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BEGIN:VEVENT
SUMMARY:Alexander Smirnov (Steklov Institute)
DTSTART;VALUE=DATE-TIME:20220119T140000Z
DTEND;VALUE=DATE-TIME:20220119T153000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/1
DESCRIPTION:Title: The 10th Discriminant and Tensor Powers of Z\nby Alexander Smir
nov (Steklov Institute) as part of F1 World Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Connes (IHES)
DTSTART;VALUE=DATE-TIME:20220202T140000Z
DTEND;VALUE=DATE-TIME:20220202T153000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/2
DESCRIPTION:Title: F1\, q and zeta\nby Alain Connes (IHES) as part of F1 World Sem
inar\n\n\nAbstract\nThis work is joint work with C. Consani. I will start
from the role of the limit $q \\rightarrow 1$ in the classical number theo
ry formulas of Hasse-Weil when dealing with Riemann’s zeta function\, an
d will then explore the various geometric paradigms corresponding to the l
imit. First the paradigm of characteristic one\, which is tropical and the
n the paradigm of the sphere spectrum which is based on Segal’s gamma ri
ngsand leads to a new algebraic geometry\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Sistko (Manhattan College)
DTSTART;VALUE=DATE-TIME:20220216T140000Z
DTEND;VALUE=DATE-TIME:20220216T153000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/3
DESCRIPTION:Title: $\\mathbb{F}_1$-Representations of Quivers and Euler Characteristic
s of Quiver Grassmannians\nby Alex Sistko (Manhattan College) as part
of F1 World Seminar\n\n\nAbstract\nTo any quiver $Q$\, we can associate it
s category of finite-dimensional representations over $\\mathbb{F}_1$. Thi
s is a finitary proto-exact category\, which admits a version of the Krull
-Schmidt Theorem and a Hall algebra. For any field $k$\, there is also a f
aithful functor which carries $\\mathbb{F}_1$-representations to $k$-repre
sentations: the case where $k$ is the complex numbers is of particular int
erest\, where Euler characteristics of quiver Grassmannians find relevance
to cluster theory. Recently\, it was shown that the category of $\\mathb
b{F}_1$-representations of Q admits a description via coefficient quivers.
In this talk\, we show how this description helps us generalize existing
techniques to compute Euler characteristics of quiver Grassmannians and pl
ace them in a new context. We introduce the nice length of an $\\mathbb{F}
_1$-representation\, and show that when this quantity is finite\, there is
a simple combinatorial interpretation to the Euler characteristics of the
quiver Grassmannians. We recover several results from the literature\, an
d identify new classes of $\\mathbb{F}_1$-representations towards which th
e classic techniques apply. Time permitting\, we also discuss the category
of $\\mathbb{F}_1$-representations with finite nice length and recent eff
orts to describe it. This is joint work with Jaiung Jun.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Eur (Harvard University)
DTSTART;VALUE=DATE-TIME:20220302T140000Z
DTEND;VALUE=DATE-TIME:20220302T153000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/4
DESCRIPTION:Title: Tautological classes of matroids\nby Chris Eur (Harvard Univers
ity) as part of F1 World Seminar\n\n\nAbstract\nAlgebraic geometry has fur
nished fruitful tools for studying matroids\, which are combinatorial abst
ractions of hyperplane arrangements. We first survey some recent developme
nts\, pointing out how these developments remained partially disjoint. We
then introduce certain vector bundles (K-classes) on permutohedral varieti
es\, which we call "tautological bundles (classes)" of matroids\, as a new
framework that unifies\, recovers\, and extends these recent developments
. Our framework leads to new questions that further probe the boundary bet
ween combinatorics and geometry. Joint work with Andrew Berget\, Hunter Sp
ink\, and Dennis Tseng.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oren Ben-Bassat (University of Haifa)
DTSTART;VALUE=DATE-TIME:20220316T130000Z
DTEND;VALUE=DATE-TIME:20220316T143000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/5
DESCRIPTION:Title: Derived Analytic Geometry\nby Oren Ben-Bassat (University of Ha
ifa) as part of F1 World Seminar\n\n\nAbstract\nI will start by reviewing
some work of others: sketching a (higher) categorical approach to geometry
. After that\, I will explain how using this approach (derived) analytic g
eometry can be viewed in a precise way as a type of algebraic geometry. I
will explain and use in a fundamental way Banach rings and categories of B
anach modules over a Banach ring. The theories of derived analytic geomet
ry from this perspective include both archimedean and non-archimedean anal
ytic theories. I will give examples of homotopy epimorphisms between alge
bras of analytic nature. I will include examples and relevance in the rigi
d analytic context and an arithmetic context. I will discuss descent theor
ems and time permitting\, other topics such as blow-ups.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Tulane University)
DTSTART;VALUE=DATE-TIME:20220330T130000Z
DTEND;VALUE=DATE-TIME:20220330T143000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/6
DESCRIPTION:Title: Tropical Geometry and the Commutative Algebra of Semirings\nby
Kalina Mincheva (Tulane University) as part of F1 World Seminar\n\n\nAbstr
act\nTropical geometry provides a new set of purely combinatorial tools\,
which has been used to approach classical problems. In the recent years\,
there has been a lot of effort dedicated to developing the necessary tools
for commutative algebra using different frameworks\, among which prime co
ngruences\, tropical ideals\, tropical schemes. These approaches allows fo
r the exploration of the properties of tropicalized spaces without tying
them up to the original varieties and working with geometric structures in
herently defined in characteristic one (that is\, additively idempotent) s
emifields. In this talk we explore the relationship between tropical ideal
s and congruences and what they remember about the geometry of a tropical
variety. The talk will give some overview of recent results and work in pr
ogress.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Matherne (University of Bonn)
DTSTART;VALUE=DATE-TIME:20220427T130000Z
DTEND;VALUE=DATE-TIME:20220427T143000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/7
DESCRIPTION:Title: Equivariant log-concavity\, matroids\, and representation stability
\nby Jacob Matherne (University of Bonn) as part of F1 World Seminar\n
\n\nAbstract\nAdiprasito\, Huh\, and Katz proved that the Betti numbers of
the Orlik-Solomon algebra of any matroid form a log-concave sequence. No
w suppose that the matroid has symmetries. Then\, the Orlik-Solomon algebr
a becomes a graded representation of that symmetry group. In this situati
on\, I will conjecture an equivariant version of the log-concavity result
above. Then\, I will show how one can use the theory of representation st
ability to prove infinitely-many cases of this conjecture for the braid ma
troid\, acted on by the symmetric group. This is joint work with Dane Miy
ata\, Nicholas Proudfoot\, and Eric Ramos.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Van Maldeghem (Ghent University)
DTSTART;VALUE=DATE-TIME:20220525T130000Z
DTEND;VALUE=DATE-TIME:20220525T143000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/8
DESCRIPTION:Title: Classical and exceptional geometries of order one\nby Hendrik V
an Maldeghem (Ghent University) as part of F1 World Seminar\n\n\nAbstract\
nIn the spirit of Jacques Tits' original observation about geometries over
the field of order 1\, we review properties of these geometries. In parti
cular we demonstrate how such properties can tell us something new about t
heir analogues over proper fields. Along the way we discuss Galois descent
\, a Magic Square\, triality and split octonions\, all over Fun.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manoel Jarra (Instituto de Matemática Pura e Aplicada)
DTSTART;VALUE=DATE-TIME:20220413T130000Z
DTEND;VALUE=DATE-TIME:20220413T143000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/9
DESCRIPTION:Title: Flag matroids with coefficients\nby Manoel Jarra (Instituto de
Matemática Pura e Aplicada) as part of F1 World Seminar\n\n\nAbstract\nMa
troids encode the combinatorics of independence in linear subspaces\, as w
ell flag matroids do for flags of subspaces. There is a way back: when rep
resenting a (flag) matroid over a field\, we get a (flag of) linear subspa
ce(s). In recent years\, Baker and Bowler generalized this picture to a mo
re general type of algebraic object that includes fields and hyperfields a
s particular cases. In this talk we explain how to extend this theory to f
lag matroids\, including a geometric interpretation in terms of their modu
li space. This is a joint work with Oliver Lorscheid.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Institute of Technology)
DTSTART;VALUE=DATE-TIME:20221116T143000Z
DTEND;VALUE=DATE-TIME:20221116T153000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/11
DESCRIPTION:Title: Foundations of Matroids\nby Matt Baker (Georgia Institute of T
echnology) as part of F1 World Seminar\n\n\nAbstract\nMatroid theorists ar
e interested in questions concerning representability of matroids over fie
lds. More generally\, one can ask about representability over partial fiel
ds in the sense of Semple and Whittle. Pendavingh and van Zwam introduced
the universal partial field of a matroid\, which governs the representatio
ns of over all partial fields. Unfortunately\, most matroids are not repre
sentable over any partial field\, and in this case\, the universal partial
field is not defined. Oliver Lorscheid and I have introduced a generaliza
tion of the universal partial field which we call the foundation of a matr
oid\; it is always well-defined. The foundation is a type of algebraic obj
ect which we call a pasture\; pastures include both hyperfields and partia
l fields. As a particular application of this point of view\, I will expla
in the classification of all possible foundations for matroids having no m
inor 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 s
ays that a matroid is both ternary and orientable if and only if it is dya
dic.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samarpita Ray (Indiana University)
DTSTART;VALUE=DATE-TIME:20221130T143000Z
DTEND;VALUE=DATE-TIME:20221130T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/12
DESCRIPTION:Title: The topological shadow of $\\mathbb{F}_1$-geometry: congruence spa
ces\nby Samarpita Ray (Indiana University) as part of F1 World Seminar
\n\n\nAbstract\nIn this talk\, we introduce a topological shadow for monoi
d schemes\, which we call the congruence space. It is constructed from mon
oid congruences (instead of ideals) and carries the "right" topological in
formation about closed subsets. This allows us to extend topological chara
cterizations (and definitions) of several notions from usual scheme theory
to monoid schemes\, such as closed immersions and subschemes\, as well as
separated and proper morphisms. This is a joint work with Oliver Lorschei
d\, and soon to appear.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nethanel Friedenberg (Tulane University)
DTSTART;VALUE=DATE-TIME:20230222T143000Z
DTEND;VALUE=DATE-TIME:20230222T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/13
DESCRIPTION:Title: Towards tropical adic spaces\nby Nethanel Friedenberg (Tulane
University) as part of F1 World Seminar\n\n\nAbstract\nAfter a brief intro
duction to tropical geometry\, I will introduce a new approach to endowing
tropical varieties with additional structure. The approach will be analyt
ic in nature\, and so we will focus on the algebra of tropical power serie
s. We introduce the continuous spectrum of a topological semiring\, and sh
ow that\, in the case of tropical power series\, it can be understood as a
set of prime congruences on the algebra of tropical polynomials. If time
permits\, we will see that the dimension behaves as expected and that the
points the continuous spectrum can be interpreted in terms of more classic
al geometry.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaeho Shin (Seoul National University)
DTSTART;VALUE=DATE-TIME:20230125T143000Z
DTEND;VALUE=DATE-TIME:20230125T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/14
DESCRIPTION:Title: Birational Geometry of Matroids and Abstract Hyperplane Arrangemen
ts\nby Jaeho Shin (Seoul National University) as part of F1 World Semi
nar\n\n\nAbstract\nA matroid is a machine that captures linearity of mathe
matical objects and produces combinatorial structures. Matroids arise ever
ywhere\, as linearity does. One of the most natural appearances of matroid
s is from hyperplane arrangements. Although much research on the three thi
ngs: matroids\, matroid polytopes\, and hyperplane arrangements in a trila
teral relation has been done\, the gaps in our knowledge base remain subst
antial. For example\, we do not have matroidal counterparts corresponding
to matroid subdivisions\, and only some matroid subdivisions are associate
d with stable hyperplane arrangements\, which indicates that the trilatera
l relation needs improvement. Further\, we need to learn more about the fa
ce structure of a matroid polytope and how to glue or subdivide base polyt
opes\, which are inarguably essential questions. It is also an interesting
question if the geometry of hyperplane arrangements can be implemented ov
er matroids\, and then how much of it. This talk will discuss how to devel
op a theory combining the three things into a trinity relation to answer a
s many questions as possible\, such as the previously mentioned ones.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20230208T143000Z
DTEND;VALUE=DATE-TIME:20230208T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/15
DESCRIPTION:Title: Cancelled\nby TBA as part of F1 World Seminar\n\n\nAbstract\nC
ancelled\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Caramello (University of Insubria)
DTSTART;VALUE=DATE-TIME:20230322T133000Z
DTEND;VALUE=DATE-TIME:20230322T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/17
DESCRIPTION:Title: Grothendieck toposes as unifying 'bridges' in Mathematics\nby
Olivia Caramello (University of Insubria) as part of F1 World Seminar\n\n\
nAbstract\nI will explain the sense in which Grothendieck toposes can act
as unifying 'bridges' for relating different mathematical theories to each
other and studying them from a multiplicity of points of view. I shall fi
rst present the general techniques underpinning this theory and then discu
ss a number of selected applications in different mathematical fields.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Kock (Universitat Autonoma de Barcelona)
DTSTART;VALUE=DATE-TIME:20230405T133000Z
DTEND;VALUE=DATE-TIME:20230405T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/18
DESCRIPTION:Title: Some basic steps in objective linear algebra\nby Joachim Kock
(Universitat Autonoma de Barcelona) as part of F1 World Seminar\n\n\nAbstr
act\nThe 'objective method'\, advocated by Lawvere\, seeks to calculate di
rectly with combinatorial objects\, rather than with their numbers. In alg
ebraic combinatorics\, this is largely a question of doing linear algebra
over the 'ground field' of finite sets (or groupoids or infinity-groupoids
). The role of vector spaces is played by slice categories\, and the role
of linear maps is played by linear functors (which here means colimit-pres
erving functors)\, which in turn can be represented by spans\, so that 'ma
trix multiplication' is given by pullbacks. The ordinary vector-space leve
l is recovered from the objective level by taking (homotopy) cardinality.
After explaining the basic theory\, the talk will focus on finiteness cond
itions and the objective version of the duality between vector spaces and
pro-finite-dimensional vector spaces\, including a neat combinatorial inte
rpretation of continuity. To finish I will briefly outline how the basic s
et-up supports more elaborate algebraic structures\, such as incidence bia
lgebras\, Möbius inversion\, and antipodes.\n\nThis is based on joint wor
k with Imma Gálvez and Andy Tonks.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inna Zakharevich (Cornell University)
DTSTART;VALUE=DATE-TIME:20230420T150000Z
DTEND;VALUE=DATE-TIME:20230420T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/19
DESCRIPTION:Title: Coinvariants\, assembler K-theory\, and scissors congruence\nb
y Inna Zakharevich (Cornell University) as part of F1 World Seminar\n\n\nA
bstract\nFor a geometry $X$ (such as Euclidean\, spherical\, or hyperbolic
) with isometry group $G$ the scissors congruence group $\\mathcal{P}(X\,G
)$ is defined to be the free abelian group generated by polytopes in $X$\,
modulo the relation that for polytopes $P$ and $Q$ that intersect only on
the boundary\, $[P\\cup Q] = [P] + [Q]$\, and for $g\\in G$\, $[P] = [g \
\cdot P]$. This group classifies polytopes up to "scissors congruence\,"
i.e. cutting up into pieces\, rearranging the pieces\, and gluing them bac
k together. With some basic group homology one can see that $\\mathcal{P}
(X\,G) \\cong H_0(G\, \\mathcal{P}(X\,1))$. Using combinatorial $K$-theor
y $\\mathcal{P}(X\,G)$ can be expressed as the $K_0$ of a spectrum $K(X\,G
)$. In this talk\, we will generalize this formula to show that\, in fact
\, $K(X\,G) \\simeq K(X\,1)_{hG}$\, and in fact more generally that this i
s true for any assembler with a $G$-action. This is joint work with Anna
Marie Bohmann\, Teena Gerhardt\, Cary Malkiewich\, and Mona Merling.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (l'École Polytechnique)
DTSTART;VALUE=DATE-TIME:20230503T133000Z
DTEND;VALUE=DATE-TIME:20230503T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/20
DESCRIPTION:Title: Postponed\nby Omid Amini (l'École Polytechnique) as part of F
1 World Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hernan Iriarte (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20230517T133000Z
DTEND;VALUE=DATE-TIME:20230517T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/21
DESCRIPTION:Title: Weak continuity on the variation of Newton Okounkov bodies\nby
Hernan Iriarte (University of Texas at Austin) as part of F1 World Semina
r\n\n\nAbstract\nWe start by presenting new tools and results suitable for
the study of valuations of higher rank on function fields of algebraic va
rieties. This will be based on a study of higher rank quasi-monomial valua
tions taking values in the lexicographically ordered group $\\mathbb{R}^k$
. This gives us a space of higher rank valuations that we endow with a wea
k "tropical" topology. In this setting\, we show that the Newton Okounkov
bodies of a given line bundle vary continuously with respect to the valuat
ion. We explain how this result fits in the literature and how it gives us
a restriction in the existence of mutations of Newton Okounkov bodies. Jo
int work with Omid Amini.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (l'École Polytechnique)
DTSTART;VALUE=DATE-TIME:20230920T133000Z
DTEND;VALUE=DATE-TIME:20230920T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/22
DESCRIPTION:Title: Higher rank inner products\, higher rank Voronoi tilings\, and met
ric degenerations of polarized tori\nby Omid Amini (l'École Polytechn
ique) as part of F1 World Seminar\n\n\nAbstract\nThe aim of the talk is to
introduce higher rank inner products on real and complex vector spaces an
d to discuss properties of their corresponding Voronoi tilings. I will exp
lain how the framework can be used to describe metric degenerations of pol
arized tori\, using Gromov-Hausdorff limits of Voronoi tilings\, and prese
nt applications in asymptotic complex geometry. Based on joint work with N
oema Nicolussi.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20231101T133000Z
DTEND;VALUE=DATE-TIME:20231101T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/23
DESCRIPTION:Title: Multimatroids and Rational Curves with Cyclic Action (postponed)\nby Shiyue Li (Institute for Advanced Study) as part of F1 World Semina
r\n\n\nAbstract\nI will share with you a connection between multimatroids
and moduli spaces of rational curves with cyclic action. Multimatroids are
generalizations of matroids and delta-matroids that naturally arise from
topological graph theory. The main result is a combinatorial formula for c
ertain intersection numbers on the moduli space by relating to the volumes
of independence polytopal complexes of multimatroids. Based on past and o
n-going joint works with Emily Clader\, Chiara Damiolini\, Chris Eur\, Dao
ji Huang\, and Rohini Ramadas.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Reyes (UC Irvine)
DTSTART;VALUE=DATE-TIME:20231004T150000Z
DTEND;VALUE=DATE-TIME:20231004T163000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/24
DESCRIPTION:Title: Categories of hypergroups and hyperstructures\nby Manuel Reyes
(UC Irvine) as part of F1 World Seminar\n\n\nAbstract\nA hyperoperation o
n a set M is an operation that associates to each pair of elements a subse
t of M. Hypergroups and hyperrings are two examples of structures defined
in terms of hyperoperations. While they were respectively defined in the 1
930s and 1950s\, they have recently gained prominence through various appe
arances in number theory\, combinatorics\, and absolute algebraic geometry
. However\, to date there has been relatively little attention given to ca
tegories of hyperstructures.\n\nWe will discuss several categories of hype
rstructures that generalize hypergroups. A common theme is that in order f
or these categories to enjoy good properties like (co)completeness\, we mu
st allow for the product or sum of two elements to be the empty subset\, w
hich is explicitly forbidden for hypergroups. In particular\, we will intr
oduce a category of hyperstructures called mosaics whose subcategory of co
mmutative objects possess a closed monoidal structure reminiscent of the t
ensor product of abelian groups. This is joint work with So Nakamura.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uly Alvarez (University of Alabama)
DTSTART;VALUE=DATE-TIME:20231115T143000Z
DTEND;VALUE=DATE-TIME:20231115T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/25
DESCRIPTION:Title: Cluster algebras and quiver grassmannians\nby Uly Alvarez (Uni
versity of Alabama) as part of F1 World Seminar\n\n\nAbstract\nSince their
conception\, cluster algebras have made appearances in different fields s
uch as algebra\, combinatorics\, geometry\, and topology. For example\, a
class of objects called quiver Grassmannians have been useful in describin
g the generators of cluster algebras using the Euler characteristic. This
has motivated the task of finding cell decomposition of quiver Grassmannia
ns. \nKyungyong Lee and I have been working on this problem for a class of
quivers which we will call surface quivers.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shai Haran (Technion)
DTSTART;VALUE=DATE-TIME:20231018T133000Z
DTEND;VALUE=DATE-TIME:20231018T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/26
DESCRIPTION:Title: Non additive geometry\nby Shai Haran (Technion) as part of F1
World Seminar\n\n\nAbstract\nReplacing Rings (with addition and multiplica
tion) by the collection of all matrices over them\, (with matrix multiplic
ation and block direct sums) - a structure of a “Prop” - a strict symm
etric monoidal category generated by one object\, and similarly replacing
Rings by the collection of raw and column vectors over them - a structure
of a “Bioperad” - two closed symmetric operads acting on each other\,
we define the “commutative” Props and Bioperads\, and we develop algeb
raic geometry following closely Grothendieck’s footsteps.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maxwell (University of Bristol)
DTSTART;VALUE=DATE-TIME:20231129T150000Z
DTEND;VALUE=DATE-TIME:20231129T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/27
DESCRIPTION:Title: Geometry of tropical extensions of hyperfields\nby James Maxwe
ll (University of Bristol) as part of F1 World Seminar\n\n\nAbstract\nI wi
ll introduce Relatively Algebraically Closed (RAC) maps and tropical exten
sions of hyperfields\, along with recalling the required background on hyp
erfields. Then\, the framework of ‘enriched valuations’ as hyperfield
homomorphisms to tropical extensions will be presented\, and it will be sh
own that a notable family of them are RAC. I will the discuss our main res
ults which include hyperfield analogues of Kapranov’s theorem and the fu
ndamental theorem of tropical geometry. This will highlight the utility of
the RAC property in this generalised setting. I will conclude by outlinin
g applications of our results. The work I will present is from two recent
papers\, one of which is joint work with Ben Smith (Manchester).\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20240110T143000Z
DTEND;VALUE=DATE-TIME:20240110T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/28
DESCRIPTION:Title: Multimatroids and Rational Curves with Cyclic Action\nby Shiyu
e Li (Institute for Advanced Study) as part of F1 World Seminar\n\n\nAbstr
act\nI will share with you a connection between multimatroids and moduli s
paces of rational curves with cyclic action. Multimatroids are generalizat
ions of matroids and delta-matroids that naturally arise from topological
graph theory. The main result is a combinatorial formula for certain inter
section numbers on the moduli space by relating to the volumes of independ
ence polytopal complexes of multimatroids. Based on past and on-going join
t works with Emily Clader\, Chiara Damiolini\, Chris Eur\, Daoji Huang\, a
nd Rohini Ramadas.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Schleis (University of Tübingen)
DTSTART;VALUE=DATE-TIME:20240131T143000Z
DTEND;VALUE=DATE-TIME:20240131T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/29
DESCRIPTION:Title: Tropical quiver Grassmannians\nby Victoria Schleis (University
of Tübingen) as part of F1 World Seminar\n\n\nAbstract\nGrassmannians an
d flag varieties are important moduli spaces in algebraic geometry. Quiver
Grassmannians are generalizations of these spaces arise in representation
theory as the moduli spaces of quiver subrepresentations. These represent
arrangements of vector subspaces satisfying linear relations provided by
a directed graph.\n\nThe methods of tropical geometry allow us to study th
ese algebraic objects combinatorially and computationally. We introduce ma
troidal and tropical analoga of quivers and their Grassmannians obtained i
n joint work with Alessio Borzì and separate joint work with Giulia Iezzi
\; and describe them as affine morphisms of valuated matroids and linear m
aps of tropical linear spaces.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tong Jin (Georgia Institute of Technology)
DTSTART;VALUE=DATE-TIME:20240228T143000Z
DTEND;VALUE=DATE-TIME:20240228T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/30
DESCRIPTION:Title: Three approaches to the representation space of a matroid\nby
Tong Jin (Georgia Institute of Technology) as part of F1 World Seminar\n\n
\nAbstract\nOne of the oldest problems in matroid theory is to determine w
hether a matroid is linearly representable over a given field K. In this t
alk\, we study the set of all representations of a matroid over pastures
– a generalization of fields\, so that all matroids are taken into consi
deration\, and then give algorithms to construct all equivalence classes o
f representations in three different approaches: by the pairs of circuits
and cocircuits\, by the hyperplane matrices\, and by the cross ratios in t
he lattice of flats. This is joint work with Matt Baker and Oliver Lorsche
id.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Usatine (Florida State University)
DTSTART;VALUE=DATE-TIME:20240214T143000Z
DTEND;VALUE=DATE-TIME:20240214T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/31
DESCRIPTION:Title: Gromov-Witten theory and invariants of matroids\nby Jeremy Usa
tine (Florida State University) as part of F1 World Seminar\n\n\nAbstract\
nMatroids are versatile combinatorial objects with deep connections to man
y subjects\, including chromatic polynomials of graphs\, arrangements of v
ectors and hyperplanes\, and the geometry of Grassmannians. I will discuss
joint work with Dhruv Ranganathan in which we use Gromov--Witten theory t
o associate new invariants to matroids. In particular\, I will explain how
to obtain a canonical (independent of chosen realization) quantum deforma
tion of any realizable matroid's cohomology ring.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Tolliver
DTSTART;VALUE=DATE-TIME:20240424T153000Z
DTEND;VALUE=DATE-TIME:20240424T163000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/32
DESCRIPTION:Title: Equivariant vector bundles on tropical toric schemes\nby Jeff
Tolliver as part of F1 World Seminar\n\n\nAbstract\nThe classification of
torus-equivariant vector bundles on toric varieties has been extensively s
tudied in the classical setting. I will describe an analogous theory over
idempotent semirings. Unlike the classical setting\, every equivariant v
ector bundle on a toric scheme splits uniquely as a direct sum of line bun
dles\, and so the classification reduces to the line bundle case. As I wi
ll explain\, there is a short exact sequence linking the group of equivari
ant line bundles to the Picard group and another group whose presentation
may be described explicitly in terms of the fan.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Beardsley (University of Nevada\, Reno)
DTSTART;VALUE=DATE-TIME:20240403T150000Z
DTEND;VALUE=DATE-TIME:20240403T160000Z
DTSTAMP;VALUE=DATE-TIME:20240804T061247Z
UID:F1WorldSeminar/33
DESCRIPTION:Title: Toward Higher Algebra of Connes-Consani $\\mathbb{F}_1$-modules\nby Jonathan Beardsley (University of Nevada\, Reno) as part of F1 World
Seminar\n\n\nAbstract\nI'll review the category of $\\mathbb{F}_1$-module
s introduced by Connes and Consani (which they call s-modules). To motivat
e the use of this category for algebra over $\\mathbb{F}_1$ I will describ
e some new work with S. Nakamura connecting it to combinatorial projective
geometry. After this\, I will propose a homotopical extension of Connes a
nd Consani's theory. I'll describe some elementary results\, from joint wo
rk with J. Moeller\, indicating that this is a suitable way to do "derived
" algebra over $\\mathbb{F}_1$.\n
LOCATION:https://researchseminars.org/talk/F1WorldSeminar/33/
END:VEVENT
END:VCALENDAR