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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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
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
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SUMMARY:Jacob Matherne (University of Bonn)
DTSTART;VALUE=DATE-TIME:20220427T130000Z
DTEND;VALUE=DATE-TIME:20220427T143000Z
DTSTAMP;VALUE=DATE-TIME:20230208T081530Z
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:20230208T081530Z
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/
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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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
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:20230208T081530Z
UID:F1WorldSeminar/13
DESCRIPTION:by Nethanel Friedenberg (Tulane University) as part of F1 Worl
d Seminar\n\nAbstract: TBA\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:20230208T081530Z
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:20230208T081530Z
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/
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