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BEGIN:VEVENT
SUMMARY:Alexander Smirnov (Steklov Institute)
DTSTART:20220119T140000Z
DTEND:20220119T153000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/1
DESCRIPTION:Title: The 10th Discriminant and Tensor Powers of Z\nby Alexand
er Smirnov (Steklov Institute) as part of F1 World Seminar\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Connes (IHES)
DTSTART:20220202T140000Z
DTEND:20220202T153000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/2
DESCRIPTION:Title: F1\, q and zeta\nby Alain Connes (IHES) as part of F1 Wo
rld Seminar\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 numb
er theory formulas of Hasse-Weil when dealing with Riemann’s zeta functi
on\, and will then explore the various geometric paradigms corresponding t
o the limit. First the paradigm of characteristic one\, which is tropical
and then the paradigm of the sphere spectrum which is based on Segal’s g
amma ringsand leads to a new algebraic geometry\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Sistko (Manhattan College)
DTSTART:20220216T140000Z
DTEND:20220216T153000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/3
DESCRIPTION:Title: $\\mathbb{F}_1$-Representations of Quivers and Euler Charact
eristics of Quiver Grassmannians\nby Alex Sistko (Manhattan College) a
s part of F1 World Seminar\n\n\nAbstract\nTo any quiver $Q$\, we can assoc
iate its category of finite-dimensional representations over $\\mathbb{F}_
1$. This is a finitary proto-exact category\, which admits a version of th
e Krull-Schmidt Theorem and a Hall algebra. For any field $k$\, there is a
lso a faithful functor which carries $\\mathbb{F}_1$-representations to $k
$-representations: the case where $k$ is the complex numbers is of particu
lar interest\, where Euler characteristics of quiver Grassmannians find re
levance to cluster theory. Recently\, it was shown that the category of $
\\mathbb{F}_1$-representations of Q admits a description via coefficient q
uivers. In this talk\, we show how this description helps us generalize ex
isting techniques to compute Euler characteristics of quiver Grassmannians
and place them in a new context. We introduce the nice length of an $\\ma
thbb{F}_1$-representation\, and show that when this quantity is finite\, t
here is a simple combinatorial interpretation to the Euler characteristics
of the quiver Grassmannians. We recover several results from the literatu
re\, and identify new classes of $\\mathbb{F}_1$-representations towards w
hich the classic techniques apply. Time permitting\, we also discuss the c
ategory of $\\mathbb{F}_1$-representations with finite nice length and rec
ent efforts to describe it. This is joint work with Jaiung Jun.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Eur (Harvard University)
DTSTART:20220302T140000Z
DTEND:20220302T153000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/4
DESCRIPTION:Title: Tautological classes of matroids\nby Chris Eur (Harvard
University) as part of F1 World Seminar\n\n\nAbstract\nAlgebraic geometry
has furnished fruitful tools for studying matroids\, which are combinatori
al abstractions of hyperplane arrangements. We first survey some recent de
velopments\, pointing out how these developments remained partially disjoi
nt. We then introduce certain vector bundles (K-classes) on permutohedral
varieties\, which we call "tautological bundles (classes)" of matroids\, a
s a new framework that unifies\, recovers\, and extends these recent devel
opments. Our framework leads to new questions that further probe the bound
ary between combinatorics and geometry. Joint work with Andrew Berget\, Hu
nter Spink\, and Dennis Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oren Ben-Bassat (University of Haifa)
DTSTART:20220316T130000Z
DTEND:20220316T143000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/5
DESCRIPTION:Title: Derived Analytic Geometry\nby Oren Ben-Bassat (Universit
y of Haifa) as part of F1 World Seminar\n\n\nAbstract\nI will start by rev
iewing some work of others: sketching a (higher) categorical approach to g
eometry. After that\, I will explain how using this approach (derived) ana
lytic geometry can be viewed in a precise way as a type of algebraic geome
try. I will explain and use in a fundamental way Banach rings and categori
es of Banach modules over a Banach ring. The theories of derived analytic
geometry from this perspective include both archimedean and non-archimede
an analytic theories. I will give examples of homotopy epimorphisms betwe
en algebras of analytic nature. I will include examples and relevance in t
he rigid analytic context and an arithmetic context. I will discuss descen
t theorems and time permitting\, other topics such as blow-ups.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Tulane University)
DTSTART:20220330T130000Z
DTEND:20220330T143000Z
DTSTAMP:20260404T111136Z
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
\nAbstract\nTropical geometry provides a new set of purely combinatorial t
ools\, which has been used to approach classical problems. In the recent y
ears\, there has been a lot of effort dedicated to developing the necessar
y tools for commutative algebra using different frameworks\, among which p
rime congruences\, tropical ideals\, tropical schemes. These approaches al
lows for the exploration of the properties of tropicalized spaces without
tying them up to the original varieties and working with geometric struct
ures inherently defined in characteristic one (that is\, additively idempo
tent) semifields. In this talk we explore the relationship between tropica
l ideals and congruences and what they remember about the geometry of a tr
opical variety. The talk will give some overview of recent results and wor
k in progress.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Matherne (University of Bonn)
DTSTART:20220427T130000Z
DTEND:20220427T143000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/7
DESCRIPTION:Title: Equivariant log-concavity\, matroids\, and representation st
ability\nby Jacob Matherne (University of Bonn) as part of F1 World Se
minar\n\n\nAbstract\nAdiprasito\, Huh\, and Katz proved that the Betti num
bers of the Orlik-Solomon algebra of any matroid form a log-concave sequen
ce. Now suppose that the matroid has symmetries. Then\, the Orlik-Solomon
algebra becomes a graded representation of that symmetry group. In this
situation\, I will conjecture an equivariant version of the log-concavity
result above. Then\, I will show how one can use the theory of representa
tion stability to prove infinitely-many cases of this conjecture for the b
raid matroid\, acted on by the symmetric group. This is joint work with D
ane Miyata\, Nicholas Proudfoot\, and Eric Ramos.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Van Maldeghem (Ghent University)
DTSTART:20220525T130000Z
DTEND:20220525T143000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/8
DESCRIPTION:Title: Classical and exceptional geometries of order one\nby He
ndrik Van Maldeghem (Ghent University) as part of F1 World Seminar\n\n\nAb
stract\nIn the spirit of Jacques Tits' original observation about geometri
es over the field of order 1\, we review properties of these geometries. I
n particular we demonstrate how such properties can tell us something new
about their analogues over proper fields. Along the way we discuss Galois
descent\, a Magic Square\, triality and split octonions\, all over Fun.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manoel Jarra (Instituto de Matemática Pura e Aplicada)
DTSTART:20220413T130000Z
DTEND:20220413T143000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/9
DESCRIPTION:Title: Flag matroids with coefficients\nby Manoel Jarra (Instit
uto de Matemática Pura e Aplicada) as part of F1 World Seminar\n\n\nAbstr
act\nMatroids encode the combinatorics of independence in linear subspaces
\, as well flag matroids do for flags of subspaces. There is a way back: w
hen representing a (flag) matroid over a field\, we get a (flag of) linear
subspace(s). In recent years\, Baker and Bowler generalized this picture
to a more general type of algebraic object that includes fields and hyperf
ields as particular cases. In this talk we explain how to extend this theo
ry to flag matroids\, including a geometric interpretation in terms of the
ir moduli space. This is a joint work with Oliver Lorscheid.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Institute of Technology)
DTSTART:20221116T143000Z
DTEND:20221116T153000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/11
DESCRIPTION:Title: Foundations of Matroids\nby Matt Baker (Georgia Institu
te of Technology) as part of F1 World Seminar\n\n\nAbstract\nMatroid theor
ists are interested in questions concerning representability of matroids o
ver fields. More generally\, one can ask about representability over parti
al fields in the sense of Semple and Whittle. Pendavingh and van Zwam intr
oduced the universal partial field of a matroid\, which governs the repres
entations of over all partial fields. Unfortunately\, most matroids are no
t representable over any partial field\, and in this case\, the universal
partial field is not defined. Oliver Lorscheid and I have introduced a gen
eralization of the universal partial field which we call the foundation of
a matroid\; it is always well-defined. The foundation is a type of algebr
aic object which we call a pasture\; pastures include both hyperfields and
partial fields. As a particular application of this point of view\, I wil
l explain the classification of all possible foundations for matroids havi
ng no minor isomorphic to U(2\,5) or U(3\,5). Among other things\, this pr
ovides 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 only if it
is dyadic.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samarpita Ray (Indiana University)
DTSTART:20221130T143000Z
DTEND:20221130T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/12
DESCRIPTION:Title: The topological shadow of $\\mathbb{F}_1$-geometry: congrue
nce spaces\nby Samarpita Ray (Indiana University) as part of F1 World
Seminar\n\n\nAbstract\nIn this talk\, we introduce a topological shadow fo
r monoid schemes\, which we call the congruence space. It is constructed f
rom monoid congruences (instead of ideals) and carries the "right" topolog
ical information about closed subsets. This allows us to extend topologica
l characterizations (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 L
orscheid\, and soon to appear.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nethanel Friedenberg (Tulane University)
DTSTART:20230222T143000Z
DTEND:20230222T160000Z
DTSTAMP:20260404T111136Z
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 brie
f introduction to tropical geometry\, I will introduce a new approach to e
ndowing tropical varieties with additional structure. The approach will be
analytic in nature\, and so we will focus on the algebra of tropical powe
r series. We introduce the continuous spectrum of a topological semiring\,
and show that\, in the case of tropical power series\, it can be understo
od as a set of prime congruences on the algebra of tropical polynomials. I
f time permits\, we will see that the dimension behaves as expected and th
at the points the continuous spectrum can be interpreted in terms of more
classical geometry.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaeho Shin (Seoul National University)
DTSTART:20230125T143000Z
DTEND:20230125T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/14
DESCRIPTION:Title: Birational Geometry of Matroids and Abstract Hyperplane Arr
angements\nby Jaeho Shin (Seoul National University) as part of F1 Wor
ld Seminar\n\n\nAbstract\nA matroid is a machine that captures linearity o
f mathematical objects and produces combinatorial structures. Matroids ari
se everywhere\, as linearity does. One of the most natural appearances of
matroids is from hyperplane arrangements. Although much research on the th
ree things: matroids\, matroid polytopes\, and hyperplane arrangements in
a trilateral relation has been done\, the gaps in our knowledge base remai
n substantial. For example\, we do not have matroidal counterparts corresp
onding to matroid subdivisions\, and only some matroid subdivisions are as
sociated with stable hyperplane arrangements\, which indicates that the tr
ilateral relation needs improvement. Further\, we need to learn more about
the face structure of a matroid polytope and how to glue or subdivide bas
e polytopes\, which are inarguably essential questions. It is also an inte
resting question if the geometry of hyperplane arrangements can be impleme
nted over matroids\, and then how much of it. This talk will discuss how t
o develop a theory combining the three things into a trinity relation to a
nswer as many questions as possible\, such as the previously mentioned one
s.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230208T143000Z
DTEND:20230208T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/15
DESCRIPTION:Title: Cancelled\nby TBA as part of F1 World Seminar\n\n\nAbst
ract\nCancelled\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Caramello (University of Insubria)
DTSTART:20230322T133000Z
DTEND:20230322T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/17
DESCRIPTION:Title: Grothendieck toposes as unifying 'bridges' in Mathematics\nby Olivia Caramello (University of Insubria) as part of F1 World Semin
ar\n\n\nAbstract\nI will explain the sense in which Grothendieck toposes c
an act as unifying 'bridges' for relating different mathematical theories
to each other and studying them from a multiplicity of points of view. I s
hall first present the general techniques underpinning this theory and the
n discuss a number of selected applications in different mathematical fiel
ds.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Kock (Universitat Autonoma de Barcelona)
DTSTART:20230405T133000Z
DTEND:20230405T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/18
DESCRIPTION:Title: Some basic steps in objective linear algebra\nby Joachi
m Kock (Universitat Autonoma de Barcelona) as part of F1 World Seminar\n\n
\nAbstract\nThe 'objective method'\, advocated by Lawvere\, seeks to calcu
late directly with combinatorial objects\, rather than with their numbers.
In algebraic combinatorics\, this is largely a question of doing linear a
lgebra over the 'ground field' of finite sets (or groupoids or infinity-gr
oupoids). The role of vector spaces is played by slice categories\, and th
e role of linear maps is played by linear functors (which here means colim
it-preserving functors)\, which in turn can be represented by spans\, so t
hat 'matrix multiplication' is given by pullbacks. The ordinary vector-spa
ce level is recovered from the objective level by taking (homotopy) cardin
ality. After explaining the basic theory\, the talk will focus on finitene
ss conditions and the objective version of the duality between vector spac
es and pro-finite-dimensional vector spaces\, including a neat combinatori
al interpretation of continuity. To finish I will briefly outline how the
basic set-up supports more elaborate algebraic structures\, such as incide
nce bialgebras\, Möbius inversion\, and antipodes.\n\nThis is based on jo
int work with Imma Gálvez and Andy Tonks.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inna Zakharevich (Cornell University)
DTSTART:20230420T150000Z
DTEND:20230420T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/19
DESCRIPTION:Title: Coinvariants\, assembler K-theory\, and scissors congruence
\nby Inna Zakharevich (Cornell University) as part of F1 World Seminar
\n\n\nAbstract\nFor a geometry $X$ (such as Euclidean\, spherical\, or hyp
erbolic) with isometry group $G$ the scissors congruence group $\\mathcal{
P}(X\,G)$ is defined to be the free abelian group generated by polytopes i
n $X$\, 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 congrue
nce\," i.e. cutting up into pieces\, rearranging the pieces\, and gluing t
hem back together. With some basic group homology one can see that $\\mat
hcal{P}(X\,G) \\cong H_0(G\, \\mathcal{P}(X\,1))$. Using combinatorial $K
$-theory $\\mathcal{P}(X\,G)$ 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 is true for any assembler with a $G$-action. This is joint work wit
h Anna Marie Bohmann\, Teena Gerhardt\, Cary Malkiewich\, and Mona Merling
.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (l'École Polytechnique)
DTSTART:20230503T133000Z
DTEND:20230503T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/20
DESCRIPTION:Title: Postponed\nby Omid Amini (l'École Polytechnique) as pa
rt of F1 World Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hernan Iriarte (University of Texas at Austin)
DTSTART:20230517T133000Z
DTEND:20230517T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/21
DESCRIPTION:Title: Weak continuity on the variation of Newton Okounkov bodies<
/a>\nby Hernan Iriarte (University of Texas at Austin) as part of F1 World
Seminar\n\n\nAbstract\nWe start by presenting new tools and results suita
ble for the study of valuations of higher rank on function fields of algeb
raic varieties. This will be based on a study of higher rank quasi-monomia
l valuations taking values in the lexicographically ordered group $\\mathb
b{R}^k$. This gives us a space of higher rank valuations that we endow wit
h a weak "tropical" topology. In this setting\, we show that the Newton Ok
ounkov bodies of a given line bundle vary continuously with respect to the
valuation. We explain how this result fits in the literature and how it g
ives us a restriction in the existence of mutations of Newton Okounkov bod
ies. Joint work with Omid Amini.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (l'École Polytechnique)
DTSTART:20230920T133000Z
DTEND:20230920T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/22
DESCRIPTION:Title: Higher rank inner products\, higher rank Voronoi tilings\,
and metric degenerations of polarized tori\nby Omid Amini (l'École Po
lytechnique) as part of F1 World Seminar\n\n\nAbstract\nThe aim of the tal
k is to introduce higher rank inner products on real and complex vector sp
aces and to discuss properties of their corresponding Voronoi tilings. I w
ill explain how the framework can be used to describe metric degenerations
of polarized tori\, using Gromov-Hausdorff limits of Voronoi tilings\, an
d present applications in asymptotic complex geometry. Based on joint work
with Noema Nicolussi.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Institute for Advanced Study)
DTSTART:20231101T133000Z
DTEND:20231101T150000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/23
DESCRIPTION:Title: Multimatroids and Rational Curves with Cyclic Action (postp
oned)\nby Shiyue Li (Institute for Advanced Study) as part of F1 World
Seminar\n\n\nAbstract\nI will share with you a connection between multima
troids and moduli spaces of rational curves with cyclic action. Multimatro
ids are generalizations of matroids and delta-matroids that naturally aris
e from topological graph theory. The main result is a combinatorial formul
a for certain intersection numbers on the moduli space by relating to the
volumes of independence polytopal complexes of multimatroids. Based on pas
t and on-going joint works with Emily Clader\, Chiara Damiolini\, Chris Eu
r\, Daoji Huang\, and Rohini Ramadas.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Reyes (UC Irvine)
DTSTART:20231004T150000Z
DTEND:20231004T163000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/24
DESCRIPTION:Title: Categories of hypergroups and hyperstructures\nby Manue
l Reyes (UC Irvine) as part of F1 World Seminar\n\n\nAbstract\nA hyperoper
ation on a set M is an operation that associates to each pair of elements
a subset of M. Hypergroups and hyperrings are two examples of structures d
efined in terms of hyperoperations. While they were respectively defined i
n the 1930s and 1950s\, they have recently gained prominence through vario
us appearances in number theory\, combinatorics\, and absolute algebraic g
eometry. However\, to date there has been relatively little attention give
n to categories of hyperstructures.\n\nWe will discuss several categories
of hyperstructures that generalize hypergroups. A common theme is that in
order for these categories to enjoy good properties like (co)completeness\
, we must allow for the product or sum of two elements to be the empty sub
set\, which is explicitly forbidden for hypergroups. In particular\, we wi
ll introduce a category of hyperstructures called mosaics whose subcategor
y of commutative objects possess a closed monoidal structure reminiscent o
f the tensor product of abelian groups. This is joint work with So Nakamur
a.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uly Alvarez (University of Alabama)
DTSTART:20231115T143000Z
DTEND:20231115T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/25
DESCRIPTION:Title: Cluster algebras and quiver grassmannians\nby Uly Alvar
ez (University of Alabama) as part of F1 World Seminar\n\n\nAbstract\nSinc
e their conception\, cluster algebras have made appearances in different f
ields such as algebra\, combinatorics\, geometry\, and topology. For examp
le\, a class of objects called quiver Grassmannians have been useful in de
scribing the generators of cluster algebras using the Euler characteristic
. This has motivated the task of finding cell decomposition of quiver Gras
smannians. \nKyungyong Lee and I have been working on this problem for a c
lass of quivers which we will call surface quivers.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shai Haran (Technion)
DTSTART:20231018T133000Z
DTEND:20231018T150000Z
DTSTAMP:20260404T111136Z
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 mul
tiplication) by the collection of all matrices over them\, (with matrix mu
ltiplication and block direct sums) - a structure of a “Prop” - a stri
ct symmetric monoidal category generated by one object\, and similarly rep
lacing Rings by the collection of raw and column vectors over them - a str
ucture of a “Bioperad” - two closed symmetric operads acting on each o
ther\, we define the “commutative” Props and Bioperads\, and we develo
p algebraic geometry following closely Grothendieck’s footsteps.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maxwell (University of Bristol)
DTSTART:20231129T150000Z
DTEND:20231129T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/27
DESCRIPTION:Title: Geometry of tropical extensions of hyperfields\nby Jame
s Maxwell (University of Bristol) as part of F1 World Seminar\n\n\nAbstrac
t\nI will introduce Relatively Algebraically Closed (RAC) maps and tropica
l extensions of hyperfields\, along with recalling the required background
on hyperfields. Then\, the framework of ‘enriched valuations’ as hype
rfield homomorphisms to tropical extensions will be presented\, and it wil
l be shown that a notable family of them are RAC. I will the discuss our m
ain results which include hyperfield analogues of Kapranov’s theorem and
the fundamental theorem of tropical geometry. This will highlight the uti
lity of the RAC property in this generalised setting. I will conclude by o
utlining 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://stable.researchseminars.org/talk/F1WorldSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Institute for Advanced Study)
DTSTART:20240110T143000Z
DTEND:20240110T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/28
DESCRIPTION:Title: Multimatroids and Rational Curves with Cyclic Action\nb
y Shiyue Li (Institute for Advanced Study) as part of F1 World Seminar\n\n
\nAbstract\nI will share with you a connection between multimatroids and m
oduli spaces of rational curves with cyclic action. Multimatroids are gene
ralizations of matroids and delta-matroids that naturally arise from topol
ogical graph theory. The main result is a combinatorial formula for certai
n intersection numbers on the moduli space by relating to the volumes of i
ndependence polytopal complexes of multimatroids. Based on past and on-goi
ng joint works with Emily Clader\, Chiara Damiolini\, Chris Eur\, Daoji Hu
ang\, and Rohini Ramadas.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Schleis (University of Tübingen)
DTSTART:20240131T143000Z
DTEND:20240131T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/29
DESCRIPTION:Title: Tropical quiver Grassmannians\nby Victoria Schleis (Uni
versity of Tübingen) as part of F1 World Seminar\n\n\nAbstract\nGrassmann
ians and flag varieties are important moduli spaces in algebraic geometry.
Quiver Grassmannians are generalizations of these spaces arise in represe
ntation theory as the moduli spaces of quiver subrepresentations. These re
present arrangements of vector subspaces satisfying linear relations provi
ded by a directed graph.\n\nThe methods of tropical geometry allow us to s
tudy these algebraic objects combinatorially and computationally. We intro
duce matroidal and tropical analoga of quivers and their Grassmannians obt
ained in joint work with Alessio Borzì and separate joint work with Giuli
a Iezzi\; and describe them as affine morphisms of valuated matroids and l
inear maps of tropical linear spaces.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tong Jin (Georgia Institute of Technology)
DTSTART:20240228T143000Z
DTEND:20240228T160000Z
DTSTAMP:20260404T111136Z
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 Semi
nar\n\n\nAbstract\nOne of the oldest problems in matroid theory is to dete
rmine whether a matroid is linearly representable over a given field K. In
this talk\, we study the set of all representations of a matroid over pas
tures – a generalization of fields\, so that all matroids are taken into
consideration\, and then give algorithms to construct all equivalence cla
sses of representations in three different approaches: by the pairs of cir
cuits and cocircuits\, by the hyperplane matrices\, and by the cross ratio
s in the lattice of flats. This is joint work with Matt Baker and Oliver L
orscheid.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Usatine (Florida State University)
DTSTART:20240214T143000Z
DTEND:20240214T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/31
DESCRIPTION:Title: Gromov-Witten theory and invariants of matroids\nby Jer
emy Usatine (Florida State University) as part of F1 World Seminar\n\n\nAb
stract\nMatroids are versatile combinatorial objects with deep connections
to many subjects\, including chromatic polynomials of graphs\, arrangemen
ts of vectors and hyperplanes\, and the geometry of Grassmannians. I will
discuss joint work with Dhruv Ranganathan in which we use Gromov--Witten t
heory to associate new invariants to matroids. In particular\, I will expl
ain how to obtain a canonical (independent of chosen realization) quantum
deformation of any realizable matroid's cohomology ring.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Tolliver
DTSTART:20240424T153000Z
DTEND:20240424T163000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/32
DESCRIPTION:Title: Equivariant vector bundles on tropical toric schemes\nb
y Jeff Tolliver as part of F1 World Seminar\n\n\nAbstract\nThe classificat
ion of torus-equivariant vector bundles on toric varieties has been extens
ively studied in the classical setting. I will describe an analogous theo
ry over idempotent semirings. Unlike the classical setting\, every equiva
riant vector bundle on a toric scheme splits uniquely as a direct sum of l
ine bundles\, and so the classification reduces to the line bundle case.
As I will explain\, there is a short exact sequence linking the group of e
quivariant line bundles to the Picard group and another group whose presen
tation may be described explicitly in terms of the fan.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Beardsley (University of Nevada\, Reno)
DTSTART:20240403T150000Z
DTEND:20240403T160000Z
DTSTAMP:20260404T111136Z
UID:F1WorldSeminar/33
DESCRIPTION:Title: Toward Higher Algebra of Connes-Consani $\\mathbb{F}_1$-mod
ules\nby Jonathan Beardsley (University of Nevada\, Reno) as part of F
1 World Seminar\n\n\nAbstract\nI'll review the category of $\\mathbb{F}_1$
-modules introduced by Connes and Consani (which they call s-modules). To
motivate the use of this category for algebra over $\\mathbb{F}_1$ I will
describe some new work with S. Nakamura connecting it to combinatorial pro
jective geometry. After this\, I will propose a homotopical extension of C
onnes and Consani's theory. I'll describe some elementary results\, from j
oint work with J. Moeller\, indicating that this is a suitable way to do "
derived" algebra over $\\mathbb{F}_1$.\n
LOCATION:https://stable.researchseminars.org/talk/F1WorldSeminar/33/
END:VEVENT
END:VCALENDAR