BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Matthew Baker (Georgia Tech School of Mathematics)
DTSTART:20221004T200000Z
DTEND:20221004T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/1
DESCRIPTION:Title: Foundations of Matroids\nby Matthew Baker (Georgia Tech School
of Mathematics) as part of Matroids - Combinatorics\, Algebra and Geometr
y Seminar\n\nLecture held in Room 210\, The Fields Institute.\n\nAbstract\
nMatroid theorists are interested in questions concerning representability
of matroids over fields. More generally\, one can ask about representabil
ity over partial fields in the sense of Semple and Whittle. Pendavingh and
van Zwam introduced the universal partial field of a matroid\, which gove
rns the representations of over all partial fields. Unfortunately\, most m
atroids are not representable over any partial field\, and in this case\,
the universal partial field is not defined. Oliver Lorscheid and I have in
troduced a generalization of the universal partial field which we call the
foundation of a matroid\; it is always well-defined. The foundation is a
type of algebraic object which we call a pasture\; pastures include both h
yperfields and partial fields. As a particular application of this point o
f 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 th
ings\, this provides a short and conceptual proof of the 1997 theorem of L
ee and Scobee which says that a matroid is both ternary and orientable if
and only if it is dyadic.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bennet Goeckner (University of San Diego)
DTSTART:20221006T190000Z
DTEND:20221006T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/2
DESCRIPTION:Title: Type cones and products of simplices\nby Bennet Goeckner (Univ
ersity of San Diego) as part of Matroids - Combinatorics\, Algebra and Geo
metry Seminar\n\nLecture held in Room 210\, The Fields Institute.\n\nAbstr
act\nA polytope $P$ is the convex hull of finitely many points in Euclidea
n space. For polytopes $P$ and $Q$\, we say that $Q$ is a Minkowski summan
d of $P$ if there exists some polytope $R$ such that $Q+R=P$. The type con
e of $P$ encodes all of the (weak) Minkowski summands of P. In general\, c
ombinatorially isomorphic polytopes can have different type cones. We will
first consider type cones of polygons\, and then show that if $P$ is comb
inatorially isomorphic to a product of simplices\, then the type cone is s
implicial. This is joint work with Federico Castillo\, Joseph Doolittle\,
Michael Ross\, and Li Ying.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Sidman (Mount Holyoke College)
DTSTART:20221011T190000Z
DTEND:20221011T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/3
DESCRIPTION:Title: Matroid varieties\nby Jessica Sidman (Mount Holyoke College) a
s part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLectu
re held in Room 210\, The Fields Institute.\n\nAbstract\nLet $x$ denote a
$k$-dimensional subspace of $\\mathbb{C}^n$ and let $A_x$ be a $k\\times n
$ matrix 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 abo
ut 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 s
ome matroids 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://stable.researchseminars.org/talk/Matroids/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Criel Merino (Instituto de Matematicas UNAM)
DTSTART:20221013T190000Z
DTEND:20221013T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/4
DESCRIPTION:Title: The h-vector of a matroid complex\, paving matroids and the chip f
iring game.\nby Criel Merino (Instituto de Matematicas UNAM) as part o
f Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held
in Room 210 The Fields Institute.\n\nAbstract\nA non-empty set of monomial
s $\\Sigma$ is a multicomplex if for any monomial $z$ in $\\Sigma$ and a m
onomial $z'$ such that $z'|z$\, we have that $z'$ also belongs to $\\Sigma
$. A multicomplex $\\Sigma$ is called pure if all its maximal elements hav
e the same degree. This notion is a generalization of the simplicial compl
ex\, and several invariants extend directly\, as the $f$-vector of a multi
complex\, which is the vector that lists the monomials grouped by degrees.
A non-empty set of monomials $\\Sigma$ is a multicomplex if for any monom
ial $z$ in $\\Sigma$ and a monomial $z'$ such that $z'|z$\, we have that $
z'$ also belongs to $\\Sigma$. A multicomplex $\\Sigma$ is called pure if
all its maximal elements have the same degree. This notion is a generaliza
tion of the simplicial complex\, and several invariants extend directly\,
as the $f$-vector of a multicomplex\, which is the vector that lists the m
onomials grouped by degrees. The relevance of multicomplexes in matroid th
eory is partly due to a 1977 Richard Stanley conjecture that says that the
$h$-vector of a matroid complex is the $f$-vector of a pure multicomplex.
This has been proved for several families of matroids. In this talk\, we
review some results of Stanley’s conjecture\, mainly for paving and cogr
aphic matroids. A paving matroid is one in which all its circuits have a s
ize of at least the rank of the matroid. While\, the chip firing game is a
solitaire game played on a connected graph $G$ that surprisingly is relat
ed to the $h$-vector of the bond matroid of $G$.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART:20221018T190000Z
DTEND:20221018T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/5
DESCRIPTION:Title: Universal Tutte polynomial\nby Olivier Bernardi (Brandeis Univ
ersity) as part of Matroids - Combinatorics\, Algebra and Geometry Seminar
\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nThe Tutte
polynomial is an important matroid invariant. We will explain a natural w
ay to extend the Tutte polynomial from matroids to polymatroids. The Tutte
polynomial can then be expressed as a sum over the points of the polymatr
oid (this is an extension of the basis extension of the classical definiti
on of the Tutte polynomial in terms of activities). Our definition is rel
ated 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 poly
nomial in the values of the rank function of the polymatroid. In other wor
ds\, we can define a "universal Tutte polynomial" $T_n$ in $2+(2^n−1)$ v
ariables that specialize to the Tutte polynomials of all polymatroids on n
elements (the $2^n-1$ extra variables correspond to the non-trivial value
s of the rank function). \n\nThis is joint work with Tamás Kálmán and A
lex Postnikov.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Denham (Western University)
DTSTART:20221020T190000Z
DTEND:20221020T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/6
DESCRIPTION:Title: Lagrangian Geometry\nby Graham Denham (Western University) as
part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture
held in Room 210 The Fields Institute.\n\nAbstract\nIn joint work with Fe
derico Ardila and June Huh\, we introduce the conormal fan of a matroid\,
which is an analogue of the Bergman fan. We use it to give a Lagrangian i
nterpretation of the Chern-Schwartz-MacPherson cycle of a matroid. We also
develop tools for tropical Hodge theory to show that the conormal fan sat
isfies Poincaré duality\, the Hard Lefschetz property\, and the Hodge--Ri
emann relations. Together\, these imply conjectures of Brylawski and Daws
on about the log-concavity of the h-vectors of the broken circuit complex
and independence complex of a matroid.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swee Hong Chan (Rutgers University)
DTSTART:20221101T190000Z
DTEND:20221101T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/9
DESCRIPTION:Title: Combinatorial atlas for log-concave inequalities\nby Swee Hong
Chan (Rutgers University) as part of Matroids - Combinatorics\, Algebra a
nd Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nA
bstract\nThe study of log-concave inequalities for combinatorial objects h
ave seen 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 sequenc
e $f_k$ of the number of forests of the graph with $k$ edges\, form an ult
ra log-concave sequence. In this talk\, we discuss an improved version of
all these results\, proved by using a new tool called the combinatorial at
las method. This is a joint work with Igor Pak. This talk is aimed at a ge
neral audience.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Supina (KTH Royal Institute of Technology)
DTSTART:20221103T190000Z
DTEND:20221103T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/10
DESCRIPTION:Title: The universal valuation of Coxeter matroids\nby Mariel Supina
(KTH Royal Institute of Technology) as part of Matroids - Combinatorics\,
Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Insti
tute.\n\nAbstract\nMatroids subdivisions have rich connections to geometry
\, and thus we are often interested in functions on matroids that behave n
icely with respect to subdivisions\, or "valuations". Matroids are natural
ly linked to the symmetric group\; generalizing to other finite reflection
groups gives rise to Coxeter matroids. I will give an overview of these i
deas and then present some work with Chris Eur and Mario Sanchez on constr
ucting the universal valuative invariant of Coxeter matroids. Since matroi
ds and their Coxeter analogues can be understood as families of polytopes
with special combinatorial properties\, I will present these results from
a polytopal perspective.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Castillo (Universidad Catolica de Chile)
DTSTART:20221108T200000Z
DTEND:20221108T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/11
DESCRIPTION:Title: Trying to generalize Pick's theorem.\nby Federico Castillo (U
niversidad Catolica de Chile) as part of Matroids - Combinatorics\, Algebr
a and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n
\nAbstract\nWe will review Pick's theorem in dimension 2 and see some idea
s for an extension. Based on understanding the Todd class of toric varieti
es\, a variety of local formulas have been proposed. Each of these local f
ormulas can be seen as a higher Pick's theorem. I will present a conjectur
e and evidence for one particular formula to become "the" natural extensio
n.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Sanchez (Cornell University)
DTSTART:20221117T200000Z
DTEND:20221117T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/14
DESCRIPTION:Title: Valuations and Hopf Monoid of Generalized Permutahedra\nby Ma
rio Sanchez (Cornell University) as part of Matroids - Combinatorics\, Alg
ebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute
.\n\nAbstract\nMany combinatorial objects\, such as matroids\, graphs\, an
d posets\, can be realized as generalized permutahedra - a beautiful famil
y of polytopes. These realizations respect the natural multiplication of t
hese objects as well as natural "breaking" operations. Surprisingly many o
f the important invariants of these objects\, when viewed as functions on
polytopes are valuations\, that is\, they satisfy an inclusion-exclusion f
ormula with respect to subdivisions. In this talk\, I will discuss work wi
th Federico Ardila that describes the relationship between the algebraic s
tructure on generalized permutahedra and valuations. Our main contribution
is a new easy-to-apply method that converts simple valuations into more c
omplicated ones. New examples of valuations coming from this method includ
e the Kazhdan-Lustzig polynomials of matroids and the motivic zeta functio
ns of matroids.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Olarte Parra (Technische Universitat Berlin)
DTSTART:20221122T200000Z
DTEND:20221122T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/15
DESCRIPTION:Title: Transversal Valuated Matroids\nby Jorge Olarte Parra (Technis
che Universitat Berlin) as part of Matroids - Combinatorics\, Algebra and
Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbst
ract\nTransversal matroids are a class of matroids that arises from matchi
ngs in bipartite graphs. This has a generalization to valuated matroids wh
ich arise from tropical minors of a matrix. This is the so-called tropical
Stiefel map. Brualdi and Dinolt gave a construction that characterizes al
l bipartite graphs that represent a given transversal matroid. We show a v
aluated analogue of this result. In other words\, we characterize all matr
ices with fixed maximal tropical minors. This has several geometric interp
retations\, such as characterizing tropical hyperplanes with fixed stable
intersections.This is joint work with Alex Fink.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Nathanson (University of Minnesota)
DTSTART:20221124T200000Z
DTEND:20221124T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/16
DESCRIPTION:Title: Volume polynomials of matroids\nby Anastasia Nathanson (Unive
rsity of Minnesota) as part of Matroids - Combinatorics\, Algebra and Geom
etry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract
\nAssociated to any divisor in the Chow ring of a simplicial tropical fan\
, we discuss the construction a family of polytopal complexes\, called nor
mal complexes\, which we propose as an analogue of the well-studied notion
of normal polytopes from the setting of complete fans. The talk will desc
ribe certain closed convex polyhedral cones of divisors for which the “v
olume” of each divisor in the cone—that is\, the degree of its top pow
er—is equal to the volume of the associated normal complexes. We will di
scuss the theory of normal complexes developed in talk as a polytopal mode
l underlying the combinatorial Hodge theory pioneered by Adiprasito\, Huh\
, and Katz.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Novak (University of Washington)
DTSTART:20221129T200000Z
DTEND:20221129T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/17
DESCRIPTION:Title: Mixed Volumes of normal complexes\nby Lauren Novak (Universit
y of Washington) as part of Matroids - Combinatorics\, Algebra and Geometr
y Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nI
n 2021\, Nathanson and Ross demonstrated that a geometric object called a
normal complex is the correct object to unite the algebraic concept of a t
ropical fan's volume polynomial with an actual geometric volume computatio
n. That same year\, expanding on the work of Adiprasito\, Huh\, and Katz i
n proving log-concavity in characteristic polynomials of matroids\, Amini
and Piquerez established that mixed degrees of divisors of certain classes
of tropical fans are log-concave. Given that mixed volumes generate log-c
oncave sequences\, we develop a definition of mixed volumes of normal comp
lexes and use our theory to establish new techniques for determining log-c
oncavity for mixed degrees of divisors of a broad class of tropical fans.\
n
LOCATION:https://stable.researchseminars.org/talk/Matroids/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Ross (San Francisco State University)
DTSTART:20221201T193000Z
DTEND:20221201T203000Z
DTSTAMP:20260404T094310Z
UID:Matroids/18
DESCRIPTION:Title: Matroid Psi Classes\nby Dustin Ross (San Francisco State Univ
ersity) as part of Matroids - Combinatorics\, Algebra and Geometry Seminar
\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nMatroid Ch
ow rings have played a central role in recent developments in matroid theo
ry. In this talk\, I’ll discuss parallels between matroid Chow rings and
Chow rings of moduli spaces of curves\, leading to a new and simplified u
nderstanding of many important properties of matroid Chow rings.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Crowley (University of Wisconsin Madison)
DTSTART:20221206T200000Z
DTEND:20221206T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/19
DESCRIPTION:Title: Hyperplane arrangements and compactifications of vector groups\nby Colin Crowley (University of Wisconsin Madison) as part of Matroids
- Combinatorics\, Algebra and Geometry Seminar\n\nLecture held in Room 210
The Fields Institute.\n\nAbstract\nSchubert varieties of hyperplane arran
gements\, also known as matroid Schubert varieties\, play an essential rol
e in the proof of the Dowling-Wilson conjecture and in Kazhdan-Lusztig the
ory for matroids. We study these varieties as equivariant compactification
s of affine spaces\, and give necessary and sufficient conditions to chara
cterize them. We also generalize the theory to include partial compactific
ations and morphisms between them. Our results resemble the correspondence
between toric varieties and polyhedral fans.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART:20221208T200000Z
DTEND:20221208T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/20
DESCRIPTION:Title: K-rings of wonderful varieties and matroids\nby Shiyue Li (Br
own University) as part of Matroids - Combinatorics\, Algebra and Geometry
Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nAs
we have seen in many talks in this wonderful seminar\, the wonderful vari
ety of a realizable matroid and its Chow ring have played key roles in sol
ving many long-standing open questions in combinatorics and algebraic geom
etry. Yet\, its $K$-rings are underexplored until recently. I will be shar
ing with you some discoveries on the $K$-rings of the wonderful variety as
sociated with a realizable matroid: an exceptional isomorphism between the
$K$-ring and the Chow ring\, with integral coefficients\, and a Hirzebruc
h–Riemann–Roch-type formula. These generalize a recent construction of
Berget–Eur–Spink–Tseng on the permutohedral variety. We also comput
e the Euler characteristic of every line bundle on wonderful varieties\, a
nd give a purely combinatorial formula. This in turn gives a new valuative
invariant of an arbitrary matroid. As an application\, we present the $K$
-rings and compute the Euler characteristic of arbitrary line bundles of t
he Deligne–Mumford–Knudsen moduli spaces of rational stable curves wit
h distinct marked points. Joint with Matt Larson\, Sam Payne and Nick Prou
dfoot.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar Vega (Washington University in St. Louis)
DTSTART:20221025T190000Z
DTEND:20221025T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/21
DESCRIPTION:Title: Partial Permutohedra\nby Laura Escobar Vega (Washington Unive
rsity in St. Louis) as part of Matroids - Combinatorics\, Algebra and Geom
etry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract
\nPartial permutohedra are lattice polytopes which were recently introduce
d\nand studied by Heuer and Striker. For positive integers $m$ and $n$\, t
he partial 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 present results on the face lattice\, volume and Ehrhart polynomial o
f $\\cP(m\,n)$. This is joint work with Behrend\, Castillo\, Chavez\, Diaz
-Lopez\, Harris and Insko.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasu Tewari (University of Hawaii)
DTSTART:20221027T190000Z
DTEND:20221027T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/22
DESCRIPTION:Title: Quotienting by quasisymmetric polynomials\nby Vasu Tewari (Un
iversity of Hawaii) as part of Matroids - Combinatorics\, Algebra and Geom
etry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract
\nWe introduce a new basis for the polynomial ring which has its genesis i
n the computation of the cohomology class of the permutahedral variety. We
will see that this basis is very well-behaved in regards to reduction mod
ulo the ideal of quasisymmetric polynomials. This has interesting ramifica
tions of a discrete-geometric flavour that we will discuss -- for instance
\, a multivariate analogue of mixed Eulerian numbers comes up naturally\,
amongst other things. \nJoint with Philippe Nadeau (CNRS and Univ. Lyon).\
n
LOCATION:https://stable.researchseminars.org/talk/Matroids/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Simpson (University of Wisconsin Madison)
DTSTART:20221110T200000Z
DTEND:20221110T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/26
DESCRIPTION:Title: Simplicial generators for Chow rings of matroids\nby Connor S
impson (University of Wisconsin Madison) as part of Matroids - Combinatori
cs\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields I
nstitute.\n\nAbstract\nThe simplicial generators of a Chow ring of a matro
id are divisors pulled back from a product of projective spaces. Multiplyi
ng them can be interpreted combinatorially\, yielding a simple formula for
the volume polynomial of the Chow ring of a matroid. If time permits\, we
will discuss further developments these generators have inspired since th
eir introduction. Joint work with Chris Eur & Spencer Backman.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Bastidas (Université du Québec à Montréal)
DTSTART:20221115T200000Z
DTEND:20221115T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/27
DESCRIPTION:Title: Polytope algebra of generalized permutohedra\nby Jose Bastida
s (Université du Québec à Montréal) as part of Matroids - Combinatoric
s\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields In
stitute.\n\nAbstract\nDanilov-Koshevoy\, Postnikov\, and Ardila-Benedetti-
Doker taught us that any generalized permutahedron is a signed Minkowski s
um of the faces of the standard simplex. In other words\, these faces corr
espond to a maximal linearly independent collection of rays in the deforma
tion cone of the permutahedron. In contrast\, Ardila-Castillo-Eur-Postniko
v observed that the faces of the cross-polytope only span a subspace of ro
ughly half the dimension of the deformation cone of the type B permutahedr
on. In this talk\, we use McMullen's polytope algebra to help explain this
phenomenon.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Kutler (Ohio State University)
DTSTART:20230117T200000Z
DTEND:20230117T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/28
DESCRIPTION:Title: Motivic Zeta functions of hyperplane arrangements\nby Max Kut
ler (Ohio State University) as part of Matroids - Combinatorics\, Algebra
and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\n
Abstract\nWe associate to any matroid a motivic zeta function. If the matr
oid is representable by a complex hyperplane arrangement\, then thiscoinci
des with the motivic Igusa zeta function of the arrangement.Although the m
otivic zeta function is a valuative invariant which is finer than the char
acteristic polynomial\, it is not obvious how one should extract meaningfu
l combinatorial data from the motivic zeta function. One strategy is to sp
ecialize to the topological zeta function. I will survey what is known abo
ut these functions and discuss some open questions.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Novak Spink (Stanford University)
DTSTART:20230119T200000Z
DTEND:20230119T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/29
DESCRIPTION:Title: Log-concavity of matroid h-vectors and mixed Eulerian numbers
\nby Hunter Novak Spink (Stanford University) as part of Matroids - Combin
atorics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fie
lds Institute.\n\nAbstract\nThe combinatorial Chow ring of a matroid produ
ces log-concave sequences from a list of polytopes called "generalized per
mutahedra". If we take S_n-invariant polytopes\, then we obtain matroid in
variants\, but what invariants do we obtain? We will discuss how many such
invariants are linear combinations of the h-vector of the independence co
mplex of a matroid by "mixed Eulerian numbers"\, and how this proves a str
engthening of a conjecture of Dawson on the log-concavity of the matroid h
-vector.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:June Huh (Princeton University)
DTSTART:20230124T200000Z
DTEND:20230124T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/30
DESCRIPTION:Title: Stellahedral geometry of matroids\nby June Huh (Princeton Uni
versity) as part of Matroids - Combinatorics\, Algebra and Geometry Semina
r\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nThe main
result is that valuative\, homological\, and numerical equivalence relatio
ns for matroids coincide. The central construction is the "augmented tauto
logical classes of matroids\," modeled after certain vector bundles on the
stellahedral toric variety. Based on joint work with Chris Eur and Matt L
arson\, https://arxiv.org/abs/2207.10605.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Maclagan (University of Warwick)
DTSTART:20230126T200000Z
DTEND:20230126T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/31
DESCRIPTION:Title: Tropical ideals\nby Diane Maclagan (University of Warwick) as
part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLectur
e held in Room 210 The Fields Institute.\n\nAbstract\nTropical ideals are
the building blocks for the theory of tropical schemes\, which are part of
a program to build foundations for tropical geometry. From a matroid per
spective\, they are "towers" of (valuated) matroids: for each degree d we
give a (valuated) matroid on the set of monomials of degree d in a polynom
ial ring. I will introduce this theory\, and explain the relevance of bet
ter understanding these matroids for tropical and algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART:20230131T200000Z
DTEND:20230131T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/32
DESCRIPTION:Title: Matrix orbit closures and their Hilbert functions\nby Alex Fi
nk (Queen Mary University of London) as part of Matroids - Combinatorics\,
Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Insti
tute.\n\nAbstract\nIf an ordered point configuration in projective space i
s represented by a matrix of coordinates\, the resulting matrix is determi
ned up to the action of the general linear group on one side and the torus
of diagonal matrices on the other. We study orbits of matrices under the
action of the product of these groups\, as well as their images in quotien
ts of the space of matrices like the Grassmannian. The main question is wh
at properties of closures of these orbits are determined by the matroid of
the point configuration\; the main result is that their equivariant K-cla
sses are so determined. I will also draw connections to positivity and the
work of Berget\, Eur\, Spink and Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Eur (Harvard University)
DTSTART:20230202T200000Z
DTEND:20230202T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/33
DESCRIPTION:Title: Signed permutohedra and delta matroids\nby Chris Eur (Harvard
University) as part of Matroids - Combinatorics\, Algebra and Geometry Se
minar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nDelta
-matroids are type B generalizations of matroids in the theory of Coxeter
matroids. We generalize many recent developments in the algebraic geometry
of matroids to that of delta-matroids. These include the theory of tautol
ogical classes of delta-matroids\, and formulas for volumes of type B gene
ralized permutohedra. In particular\, for a class of delta-matroids that i
ncludes all graphical delta-matroids\, we show a log-concavity for "Tutte
polynomials" of delta-matroids. Time permitting\, we'll indicate some futu
re directions in the pursuit of a "Hodge theory" for Coxeter matroids.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petter Brändén (KTH Royal Institute of Technology)
DTSTART:20230207T200000Z
DTEND:20230207T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/34
DESCRIPTION:Title: Lorentzian polynomials on cones (Part I).\nby Petter Brändé
n (KTH Royal Institute of Technology) as part of Matroids - Combinatorics\
, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Inst
itute.\n\nAbstract\nWe show how the theory of Lorentzian polynomials exten
ds to cones other than the positive orthant\, and how this may be used to
prove Hodge-Riemann relations of degree one for Chow rings. Joint work wit
h Jonathan Leake.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Joswig (MPI MiS Leipzig)
DTSTART:20230209T200000Z
DTEND:20230209T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/35
DESCRIPTION:Title: Generalized Permutahedra and Positive Flag Dressians\nby Mich
ael Joswig (MPI MiS Leipzig) as part of Matroids - Combinatorics\, Algebra
and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\
nAbstract\nWe study valuated matroids\, their tropical incidence relations
\, flag matroids and total positivity. This leads to a characterization of
subdivisions of regular permutahedra into generalized permutahedra. Furth
er\, we get a characterization of those subdivisions arising from positive
valuated flag matroids.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Piquerez (University of Nantes)
DTSTART:20230214T200000Z
DTEND:20230214T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/36
DESCRIPTION:Title: Tropical Hodge theory\nby Matthieu Piquerez (University of Na
ntes) as part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n
\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nDuring the l
ast decade\, several important long-standing conjectures about matroids\,
as the Heron-Rota-Welsh conjecture\, has been solved thanks to the develop
ment of the combinatorial Hodge theory by Huh and his collaborators. Class
ical Hodge theory is about the cohomology of complex varieties. For matroi
ds representable over the complex field\, this theory applied to some comp
lex varieties associated to the matroids implies the Heron-Rota-Welsh conj
ecture. For a general matroid\, Adiprasito\, Huh and Katz achieved to deve
lop a combinatorial Hodge theory for (Chow rings of) matroids which works
as if one can associate a complex variety to the matroid\, though this is
not the case. The proof is very clever but does not give much insight into
why this combinatorial Hodge theory works in general.\n\nActually\, every
matroid is in some sense representable over the tropical hyperfield. More
over\, in a joint work with Amini\, we developed a tropical Hodge theory.
Hence\, to every matroid one can associate a tropical variety (the canonic
ally compactified Bergman fan)\, and the Hodge properties of this variety
imply the Heron-Rota-Welsh conjecture. We thus get a geometric proof of th
e conjecture\, as well as an extension of the applicability of the combina
torial Hodge theory. The heart of our proof relies on a very interesting i
nduction\, based on the deletion-contraction induction."\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schroter (Goethe-Universität Frankfurt)
DTSTART:20230216T200000Z
DTEND:20230216T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/37
DESCRIPTION:Title: Valuative invariants for large classes of matroids\nby Benjam
in Schroter (Goethe-Universität Frankfurt) as part of Matroids - Combinat
orics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Field
s Institute.\n\nAbstract\nValuations on polytopes are maps that combine th
e geometry of polytopes with relations in a group. It turns out that many
important invariants of matroids are valuative on the collection of matroi
d base polytopes\, e.g.\, the Tutte polynomial and its specializations or
the Hilbert–Poincaré series of the Chow ring of a matroid.\n\nIn this t
alk I will present a framework that allows us to compute such invariants o
n large classes of matroids\, e.g.\, sparse paving and elementary split ma
troids\, explicitly. The concept of split matroids introduced by Joswig an
d myself is relatively new. However\, this class appears naturally in this
context. Moreover\, (sparse) paving matroids are split. I will demonstrat
e the framework by looking at Ehrhart polynomials and further examples. \n
\nThis talk is based on the preprint `Valuative invariants for large class
es of matroids' which is joint work with Luis Ferroni.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Rau (Universidad de los Andes)
DTSTART:20230228T190000Z
DTEND:20230228T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/38
DESCRIPTION:Title: The Lefschetz-Hopf trace formula for matroidal automorphisms\
nby Johannes Rau (Universidad de los Andes) as part of Matroids - Combinat
orics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Field
s Institute.\n\nAbstract\nThe Lefschetz-Hopf trace formula is a beautiful
topological statement that relates the fixed points of a map to an alterna
ting sum of traces on homology groups. The related Poincaré-Hopf index fo
rmula computes the Euler characteristic of a space in terms of the zeros o
f a vector field. In my talk\, I want to present analogous statements in t
ropical geometry\, in particular\, for matroid fans. In doing so\, we use
two ingredients that have received much attention over the last years: tro
pical homology on the homology side and tropical intersection theory on th
e fixed point/vector field side. The two sides will be connected using a c
ertain variant of the beta invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edvard Aksnes (University of Oslo)
DTSTART:20230302T200000Z
DTEND:20230302T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/39
DESCRIPTION:Title: Tropical Poincaré duality spaces\nby Edvard Aksnes (Universi
ty of Oslo) as part of Matroids - Combinatorics\, Algebra and Geometry Sem
inar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nBergma
n fans of matroids are the tropical equivalent of linear spaces. In the co
ntext of tropical homology\, such fans can be shown to satisfy tropical Po
incaré duality\, i.e. a duality between tropical homology and cohomology.
Thanks to work of Amini and Piquerez\, satisfying tropical Poincaré dual
ity is related to the combinatorial Hodge theory of the Matroid Chow ring
of Adiprasito-Huh-Katz. In this talk\, we will give some results on the pr
oblem of classifying which fans satisfy tropical Poincaré duality\, and g
ive some perspectives on recent work relating tropical Poincaré duality a
nd the cohomology of subvarieties of tori.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Shaw (University of Oslo)
DTSTART:20230307T200000Z
DTEND:20230307T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/40
DESCRIPTION:Title: The birational geometry of matroids\nby Kris Shaw (University
of Oslo) as part of Matroids - Combinatorics\, Algebra and Geometry Semin
ar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nIn this
talk\, I will consider isomorphisms of Bergman fans of matroids. Motivate
d by algebraic geometry\, such isomorphisms can be considered as matroid a
nalogs of birational maps. If the matroids in question are not totally dis
connected\, I will explain that an isomorphism respecting their fine fan s
tructures must be induced by a matroid isomorphism. However\, if we switch
to the coarse fan structure\, this is no longer the case. I will introduc
e Cremona automorphisms of the coarse structure of certain Bergman fans. T
hese produce a class of Bergman fan isomorphisms which are not induced by
matroid automorphisms. I will then explain that the automorphism group of
the coarse fan structure is generated by matroid automorphisms and Cremona
maps in the case of rank 3 matroids which are not parallel connections an
d for modularly complemented matroids. This is based on joint work with An
nette Werner.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Leake (University of Waterloo)
DTSTART:20230309T200000Z
DTEND:20230309T210000Z
DTSTAMP:20260404T094310Z
UID:Matroids/41
DESCRIPTION:Title: Lorentzian polynomial on cones Part II\nby Jonathan Leake (Un
iversity of Waterloo) as part of Matroids - Combinatorics\, Algebra and Ge
ometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstra
ct\nIn Part I\, Petter Brändén extended the theory of Lorentzian polynom
ials to cones beyond the positive orthant\, and showed how this could be u
sed to prove Hodge-Riemann relations of degree one for Chow rings. In this
talk\, we will recap the main points of his talk\, and then we will apply
the theory of Lorentzian polynomials on cones to some specific important
examples. Part I will not be required to understand this talk. Joint work
with Petter Brändén.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Bonin (The George Washington University)
DTSTART:20230321T190000Z
DTEND:20230321T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/42
DESCRIPTION:Title: An overview of recent developments on non-isomorphic matroids tha
t have the same G-invariant\nby Joseph Bonin (The George Washington Un
iversity) as part of Matroids - Combinatorics\, Algebra and Geometry Semin
ar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nThe G-in
variant\, which was introduced by Derksen\, is a matroid invariant that co
ntains all of the data in the Tutte polynomial\, and far more. The theory
of chromatic uniqueness and chromatic equivalence for graphs\, based on t
he chromatic polynomial\, has been developed extensively\, and there are m
any results for the analogous notions using the Tutte polynomial\, for bot
h graphs and matroids. The corresponding questions for the G-invariant ar
e ripe for exploration. This talk will survey recent results that yield no
n-isomorphic matroids that have the same G-invariant\, all aimed at sheddi
ng light on what minimal structure determines the G-invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suho Oh (Texas State University)
DTSTART:20230323T190000Z
DTEND:20230323T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/43
DESCRIPTION:Title: Extending Shellings\nby Suho Oh (Texas State University) as p
art of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture
held in Room 210 The Fields Institute.\n\nAbstract\nThe independent comple
x of a matroid is a shellable simplicial complex: their facets can be orde
red nicely\, which translates to interesting properties in algebra and com
binatorics. Simon in 1994 conjectured that any shellable complex can be ex
tended to the k-skeleton of a simplex while maintaining the shelling prope
rty. We go over various tools and results related to this problem. In part
icular\, we will be going over a recent joint work with M. Coleman\, A. Do
chtermann and N. Geist on proving this conjecture for a smaller class\, wh
ich contains the entire class of matroids.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Ferroni (KTH Royal Institute of Technology)
DTSTART:20230328T190000Z
DTEND:20230328T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/44
DESCRIPTION:Title: Ehrhart polynomials of matroid polytopes\nby Luis Ferroni (KT
H Royal Institute of Technology) as part of Matroids - Combinatorics\, Alg
ebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute
.\n\nAbstract\nA fundamental invariant associated to a lattice polytope is
its Ehrhart polynomial\, which encodes the number of lattice points insid
e all the integer dilations of the polytope and much more arithmetic\, alg
ebraic and combinatorial information. One may associate to any matroid two
polytopes called respectively the base polytope and the independence poly
tope\; both of these polytopes can be seen as part of the larger family of
generalized permutohedra. A conjecture of De Loera\, Haws and Köppe asse
rted that the Ehrhart polynomials of base polytopes of matroids had positi
ve coefficients only\; more generally\, Castillo and Liu conjectured this
was true for all generalized permutohedra (in particular\, also for indepe
ndence polytopes). We will show how to construct counterexamples to these
conjectures\; we will exhibit examples of matroids whose base and independ
ence polytopes attain negative Ehrhart coefficients. On the positive side\
, we will discuss about some families of matroids that satisfy Ehrhart pos
itivity. Several open problems regarding Ehrhart polynomials of matroids w
ill be stated.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spencer Backman (University of Vermont)
DTSTART:20230330T190000Z
DTEND:20230330T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/45
DESCRIPTION:Title: Higher Categorical Associahedra\nby Spencer Backman (Universi
ty of Vermont) as part of Matroids - Combinatorics\, Algebra and Geometry
Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nThe
associahedron is a well-known poset with connections to many different ar
eas of combinatorics\, algebra\, geometry\, topology\, and physics. The as
sociahedron has several different realizations as the face poset of a conv
ex polytope and one realization\, due to Loday\, is a generalized permutah
edron\, i.e. a polymatroid. From the perspective of symplectic geometry\,
the associahedron encodes the combinatorics of morphisms in the Fukaya cat
egory of a symplectic manifold. In 2017\, Bottman introduced a family of p
osets called 2-associahedra which encode the combinatorics of functors bet
ween Fukaya categories\, and he conjectured that they can be realized as t
he face posets of convex polytopes. In this talk we will introduce categor
ical n-associahedra as a natural extension of associahedra and 2-associahe
dra\, and we will produce a family of complete polyhedral fans called velo
city fans whose face posets are the categorical n-associahedra. Categorica
l n-associahedra cannot be realized by generalized permutahedra or any of
their known extensions. On the other hand\, our velocity fan specializes t
o the normal fan of Loday’s associahedron suggesting a new extension of
generalized permutahedra. This is joint work with Nathaniel Bottman and Da
ria Poliakova.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Larson (Stanford University)
DTSTART:20230404T190000Z
DTEND:20230404T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/46
DESCRIPTION:Title: Geometry of polymatroids\nby Matt Larson (Stanford University
) as part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLe
cture held in Room 210 The Fields Institute.\n\nAbstract\nJust as matroids
are combinatorial abstractions of hyperplane arrangements\, polymatroids
are combinatorial abstractions of subspace arrangements. In recent years\,
algebraic geometry has inspired many theorems about matroids. I will desc
ribe work establishing polymatroidal analogues of some of these results\,
often by reducing to the case of matroids. Joint work with Colin Crowley\,
Christopher Eur\, June Huh\, Connor Simpson\, and Botong Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Oxley (Louisiana State University)
DTSTART:20230406T190000Z
DTEND:20230406T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/47
DESCRIPTION:Title: Graphs\, Matroids\, Cographs and Comatroids\nby James Oxley (
Louisiana State University) as part of Matroids - Combinatorics\, Algebra
and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\n
Abstract\n“If a theorem about graphs can be expressed in terms of edges
and circuits only it probably exemplifies a more general theorem about mat
roids.” These words of Bill Tutte from 1979 have had a profound influenc
e on research in matroid theory. This talk will discuss an example of rece
nt work that was motivated by Tutte’s guiding principle. The class of co
graphs or complement- reducible graphs is the class of graphs that can be
generated from K1 using the operations of disjoint union and complementati
on. We define 2-cographs to be the graphs we get by also allowing the oper
ation of 1-sum. By analogy\, we introduce the class of binary comatroids a
s the class of matroids that can be generated from the empty matroid using
the operations of direct sum and taking complements inside of binary proj
ective space. This talk will explore the properties of 2-cographs and bina
ry comatroids. The main results characterize these classes in terms of for
bidden induced minors. This is joint work with Jagdeep Singh.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Ardila (San Francisco State University)
DTSTART:20230411T190000Z
DTEND:20230411T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/48
DESCRIPTION:Title: Combinatorial Intersection Theory: A Few Examples\nby Federic
o Ardila (San Francisco State University) as part of Matroids - Combinator
ics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields
Institute.\n\nAbstract\nIntersection theory studies how subvarieties of an
algebraic variety X intersect. Algebraically\, this information is encode
d in the Chow ring A(X). When X is the toric variety of a simplicial fan\,
Brion gave a presentation of A(X) in terms of generators and relations\,
and Fulton and Sturmfels gave a ""fan displacement rule” to intersect cl
asses in A(X)\, which holds more generally in tropical intersection theory
. In these settings\, intersection theoretic questions translate to algebr
aic combinatorial computations in one point of view\, or to polyhedral com
binatorial questions in the other. Both of these paths lead to interesting
combinatorial problems\, and in some cases\, they are important ingredien
ts in the proofs of long-standing conjectural inequalities.\n\nThis talk w
ill survey a few problems on matroids and root systems that arise in combi
natorial intersection theory. It will feature joint work with Montse Corde
ro\, Graham Denham\, Chris Eur\, June Huh\, Carly Klivans\, and Raúl Pena
guião. The talk will not assume previous knowledge of the words in the ab
stract.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cynthia Vinzant (University of Washington)
DTSTART:20230413T190000Z
DTEND:20230413T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/49
DESCRIPTION:Title: Positively Hyperbolic Varieties\, Tropicalization\, and Positroid
s\nby Cynthia Vinzant (University of Washington) as part of Matroids -
Combinatorics\, Algebra and Geometry Seminar\n\nLecture held in Room 210
The Fields Institute.\n\nAbstract\nHyperbolic varieties are a generalizati
on of real-rooted polynomials for varieties of codimension more than one.
One prominent example is the image of linear space under coordinate-wise i
nversion. I will discuss the combinatorial structure of varieties that are
hyperbolic with respect to the nonnegative Grassmannian\, which is intima
tely related with the theory of positroids. These varieties generalize mul
tivariate stable polynomials and their tropicalizations are locally subfan
s of the type-A hyperplane arrangement\, in which the maximal cones satisf
y a non-crossing condition. This is based on joint work with Felipe Rincó
n and Josephine Yu.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Kung (University of North Texas)
DTSTART:20230418T190000Z
DTEND:20230418T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/50
DESCRIPTION:Title: Tutte polynomial evaluations which are exponential sums.\nby
Joseph Kung (University of North Texas) as part of Matroids - Combinatoric
s\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields In
stitute.\n\nAbstract\nAn exponential sum is a sum $\\sum_{I=0}^{m-1} a_i \
\omega^I$\, where $\\omega$ is a primitive $m$th root of unity. We will
show several examples of Tutte polynomial evaluations which are exponentia
l sums. In particular\, for a matroid $G$ representable over a finite fie
ld of order $q$\, then the evaluation $q^{r(M)} \\chi (G\;q)$\, where $\\
chi$ is the characteristic polynomial\, can be written as an exponential
sum in which the coefficients $a_i$ have an enumerative interpretation.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christin Bibby (Louisiana State University)
DTSTART:20230420T190000Z
DTEND:20230420T200000Z
DTSTAMP:20260404T094310Z
UID:Matroids/51
DESCRIPTION:Title: Matroid schemes and geometric posets\nby Christin Bibby (Loui
siana State University) as part of Matroids - Combinatorics\, Algebra and
Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbst
ract\nThe intersection data of an arrangement of hyperplanes is described
by a geometric lattice\, or equivalently a simple matroid. There is a rich
interplay between this combinatorial structure and the topology of the ar
rangement complement. In this talk\, we will similarly characterize the co
mbinatorial structure underlying certain arrangements of subvarieties by d
efining a class of geometric posets and a generalization of matroids calle
d matroid schemes. We will discuss some notions from matroid theory which
extend to this setting and touch on the topological implications of this f
ramework.\n
LOCATION:https://stable.researchseminars.org/talk/Matroids/51/
END:VEVENT
END:VCALENDAR