (Georgia Tech School of Mathematics)
DTSTART;VALUE=DATE-TIME:20221004T200000Z
DTEND;VALUE=DATE-TIME:20221004T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/1
DESCRIPTION:Title: Foundations of Matroids\nby Matthew Baker (Georgia Tech School of Mat
hematics) as part of Matroids - Combinatorics\, Algebra and Geometry Semin
ar\n\nLecture held in Room 210\, The Fields Institute.\n\nAbstract\nMatroi
d theorists are interested in questions concerning representability of mat
roids over fields. More generally\, one can ask about representability ove
r partial fields in the sense of Semple and Whittle. Pendavingh and van Zw
am introduced the universal partial field of a matroid\, which governs the
representations of over all partial fields. Unfortunately\, most matroids
are not representable over any partial field\, and in this case\, the uni
versal partial field is not defined. Oliver Lorscheid and I have introduce
d a generalization of the universal partial field which we call the founda
tion of a matroid\; it is always well-defined. The foundation is a type of
algebraic object which we call a pasture\; pastures include both hyperfie
lds and partial fields. As a particular application of this point of view\
, I will explain the classification of all possible foundations for matroi
ds having no minor isomorphic to U(2\,5) or U(3\,5). Among other things\,
this provides a short and conceptual proof of the 1997 theorem of Lee and
Scobee which says that a matroid is both ternary and orientable if and onl
y if it is dyadic.\n
LOCATION:https://researchseminars.org/talk/Matroids/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bennet Goeckner (University of San Diego)
DTSTART;VALUE=DATE-TIME:20221006T190000Z
DTEND;VALUE=DATE-TIME:20221006T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/2
DESCRIPTION:Title: Type cones and products of simplices\nby Bennet Goeckner (University
of San Diego) as part of Matroids - Combinatorics\, Algebra and Geometry S
eminar\n\nLecture held in Room 210\, The Fields Institute.\n\nAbstract\nA
polytope $P$ is the convex hull of finitely many points in Euclidean space
. For polytopes $P$ and $Q$\, we say that $Q$ is a Minkowski summand of $P
$ if there exists some polytope $R$ such that $Q+R=P$. The type cone of $P
$ encodes all of the (weak) Minkowski summands of P. In general\, combinat
orially isomorphic polytopes can have different type cones. We will first
consider type cones of polygons\, and then show that if $P$ is combinatori
ally isomorphic to a product of simplices\, then the type cone is simplici
al. This is joint work with Federico Castillo\, Joseph Doolittle\, Michael
Ross\, and Li Ying.\n
LOCATION:https://researchseminars.org/talk/Matroids/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Sidman (Mount Holyoke College)
DTSTART;VALUE=DATE-TIME:20221011T190000Z
DTEND;VALUE=DATE-TIME:20221011T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/3
DESCRIPTION:Title: Matroid varieties\nby Jessica Sidman (Mount Holyoke College) as part
of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held
in Room 210\, The Fields Institute.\n\nAbstract\nLet $x$ denote a $k$-dim
ensional subspace of $\\mathbb{C}^n$ and let $A_x$ be a $k\\times n$ matri
x whose rows are a basis for $x$. The matroid $M_x$ on the columns of $A_x
$ is invariant under a change of basis for $x$. What can we say about the
set $\\Gamma_x$ of all $k$-dimensional subspaces $y$ such that $M_y = M_x?
$. We will explore this question algebraically\, showing that for some mat
roids that arise geometrically many non-trivial equations vanishing on $\\
Gamma_x$ can be derived geometrically. This is joint work with Will Traves
and Ashley Wheeler.\n
LOCATION:https://researchseminars.org/talk/Matroids/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Criel Merino (Instituto de Matematicas UNAM)
DTSTART;VALUE=DATE-TIME:20221013T190000Z
DTEND;VALUE=DATE-TIME:20221013T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/4
DESCRIPTION:Title: The h-vector of a matroid complex\, paving matroids and the chip firing g
ame.\nby Criel Merino (Instituto de Matematicas UNAM) as part of Matro
ids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held in Room
210 The Fields Institute.\n\nAbstract\nA non-empty set of monomials $\\Si
gma$ is a multicomplex if for any monomial $z$ in $\\Sigma$ and a monomial
$z'$ such that $z'|z$\, we have that $z'$ also belongs to $\\Sigma$. A mu
lticomplex $\\Sigma$ is called pure if all its maximal elements have the s
ame degree. This notion is a generalization of the simplicial complex\, an
d several invariants extend directly\, as the $f$-vector of a multicomplex
\, which is the vector that lists the monomials grouped by degrees. A non-
empty set of monomials $\\Sigma$ is a multicomplex if for any monomial $z$
in $\\Sigma$ and a monomial $z'$ such that $z'|z$\, we have that $z'$ als
o belongs to $\\Sigma$. A multicomplex $\\Sigma$ is called pure if all its
maximal elements have the same degree. This notion is a generalization of
the simplicial complex\, and several invariants extend directly\, as the
$f$-vector of a multicomplex\, which is the vector that lists the monomial
s grouped by degrees. The relevance of multicomplexes in matroid theory is
partly due to a 1977 Richard Stanley conjecture that says that the $h$-ve
ctor of a matroid complex is the $f$-vector of a pure multicomplex. This h
as been proved for several families of matroids. In this talk\, we review
some results of Stanley’s conjecture\, mainly for paving and cographic m
atroids. A paving matroid is one in which all its circuits have a size of
at least the rank of the matroid. While\, the chip firing game is a solita
ire game played on a connected graph $G$ that surprisingly is related to t
he $h$-vector of the bond matroid of $G$.\n
LOCATION:https://researchseminars.org/talk/Matroids/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART;VALUE=DATE-TIME:20221018T190000Z
DTEND;VALUE=DATE-TIME:20221018T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/5
DESCRIPTION:Title: Universal Tutte polynomial\nby Olivier Bernardi (Brandeis University)
as part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLec
ture held in Room 210 The Fields Institute.\n\nAbstract\nThe Tutte polynom
ial is an important matroid invariant. We will explain a natural way to e
xtend the Tutte polynomial from matroids to polymatroids. The Tutte polyno
mial can then be expressed as a sum over the points of the polymatroid (th
is is an extension of the basis extension of the classical definition of
the Tutte polynomial in terms of activities). Our definition is related to
previous works of Cameron and Fink and of Kálmán and Postnikov. \n\nOne
of the great properties of our Tutte polynomial is that it is polynomial
in the values of the rank function of the polymatroid. In other words\, we
can define a "universal Tutte polynomial" $T_n$ in $2+(2^n−1)$ variable
s that specialize to the Tutte polynomials of all polymatroids on n elemen
ts (the $2^n-1$ extra variables correspond to the non-trivial values of th
e rank function). \n\nThis is joint work with Tamás Kálmán and Alex Pos
tnikov.\n
LOCATION:https://researchseminars.org/talk/Matroids/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Denham (Western University)
DTSTART;VALUE=DATE-TIME:20221020T190000Z
DTEND;VALUE=DATE-TIME:20221020T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/6
DESCRIPTION:Title: Lagrangian Geometry\nby Graham Denham (Western University) as part of
Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held i
n Room 210 The Fields Institute.\n\nAbstract\nIn joint work with Federico
Ardila and June Huh\, we introduce the conormal fan of a matroid\, which i
s an analogue of the Bergman fan. We use it to give a Lagrangian interpre
tation of the Chern-Schwartz-MacPherson cycle of a matroid. We also develo
p tools for tropical Hodge theory to show that the conormal fan satisfies
Poincaré duality\, the Hard Lefschetz property\, and the Hodge--Riemann r
elations. Together\, these imply conjectures of Brylawski and Dawson abou
t the log-concavity of the h-vectors of the broken circuit complex and ind
ependence complex of a matroid.\n
LOCATION:https://researchseminars.org/talk/Matroids/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (Rutgers University)
DTSTART;VALUE=DATE-TIME:20221101T190000Z
DTEND;VALUE=DATE-TIME:20221101T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/9
DESCRIPTION:Title: Combinatorial atlas for log-concave inequalities\nby Swee Hong Chan (
Rutgers University) as part of Matroids - Combinatorics\, Algebra and Geom
etry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract
\nThe study of log-concave inequalities for combinatorial objects have see
n much progress in recent years. One such progress is the solution to the
strongest form of Mason’s conjecture (independently by Anari et. al. and
Brándën-Huh). In the case of graphs\, this says that the sequence $f_k$
of the number of forests of the graph with $k$ edges\, form an ultra log-
concave sequence. In this talk\, we discuss an improved version of all the
se results\, proved by using a new tool called the combinatorial atlas met
hod. This is a joint work with Igor Pak. This talk is aimed at a general a
udience.\n
LOCATION:https://researchseminars.org/talk/Matroids/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Supina (KTH Royal Institute of Technology)
DTSTART;VALUE=DATE-TIME:20221103T190000Z
DTEND;VALUE=DATE-TIME:20221103T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/10
DESCRIPTION:Title: The universal valuation of Coxeter matroids\nby Mariel Supina (KTH R
oyal Institute of Technology) as part of Matroids - Combinatorics\, Algebr
a and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n
\nAbstract\nMatroids subdivisions have rich connections to geometry\, and
thus we are often interested in functions on matroids that behave nicely w
ith respect to subdivisions\, or "valuations". Matroids are naturally link
ed to the symmetric group\; generalizing to other finite reflection groups
gives rise to Coxeter matroids. I will give an overview of these ideas an
d then present some work with Chris Eur and Mario Sanchez on constructing
the universal valuative invariant of Coxeter matroids. Since matroids and
their Coxeter analogues can be understood as families of polytopes with sp
ecial combinatorial properties\, I will present these results from a polyt
opal perspective.\n
LOCATION:https://researchseminars.org/talk/Matroids/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Castillo (Universidad Catolica de Chile)
DTSTART;VALUE=DATE-TIME:20221108T200000Z
DTEND;VALUE=DATE-TIME:20221108T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/11
DESCRIPTION:Title: Trying to generalize Pick's theorem.\nby Federico Castillo (Universi
dad Catolica de Chile) as part of Matroids - Combinatorics\, Algebra and G
eometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstr
act\nWe will review Pick's theorem in dimension 2 and see some ideas for a
n extension. Based on understanding the Todd class of toric varieties\, a
variety of local formulas have been proposed. Each of these local formulas
can be seen as a higher Pick's theorem. I will present a conjecture and e
vidence for one particular formula to become "the" natural extension.\n
LOCATION:https://researchseminars.org/talk/Matroids/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Sanchez (Cornell University)
DTSTART;VALUE=DATE-TIME:20221117T200000Z
DTEND;VALUE=DATE-TIME:20221117T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/14
DESCRIPTION:Title: Valuations and Hopf Monoid of Generalized Permutahedra\nby Mario San
chez (Cornell University) as part of Matroids - Combinatorics\, Algebra an
d Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAb
stract\nMany combinatorial objects\, such as matroids\, graphs\, and poset
s\, can be realized as generalized permutahedra - a beautiful family of po
lytopes. These realizations respect the natural multiplication of these ob
jects as well as natural "breaking" operations. Surprisingly many of the i
mportant invariants of these objects\, when viewed as functions on polytop
es are valuations\, that is\, they satisfy an inclusion-exclusion formula
with respect to subdivisions. In this talk\, I will discuss work with Fede
rico Ardila that describes the relationship between the algebraic structur
e on generalized permutahedra and valuations. Our main contribution is a n
ew easy-to-apply method that converts simple valuations into more complica
ted ones. New examples of valuations coming from this method include the K
azhdan-Lustzig polynomials of matroids and the motivic zeta functions of m
atroids.\n
LOCATION:https://researchseminars.org/talk/Matroids/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Olarte Parra (Technische Universitat Berlin)
DTSTART;VALUE=DATE-TIME:20221122T200000Z
DTEND;VALUE=DATE-TIME:20221122T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/15
DESCRIPTION:Title: Transversal Valuated Matroids\nby Jorge Olarte Parra (Technische Uni
versitat Berlin) as part of Matroids - Combinatorics\, Algebra and Geometr
y Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nT
ransversal matroids are a class of matroids that arises from matchings in
bipartite graphs. This has a generalization to valuated matroids which ari
se from tropical minors of a matrix. This is the so-called tropical Stiefe
l map. Brualdi and Dinolt gave a construction that characterizes all bipar
tite graphs that represent a given transversal matroid. We show a valuated
analogue of this result. In other words\, we characterize all matrices wi
th fixed maximal tropical minors. This has several geometric interpretatio
ns\, such as characterizing tropical hyperplanes with fixed stable interse
ctions.This is joint work with Alex Fink.\n
LOCATION:https://researchseminars.org/talk/Matroids/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Nathanson (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20221124T200000Z
DTEND;VALUE=DATE-TIME:20221124T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/16
DESCRIPTION:Title: Volume polynomials of matroids\nby Anastasia Nathanson (University o
f Minnesota) as part of Matroids - Combinatorics\, Algebra and Geometry Se
minar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nAssoc
iated to any divisor in the Chow ring of a simplicial tropical fan\, we di
scuss the construction a family of polytopal complexes\, called normal com
plexes\, which we propose as an analogue of the well-studied notion of nor
mal polytopes from the setting of complete fans. The talk will describe ce
rtain closed convex polyhedral cones of divisors for which the “volume
” of each divisor in the cone—that is\, the degree of its top power—
is equal to the volume of the associated normal complexes. We will discuss
the theory of normal complexes developed in talk as a polytopal model und
erlying the combinatorial Hodge theory pioneered by Adiprasito\, Huh\, and
Katz.\n
LOCATION:https://researchseminars.org/talk/Matroids/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Novak (University of Washington)
DTSTART;VALUE=DATE-TIME:20221129T200000Z
DTEND;VALUE=DATE-TIME:20221129T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/17
DESCRIPTION:Title: Mixed Volumes of normal complexes\nby Lauren Novak (University of Wa
shington) as part of Matroids - Combinatorics\, Algebra and Geometry Semin
ar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nIn 2021\
, Nathanson and Ross demonstrated that a geometric object called a normal
complex is the correct object to unite the algebraic concept of a tropical
fan's volume polynomial with an actual geometric volume computation. That
same year\, expanding on the work of Adiprasito\, Huh\, and Katz in provi
ng log-concavity in characteristic polynomials of matroids\, Amini and Piq
uerez established that mixed degrees of divisors of certain classes of tro
pical fans are log-concave. Given that mixed volumes generate log-concave
sequences\, we develop a definition of mixed volumes of normal complexes a
nd use our theory to establish new techniques for determining log-concavit
y for mixed degrees of divisors of a broad class of tropical fans.\n
LOCATION:https://researchseminars.org/talk/Matroids/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Ross (San Francisco State University)
DTSTART;VALUE=DATE-TIME:20221201T193000Z
DTEND;VALUE=DATE-TIME:20221201T203000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/18
DESCRIPTION:Title: Matroid Psi Classes\nby Dustin Ross (San Francisco State University)
as part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLec
ture held in Room 210 The Fields Institute.\n\nAbstract\nMatroid Chow ring
s have played a central role in recent developments in matroid theory. In
this talk\, I’ll discuss parallels between matroid Chow rings and Chow r
ings of moduli spaces of curves\, leading to a new and simplified understa
nding of many important properties of matroid Chow rings.\n
LOCATION:https://researchseminars.org/talk/Matroids/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Crowley (University of Wisconsin Madison)
DTSTART;VALUE=DATE-TIME:20221206T200000Z
DTEND;VALUE=DATE-TIME:20221206T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/19
DESCRIPTION:Title: Hyperplane arrangements and compactifications of vector groups\nby C
olin Crowley (University of Wisconsin Madison) as part of Matroids - Combi
natorics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fi
elds Institute.\n\nAbstract\nSchubert varieties of hyperplane arrangements
\, also known as matroid Schubert varieties\, play an essential role in th
e proof of the Dowling-Wilson conjecture and in Kazhdan-Lusztig theory for
matroids. We study these varieties as equivariant compactifications of af
fine spaces\, and give necessary and sufficient conditions to characterize
them. We also generalize the theory to include partial compactifications
and morphisms between them. Our results resemble the correspondence betwee
n toric varieties and polyhedral fans.\n
LOCATION:https://researchseminars.org/talk/Matroids/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART;VALUE=DATE-TIME:20221208T200000Z
DTEND;VALUE=DATE-TIME:20221208T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/20
DESCRIPTION:Title: K-rings of wonderful varieties and matroids\nby Shiyue Li (Brown Uni
versity) as part of Matroids - Combinatorics\, Algebra and Geometry Semina
r\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nAs we hav
e seen in many talks in this wonderful seminar\, the wonderful variety of
a realizable matroid and its Chow ring have played key roles in solving ma
ny long-standing open questions in combinatorics and algebraic geometry. Y
et\, its $K$-rings are underexplored until recently. I will be sharing wit
h you some discoveries on the $K$-rings of the wonderful variety associate
d with a realizable matroid: an exceptional isomorphism between the $K$-ri
ng and the Chow ring\, with integral coefficients\, and a Hirzebruch–Rie
mann–Roch-type formula. These generalize a recent construction of Berget
–Eur–Spink–Tseng on the permutohedral variety. We also compute the E
uler characteristic of every line bundle on wonderful varieties\, and give
a purely combinatorial formula. This in turn gives a new valuative invari
ant of an arbitrary matroid. As an application\, we present the $K$-rings
and compute the Euler characteristic of arbitrary line bundles of the Deli
gne–Mumford–Knudsen moduli spaces of rational stable curves with disti
nct marked points. Joint with Matt Larson\, Sam Payne and Nick Proudfoot.\
n
LOCATION:https://researchseminars.org/talk/Matroids/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar Vega (Washington University in St. Louis)
DTSTART;VALUE=DATE-TIME:20221025T190000Z
DTEND;VALUE=DATE-TIME:20221025T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/21
DESCRIPTION:Title: Partial Permutohedra\nby Laura Escobar Vega (Washington University i
n St. Louis) as part of Matroids - Combinatorics\, Algebra and Geometry Se
minar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nParti
al permutohedra are lattice polytopes which were recently introduced\nand
studied by Heuer and Striker. For positive integers $m$ and $n$\, the part
ial permutohedron~$\\cP(m\,n)$ is the convex hull of all vectors in $\\{0\
,1\,\\ldots\,n\\}^m$ with distinct nonzero entries. In this talk I will pr
esent results on the face lattice\, volume and Ehrhart polynomial of $\\cP
(m\,n)$. This is joint work with Behrend\, Castillo\, Chavez\, Diaz-Lopez\
, Harris and Insko.\n
LOCATION:https://researchseminars.org/talk/Matroids/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasu Tewari (University of Hawaii)
DTSTART;VALUE=DATE-TIME:20221027T190000Z
DTEND;VALUE=DATE-TIME:20221027T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/22
DESCRIPTION:Title: Quotienting by quasisymmetric polynomials\nby Vasu Tewari (Universit
y of Hawaii) as part of Matroids - Combinatorics\, Algebra and Geometry Se
minar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nWe in
troduce a new basis for the polynomial ring which has its genesis in the c
omputation of the cohomology class of the permutahedral variety. We will s
ee that this basis is very well-behaved in regards to reduction modulo the
ideal of quasisymmetric polynomials. This has interesting ramifications o
f a discrete-geometric flavour that we will discuss -- for instance\, a mu
ltivariate analogue of mixed Eulerian numbers comes up naturally\, amongst
other things. \nJoint with Philippe Nadeau (CNRS and Univ. Lyon).\n
LOCATION:https://researchseminars.org/talk/Matroids/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Simpson (University of Wisconsin Madison)
DTSTART;VALUE=DATE-TIME:20221110T200000Z
DTEND;VALUE=DATE-TIME:20221110T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/26
DESCRIPTION:Title: Simplicial generators for Chow rings of matroids\nby Connor Simpson
(University of Wisconsin Madison) as part of Matroids - Combinatorics\, Al
gebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Institut
e.\n\nAbstract\nThe simplicial generators of a Chow ring of a matroid are
divisors pulled back from a product of projective spaces. Multiplying them
can be interpreted combinatorially\, yielding a simple formula for the vo
lume polynomial of the Chow ring of a matroid. If time permits\, we will d
iscuss further developments these generators have inspired since their int
roduction. Joint work with Chris Eur & Spencer Backman.\n
LOCATION:https://researchseminars.org/talk/Matroids/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Bastidas (Université du Québec à Montréal)
DTSTART;VALUE=DATE-TIME:20221115T200000Z
DTEND;VALUE=DATE-TIME:20221115T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123257Z
UID:Matroids/27
DESCRIPTION:Title: Polytope algebra of generalized permutohedra\nby Jose Bastidas (Univ
ersité du Québec à Montréal) as part of Matroids - Combinatorics\, Alg
ebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute
.\n\nAbstract\nDanilov-Koshevoy\, Postnikov\, and Ardila-Benedetti-Doker t
aught us that any generalized permutahedron is a signed Minkowski sum of t
he faces of the standard simplex. In other words\, these faces correspond
to a maximal linearly independent collection of rays in the deformation co
ne of the permutahedron. In contrast\, Ardila-Castillo-Eur-Postnikov obser
ved that the faces of the cross-polytope only span a subspace of roughly h
alf the dimension of the deformation cone of the type B permutahedron. In
this talk\, we use McMullen's polytope algebra to help explain this phenom
enon.\n
LOCATION:https://researchseminars.org/talk/Matroids/27/
END:VEVENT
END:VCALENDAR