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BEGIN:VEVENT
SUMMARY:Marta Panizzut (Universität Osnabrück)
DTSTART:20200424T120000Z
DTEND:20200424T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/1
DESCRIPTION:Title: Tropical cubic surfaces and their lines\nby Marta Panizzut (Univer
sität Osnabrück) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (Universität Bern)
DTSTART:20200424T131500Z
DTEND:20200424T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/2
DESCRIPTION:Title: Catalan-many morphisms to trees-Part I\nby Jan Draisma (Universit
ät Bern) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Vargas (Universität Bern)
DTSTART:20200424T143000Z
DTEND:20200424T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/3
DESCRIPTION:Title: Catalan-many morphisms to trees-Part II\nby Alejandro Vargas (Univ
ersität Bern) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Smith (University of Manchester)
DTSTART:20200529T120000Z
DTEND:20200529T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/4
DESCRIPTION:Title: Faces of tropical polyhedra - cancelled\nby Ben Smith (University
of Manchester) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yue Ren (Swansea University)
DTSTART:20200529T131500Z
DTEND:20200529T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/5
DESCRIPTION:Title: Tropical varieties of neural networks\nby Yue Ren (Swansea Univers
ity) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (University of Tuebingen)
DTSTART:20200529T143000Z
DTEND:20200529T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/6
DESCRIPTION:Title: The combinatorics and real lifting of tropical bitangents to plane qua
rtics\nby Hannah Markwig (University of Tuebingen) as part of Tropical
Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (University of Cambridge)
DTSTART:20200626T120000Z
DTEND:20200626T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/7
DESCRIPTION:Title: Gluing log Gromov-Witten invariants\nby Mark Gross (University of
Cambridge) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbst
ract\nI will give a progress report on joint work with Abramovich\, Chen a
nd Siebert aiming to understand gluing formulae for log Gromov-Witten inva
riants\, generalizing the Li/Ruan and Jun Li gluing formulas for relative
Gromov-Witten invariants.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Battistella (University of Heidelberg)
DTSTART:20200626T131500Z
DTEND:20200626T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/8
DESCRIPTION:Title: A smooth compactification of genus two curves in projective space\
nby Luca Battistella (University of Heidelberg) as part of Tropical Geomet
ry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nQuestions of enumerative geomet
ry can often be translated into problems of intersection theory on a compa
ct moduli space of curves in projective space. Kontsevich's stable maps wo
rk extraordinarily well when the curves are rational\, but in higher genus
the burden of degenerate contributions is heavily felt\, as the moduli sp
ace acquires several boundary components. The closure of the locus of maps
with smooth source curve is interesting but troublesome\, for its functor
of points interpretation is most often unclear\; on the other hand\, afte
r the work of Li--Vakil--Zinger and Ranganathan--Santos-Parker--Wise in ge
nus one\, points in the boundary correspond to maps that admit a nice fact
orisation through some curve with Gorenstein singularities (morally\, cont
racting any higher genus subcurve on which the map is constant). The quest
ion becomes how to construct such a universal family of Gorenstein curves.
In joint work with F. Carocci\, we construct one such family in genus two
over a logarithmic modification of the space of admissible covers. I will
focus on how tropical geometry determines this logarithmic modification v
ia tropical canonical divisors.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Yale University)
DTSTART:20200626T143000Z
DTEND:20200626T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/9
DESCRIPTION:Title: Prime tropical ideals\nby Kalina Mincheva (Yale University) as par
t of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nIn the rece
nt years\, there has been a lot of effort dedicated to developing the nece
ssary tools for commutative algebra using different frameworks\, among whi
ch prime congruences\, tropical ideals\, tropical schemes. These approache
s allows for the exploration of the properties of tropicalized spaces wit
hout tying them up to the original varieties and working with geometric st
ructures inherently defined in characteristic one (that is\, additively id
empotent) semifields. In this talk we explore the relationship between tro
pical ideals and congruences to conclude that the variety of a non-zero pr
ime (tropical) ideal is either empty or consists of a single point.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fang (Universität Köln)
DTSTART:20201204T130000Z
DTEND:20201204T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/10
DESCRIPTION:Title: Tropical flag varieties - a Lie theoretic approach\nby Xin Fang (
Universität Köln) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\
n\n\nAbstract\nIn this talk I will explain how to use Lie theory to descri
be the facets of a maximal prime cone in a type A tropical complete flag v
ariety. The face lattice of this cone encodes degeneration structures in L
ie algebra\, quiver Grassmannians and module categories of quivers. This t
alk bases on different joint works with (subsets of) G. Cerulli-Irelli\, E
. Feigin\, G. Fourier\, M. Gorsky\, P. Littelmann\, I. Makhlin and M. Rein
eke\, as well as some work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai Cheung (Harvard University)
DTSTART:20201204T141500Z
DTEND:20201204T151500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/11
DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wai Ch
eung (Harvard University) as part of Tropical Geometry in Frankfurt/Zoom T
GiF/Z\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which
are a union of algebraic tori glued by birational "mutation" maps. Parti
al compactifications of the varieties\, studied by Gross\, Hacking\, Keel\
, and Kontsevich\, generalize the polytope construction of toric varieties
. However\, it is not clear from the definitions how to characterize the p
olytopes giving compactifications of cluster varieties. We will show how t
o describe the compactifications easily by broken line convexity. As an ap
plication\, we will see the non-integral vertex in the Newton Okounkov bod
y of Gr(3\,6) comes from broken line convexity. Further\, we will also see
certain positive polytopes will give us hints about the Batyrev mirror in
the cluster setting. The mutations of the polytopes will be related to th
e almost toric fibration from the symplectic point of view. Finally\, we c
an see how to extend the idea of gluing of tori in Floer theory which then
ended up with the Family Floer Mirror for the del Pezzo surfaces of degre
e 5 and 6. The talk will be based on a series of joint works with Bossinge
r\, Lin\, Magee\, Najera-Chavez\, and Vianna.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca)
DTSTART:20201204T153000Z
DTEND:20201204T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/12
DESCRIPTION:Title: Tropical geometry of Grassmannians and their cluster structure\nb
y Lara Bossinger (UNAM Oaxaca) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\n\nAbstract\nThe Grassmannain\, or more precisely its homogen
eous coordinate ring with respect to the Plücker embedding\, was found to
be a cluster algebra by Scott in the early years of cluster theory. Since
then\, this cluster structure was studied from many different perspective
s by a number of mathematicians. As the whole subject of cluster algebras
broadly speaking divides into two main perspectives\, algebraic and geomet
ric\, so do the results regarding Grassmannian. Geometrically\, the Grassm
annian contains two open subschemes that are dual cluster varieties.\n\nIn
terestingly\, we can find tropical geometry in both directions: from the a
lgebraic point of view\, we discover relations between maximal cones in th
e tropicalization of the defining ideal (what Speyer and Sturmfels call th
e tropical Grassmannian) and seeds of the cluster algebra. From the geomet
ric point of view\, due to work of Fock--Goncharov followed by work of Gro
ss--Hacking--Keel--Kontsevich we know that the scheme theoretic tropical p
oints of the cluster varieties parametrize functions on the Grassmannian.\
n\nIn this talk I aim to explain the interaction of tropical geometry with
the cluster structure for the Grassmannian from the algebraic and the geo
metric point of view.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alheydis Geiger (Universität Tübingen)
DTSTART:20210122T130000Z
DTEND:20210122T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/13
DESCRIPTION:Title: Deformations of bitangent classes of tropical quartic curves\nby
Alheydis Geiger (Universität Tübingen) as part of Tropical Geometry in F
rankfurt/Zoom TGiF/Z\n\n\nAbstract\nOver an algebraically closed field a s
mooth quartic curve has 28 bitangent lines. Plücker proved that over the
real numbers we have either 4\, 8\, 16 or 28 real bitangents to a real qua
rtic curve. A tropical smooth quartic curve has exactly 7 bitangent classe
s which each lift either 0 or 4 times over the real numbers. The shapes of
these bitangent classes have been classified by Markwig and Cueto in 2020
\, who also determined their real lifting conditions.\nHowever\, for a fix
ed unimodular triangulation different choices of coefficients imply differ
ent edge lengths of the quartic and these can change the shape of the 7 bi
tangent classes and might therefore influence their real lifting condition
s.\nIn order to prove Plückers Theorem about the number of real bitangent
s tropically\, we have to study these deformations of the bitangent shapes
. In a joint work with Marta Panizzut we develope a polymake extension\, w
hich computes the tropical bitangents. For this we determine two refinemen
ts of the secondary fan: one for which the bitangent shapes in each cone s
tay constant and one for which the lifting conditions in each cone stay co
nstant.\nThis is still work in progress\, but there will be a small softwa
re demonstration.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Institute of Technology)
DTSTART:20210122T141500Z
DTEND:20210122T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/14
DESCRIPTION:Title: Pastures\, Polynomials\, and Matroids\nby Matt Baker (Georgia Ins
titute of Technology) as part of Tropical Geometry in Frankfurt/Zoom TGiF/
Z\n\n\nAbstract\nA pasture is\, roughly speaking\, a field in which additi
on is allowed to be both multivalued and partially undefined. Pastures are
natural objects from the point of view of F_1 geometry and Lorscheid’s
theory of ordered blueprints. I will describe a theorem about univariate p
olynomials over pastures which simultaneously generalizes Descartes’ Rul
e of Signs and the theory of NewtonPolygons. Conjecturally\, there should
be a similar picture for several polynomials in several variables generali
zing tropical intersection theory. I will also describe a novel approach t
o the theory of matroid representations which revolves around a canonical
universal pasture called the “foundation” that one can attach to any m
atroid. This is joint work with Oliver Lorscheid.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (University of Georgia)
DTSTART:20210122T153000Z
DTEND:20210122T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/15
DESCRIPTION:Title: The tropical section conjecture\nby Daniel Litt (University of Ge
orgia) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract
\nGrothendieck's section conjecture predicts that for a curve X of genus a
t least 2 over an arithmetically interesting field (say\, a number field o
r p-adic field)\, the étale fundamental group of X encodes all the inform
ation about rational points on X. In this talk I will formulate a tropical
analogue of the section conjecture and explain how to use methods from lo
w-dimensional topology and moduli theory to prove many cases of it. As a b
yproduct\, I'll construct many examples of curves for which the section co
njecture is true\, in interesting ways. For example\, I will explain how t
o prove the section conjecture for the generic curve\, and for the generic
curve with a rational divisor class\, as well as how to construct curves
over p-adic fields which satisfy the section conjecture for geometric reas
ons. This is joint work with Wanlin Li\, Nick Salter\, and Padma Srinivasa
n.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (University of Oslo)
DTSTART:20210219T130000Z
DTEND:20210219T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/16
DESCRIPTION:Title: Tropical degenerations and stable rationality\nby John Christian
Ottem (University of Oslo) as part of Tropical Geometry in Frankfurt/Zoom
TGiF/Z\n\n\nAbstract\nI will explain how tropical degenerations and birati
onal specialization techniques can be used in rationality problems. In par
ticular\, I will apply these techniques to study quartic fivefolds and com
plete intersections of a quadric and a cubic in P^6. This is joint work wi
th Johannes Nicaise.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Pacini (Universidade Federal Fluminense)
DTSTART:20210219T141500Z
DTEND:20210219T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/17
DESCRIPTION:Title: A universal tropical Jacobian over the moduli space of tropical curve
s\nby Marco Pacini (Universidade Federal Fluminense) as part of Tropic
al Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe introduce polystabl
e divisors on a tropical curve\, which are the tropical analogue of polyst
able torsion-free rank-1 sheaves on a nodal curve. We show how to construc
t a universal tropical Jacobian by means of polystable divisors on tropica
l curves. This space can be seen as a tropical counterpart of Caporaso uni
versal Picard scheme. This is a joint work with Abreu\, Andria\, and Taboa
da.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20210219T153000Z
DTEND:20210219T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/18
DESCRIPTION:Title: Wall-crossing and Newton-Okounkov bodies\nby Laura Escobar (Washi
ngton University in St. Louis) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\n\nAbstract\nA Newton-Okounkov body is a convex set associate
d to a projective variety\, equipped with a valuation. These bodies genera
lize the theory of Newton polytopes. Work of Kaveh-Manon gives an explicit
link between tropical geometry and Newton-Okounkov bodies. In joint work
with Megumi Harada we use this link to describe a wall-crossing phenomenon
for Newton-Okounkov bodies.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthea Monod (Imperial College London)
DTSTART:20210312T130000Z
DTEND:20210312T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/19
DESCRIPTION:Title: Tropical geometry of phylogenetic tree spaces\nby Anthea Monod (I
mperial College London) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nThe Billera-Holmes-Vogtmann (BHV) space is a well-studi
ed moduli space of phylogenetic trees that appears in many scientific disc
iplines\, including computational biology\, computer vision\, combinatoric
s\, and category theory. Speyer and Sturmfels identify a homeomorphism bet
ween BHV space and a version of the Grassmannian using tropical geometry\,
endowing the space of phylogenetic trees with a tropical structure\, whic
h turns out to be advantageous for computational studies. In this talk\, I
will present the coincidence between BHV space and the tropical Grassmann
ian. I will then give an overview of some recent work I have done that stu
dies the tropical Grassmannian as a metric space and the practical implica
tions of these results on probabilistic and statistical studies on real da
tasets of phylogenetic trees.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia He Yun (Brown University)
DTSTART:20210312T141500Z
DTEND:20210312T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/20
DESCRIPTION:Title: The $S_n$-equivariant rational homology of the tropical moduli spaces
$\\Delta_{2\,n}$\nby Claudia He Yun (Brown University) as part of Tro
pical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe tropical moduli
space $\\Delta_{g\,n}$ is a topological space that parametrizes isomorphi
sm classes of $n$-marked stable tropical curves of genus $g$ with total vo
lume 1. Its reduced rational homology has a natural structure of $S_n$-rep
resentations induced by permuting markings. In this talk\, we focus on $\\
Delta_{2\,n}$ and compute the characters of these $S_n$-representations fo
r $n$ up to 8. We use the fact that $\\Delta_{2\,n}$ is a symmetric $\\Del
ta$-complex\, a concept introduced by Chan\, Glatius\, and Payne. The comp
utation is done in SageMath.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Corey (University of Wisconsin-Madison)
DTSTART:20210312T153000Z
DTEND:20210312T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/21
DESCRIPTION:Title: The Ceresa class: tropical\, topological\, and algebraic\nby Dani
el Corey (University of Wisconsin-Madison) as part of Tropical Geometry in
Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe Ceresa cycle is an algebraic cyc
le attached to a smooth algebraic curve. It is homologically trivial but n
ot algebraically equivalent to zero for a very general curve. In this sens
e\, it is one of the simplest algebraic cycles that goes ``beyond homology
.'' The image of the Ceresa cycle under a certain cycle class map produces
a class in étale homology called the Ceresa class. We define the Ceresa
class for a tropical curve and for a product of commuting Dehn twists on a
topological surface. We relate these to the Ceresa class of a smooth alge
braic curve over C((t)). Our main result is that the Ceresa class in each
of these settings is torsion. Nevertheless\, this class is readily computa
ble\, frequently nonzero\, and implies nontriviality of the Ceresa cycle w
hen nonzero. This is joint work with Jordan Ellenberg and Wanlin Li.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Usatine (Brown University)
DTSTART:20210430T131500Z
DTEND:20210430T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/22
DESCRIPTION:Title: Stringy invariants and toric Artin stacks\nby Jeremy Usatine (Bro
wn University) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\n
Abstract\nStringy Hodge numbers are certain generalizations\, to the singu
lar setting\, of Hodge numbers. Unlike usual Hodge numbers\, stringy Hodge
numbers are not defined as dimensions of cohomology groups. Nonetheless\,
an open conjecture of Batyrev's predicts that stringy Hodge numbers are n
onnegative. In the special case of varieties with only quotient singularit
ies\, Yasuda proved Batyrev's conjecture by showing that the stringy Hodge
numbers are given by orbifold cohomology. For more general singularities\
, a similar cohomological interpretation remains elusive. I will discuss a
conjectural framework\, proven in the toric case\, that relates stringy H
odge numbers to motivic integration for Artin stacks\, and I will explain
how this framework applies to the search for a cohomological interpretatio
n for stringy Hodge numbers. This talk is based on joint work with Matthew
Satriano.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART:20210430T143000Z
DTEND:20210430T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/23
DESCRIPTION:Title: Topology of tropical moduli spaces of weighted stable curves in highe
r genus\nby Shiyue Li (Brown University) as part of Tropical Geometry
in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe space of tropical weighted cur
ves of genus g and volume 1 is the dual complex of the divisor of singular
curves in Hassett’s moduli space of weighted stable genus g curves. One
can derive plenty of topological properties of the Hassett spaces by stud
ying the topology of these dual complexes. In this talk\, we show that the
spaces of tropical weighted curves of genus g and volume 1 are simply-con
nected for all genus greater than zero and all rational weights\, under th
e framework of symmetric Delta-complexes and via a result by Allcock-Corey
-Payne 19. We also calculate the Euler characteristics of these spaces and
the top weight Euler characteristics of the classical Hassett spaces in t
erms of the combinatorics of the weights. I will also discuss some work in
progress on a geometric group approach to simple connectivity of these sp
aces. This is joint work with Siddarth Kannan\, Stefano Serpente\, and Cla
udia Yun.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Rincon (Queen Mary University of London)
DTSTART:20210430T120000Z
DTEND:20210430T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/24
DESCRIPTION:Title: Tropical Ideals\nby Felipe Rincon (Queen Mary University of Londo
n) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nTr
opical ideals are ideals in the tropical polynomial semiring in which any
bounded-degree piece is “matroidal”. They were conceived as a sensible
class of objects for developing algebraic foundations in tropical geometr
y. In this talk I will introduce and motivate the notion of tropical ideal
s\, and I will discuss work studying some of their main properties and the
ir possible associated varieties.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (University of Coimbra and University of Roma Tre)
DTSTART:20210528T120000Z
DTEND:20210528T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/25
DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian varieties
\nby Margarida Melo (University of Coimbra and University of Roma Tre)
as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe
moduli space of abelian varieties Ag admits well behaved toroidal compacti
fications whose dual complex can be given a tropical interpretation. There
fore\, one can use the techniques recently developed by Chan-Galatius-Payn
e in order to understand part of the topology of Ag via tropical geometry.
In this talk\, which is based in joint work with Madeleine Brandt\, Julie
tte Bruce\, Melody Chan\, Gwyneth Moreland and Corey Wolfe\, I will explai
n how to use this setup\, and in particular computations in the perfect co
ne compactification of Ag\, in order to describe its top weight cohomology
for g up to 7.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenia Tevelev (University of Massachusetts Amherst)
DTSTART:20210528T143000Z
DTEND:20210528T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/26
DESCRIPTION:Title: Compactifications of moduli of points and lines in the (tropical) pla
ne\nby Jenia Tevelev (University of Massachusetts Amherst) as part of
Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nProjective duali
ty identifies moduli spaces of points and lines in the projective plane. T
he latter space admits Kapranov's Chow quotient compactification\, studied
also by Lafforgue\, Hacking-Keel-Tevelev\, and Alexeev\, which gives an e
xample of a KSBA moduli space of stable surfaces: it carries a family of r
educible degenerations of the projective plane with "broken lines". From t
he tropical perspective\, these degenerations are encoded in matroid decom
positions and tropical planes and their moduli space in the Dressian and t
he tropical Grasmannian. In 1991\, Gerritzen and Piwek proposed a dual per
spective\, a compact moduli space parametrizing reducible degenerations of
the projective plane with n smooth points. In a joint paper with Luca Sch
affler\, we investigate the extension of projective duality to degeneratio
ns\, answering a question of Kapranov.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baldur Sigurðsson (Vietnam Academy of Sciences and Technology)
DTSTART:20210528T131500Z
DTEND:20210528T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/27
DESCRIPTION:Title: Local tropical Cartier divisors and the multiplicity\nby Baldur S
igurðsson (Vietnam Academy of Sciences and Technology) as part of Tropica
l Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe consider the group o
f local tropical cycles in the local\ntropicalization of the local analyti
c ring of a toric variety\, in\nparticular\, Cartier divisors defined by a
function germ. We see a\nformula for the multiplicity\, a result which is
motivated by a classical\ntheorem of Wagreich for normal surface singular
ities.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hülya Argüz (Université de Versailles)
DTSTART:20210625T120000Z
DTEND:20210625T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/28
DESCRIPTION:Title: Tropical enumeration of real log curves in toric varieties and log We
lschinger invariants\nby Hülya Argüz (Université de Versailles) as
part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe give
a new proof of a central theorem in real enumerative geometry: the Mikhalk
in correspondence theorem for Welschinger invariants. The proof goes throu
gh totally different techniques as the original proof of Mikhalkin and is
an adaptation to the real setting of the approach of Nishinou-Siebert to t
he complex correspondence theorem. It uses log-geometry as a central tool.
We will discuss how this reinterpretation in terms of log-geometry may le
ad to new developments\, as for example a real version of mirror symmetry.
This is joint work with Pierrick Bousseau.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Mereta (Swansea University)
DTSTART:20210625T131500Z
DTEND:20210625T141500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/29
DESCRIPTION:Title: Tropical differential equations\nby Stefano Mereta (Swansea Unive
rsity) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract
\nIn 2015 Dimitri Grigoriev introduced a way to tropicalize differential e
quation with coefficients in a power series ring and defined what a soluti
on for such a tropicalized equation should be. In 2016 Aroca\, Garay and T
oghani proved a fundamental theorem analogue to the fundamental theorem of
tropical geometry for power series over a trivially valued field. In this
talk I will introduce the basic ideas moving then towards a functor of po
ints approach to the subject by means of the recently developed tropical s
cheme theory\, as introduced by Giansiracusa and Giansiracusa\, looking at
solutions to such equations as morphisms between so-called pairs. I will
also give a generalisation to power series ring with non-trivially valued
coefficients and state a colimit theorem along the lines of Payne's invers
e limit theorem.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Katz (Ohio State University)
DTSTART:20210625T143000Z
DTEND:20210625T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/30
DESCRIPTION:Title: Combinatorial and p-adic iterated integrals\nby Eric Katz (Ohio S
tate University) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n
\nAbstract\nThe classical operations of algebraic geometry often have comb
inatorial analogues. We will discuss the combinatorial analogue of Chen’
s iterated integrals. These have a richer\, non-abelian structure than cla
ssical integrals. We will describe the tropical analogue of the unipotent
Torelli theorem of Hain and Pulte and make connections between iterated in
tegrals and monodromy with applications to p-adic integration.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mima Stanojkovski (RWTH Aachen University)
DTSTART:20220121T130000Z
DTEND:20220121T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/31
DESCRIPTION:Title: Orders and polytropes: matrices from valuations\nby Mima Stanojko
vski (RWTH Aachen University) as part of Tropical Geometry in Frankfurt/Zo
om TGiF/Z\n\n\nAbstract\nLet K be a discretely valued field with ring of i
ntegers R. To a d-by-d matrix M with integral coefficients one can associa
te an R-module\, in K^{d x d}\, and a polytope\, in the Euclidean space of
dimension d-1. We will look at the interplay between these two objects\,
from the point of view of tropical geometry and building on work of Pleske
n and Zassenhaus. This is joint work with Y. El Maazouz\, M. A. Hahn\, G.
Nebe\, and B. Sturmfels.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben Gurioin University)
DTSTART:20220121T141500Z
DTEND:20220121T151500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/32
DESCRIPTION:Title: Applications of tropical geometry to irreducibility problems in algeb
raic geometry\nby Ilya Tyomkin (Ben Gurioin University) as part of Tro
pical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nIn my talk\, I will
discuss a novel tropical approach to classical irreducibility problems of
Severi varieties and of Hurwitz schemes. I will explain how to prove such
irreducibility results by investigating the properties of tropicalization
s of one-parameter families of curves and of the induced maps to the tropi
cal moduli space of parametrized tropical curves. The talk is based on a s
eries of joint works with Karl Christ and Xiang He.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harry Richman (University of Washington)
DTSTART:20220121T153000Z
DTEND:20220121T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/33
DESCRIPTION:Title: Uniform bounds for torsion packets on tropical curves\nby Harry R
ichman (University of Washington) as part of Tropical Geometry in Frankfur
t/Zoom TGiF/Z\n\n\nAbstract\nSay two points x\, y on an algebraic curve ar
e in the same torsion packet if [x - y] is a torsion element of the Jacobi
an. In genus 0 and 1\, torsion packets have infinitely many points. In hig
her genus\, a theorem of Raynaud states that all torsion packets are finit
e. It was long conjectured\, and only recently proven*\, that the size of
a torsion packet is bounded uniformly in terms of the genus of the underly
ing curve. We study the tropical analogue of this construction for a metri
c graph. On a higher genus metric graph\, torsion packets are not always f
inite\, but they are finite under an additional "genericity" assumption on
the edge lengths. Under this genericity assumption\, the torsion packets
satisfy a uniform bound in terms of the genus of the underlying graph. (*b
y Kuehne and Looper-Silverman-Wilmes in 2021)\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Rau (Universidad de los Andes)
DTSTART:20220218T130000Z
DTEND:20220218T135000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/34
DESCRIPTION:Title: Patchworks of real algebraic varieties in higher codimension\nby
Johannes Rau (Universidad de los Andes) as part of Tropical Geometry in Fr
ankfurt/Zoom TGiF/Z\n\n\nAbstract\nI will present a combinatorial setup\,
based on smooth tropical varieties and real phase structures\, which after
"unfolding" produces a certain class of PL-manifolds (called patchworks).
We have two motivations in mind: Firstly\, in the spirit of Viro's combi
natorial patchwoking for hypersurfaces\, these patchworks can be used to d
escribe the topology of real algebraic varieties close to the tropical lim
it. Secondly\, even if not "realisable" by real algebraic varieties\, real
phase structures provide a geometric framework for combinatorial structur
es such as oriented matroids. Joint work with Arthur Renaudineau and Kris
Shaw.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Kannan (Brown University)
DTSTART:20220218T141500Z
DTEND:20220218T151500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/35
DESCRIPTION:Title: Cut-and-paste invariants of moduli spaces of relative stable maps to
$\\mathbb{P}^1$\nby Siddharth Kannan (Brown University) as part of Tro
pical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nI will discuss ongo
ing work studying moduli spaces of genus zero stable maps to $\\mathbb{P}^
1$\, with fixed ramification profiles over $0$ and infinity. I will descri
be a chamber decomposition of the space of ramification data such that the
Grothendieck class of the moduli space is constant on the chambers. Final
ly\, for the sequence of ramification data corresponding to maximal ramifi
cation over $0$ and no ramification over infinity\, I will describe a recu
rsive algorithm to compute the generating function for Euler characteristi
cs of these spaces.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rohini Ramadas (University of Warwick)
DTSTART:20220218T153000Z
DTEND:20220218T163000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/36
DESCRIPTION:Title: The $S_n$ action on the homology groups of $\\overline{M}_{0\,n}$
\nby Rohini Ramadas (University of Warwick) as part of Tropical Geometry i
n Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe symmetric group on $n$ letters
acts on $\\overline{M}_{0\,n}$\, and thus on its (co-)homology groups. The
induced actions on (co-)homology have been studied by\, eg.\, Getzler\, B
ergstrom-Minabe\, Castravet-Tevelev. We ask: does $H_{2k}(\\overline{M}_{0
\,n})$ admit an equivariant basis\, i.e. one that is permuted by $S_n$? We
describe progress towards answering this question. This talk includes joi
nt work with Rob Silversmith.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana María Botero (University of Regensburg)
DTSTART:20220513T130000Z
DTEND:20220513T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/37
DESCRIPTION:Title: Toroidal b-divisors and Monge-Ampère measures\nby Ana María Bot
ero (University of Regensburg) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Ignacio Burgos Gil (Instituto de Ciencias Matemáticas)
DTSTART:20220520T143000Z
DTEND:20220520T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/38
DESCRIPTION:Title: Chern-Weil theory and Hilbert-Samuel theorem for semi-positive singul
ar toroidal metrics on line bundles\nby José Ignacio Burgos Gil (Inst
ituto de Ciencias Matemáticas) as part of Tropical Geometry in Frankfurt/
Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jensen (University of Kentucky)
DTSTART:20220610T130000Z
DTEND:20220610T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/39
DESCRIPTION:Title: Brill-Noether Theory over the Hurwitz Space\nby David Jensen (Uni
versity of Kentucky) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z
\n\n\nAbstract\nBrill-Noether theory is the study of line bundles on algeb
raic curves. A series of results in the 80's describe the varieties parame
terizing line bundles with given invariants on a sufficiently general curv
e. More recently\, several mathematicians have turned their attention to
the Brill-Noether theory of general covers -- that is\, curves that are ge
neral in the Hurwitz space rather than in the moduli space of curves. We
will survey these recent results and\, time permitting\, some generalizati
ons.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaelin Cook-Powell (Emory University)
DTSTART:20220610T141500Z
DTEND:20220610T151500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/40
DESCRIPTION:Title: The combinatorics of the Brill-Noether Theory of general covers\n
by Kaelin Cook-Powell (Emory University) as part of Tropical Geometry in F
rankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe study of line bundles on algebraic
curves has historically had deep connections with combinatorics. For exam
ple\, standard young tableaux have been used to study line bundles of suff
iciently general curves. Recently a variation of tableaux\, known as k-uni
form displacement tableaux\, have been used to study line bundles of gener
al covers -- that is curves general in the Hurwitz space. We will discuss
how these displacement tableaux relate to line bundles of general covers a
nd examine how they are used to produce new results in Brill-Noether Theor
y.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Manzaroli (University of Tuebingen)
DTSTART:20220708T120000Z
DTEND:20220708T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/41
DESCRIPTION:Title: Tropical homology over discretely valued fields\nby Matilde Manza
roli (University of Tuebingen) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Corey (TU Berlin)
DTSTART:20220708T133000Z
DTEND:20220708T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/42
DESCRIPTION:Title: Initial degenerations of flag varieties\nby Dan Corey (TU Berlin)
as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Zakharov (Central Michigan University)
DTSTART:20220708T144500Z
DTEND:20220708T154500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/43
DESCRIPTION:Title: An analogue of Kirchhoff's theorem for the tropical Prym variety\
nby Dmitry Zakharov (Central Michigan University) as part of Tropical Geom
etry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabrina Pauli (Universität Duisburg-Essen)
DTSTART:20221125T130000Z
DTEND:20221125T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/44
DESCRIPTION:Title: Quadratically enriched tropical intersections 1\nby Sabrina Pauli
(Universität Duisburg-Essen) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\n\nAbstract\nTropical geometry has been proven to be a powerf
ul computational tool in enumerative geometry over the complex and real nu
mbers. Results from motivic homotopy theory allow to study questions in en
umerative geometry over an arbitrary field k.\nIn these two talks we prese
nt one of the first examples of how to use tropical geometry for questions
in enuemrative geometry over k\, namely a proof of the quadratically enri
ched Bézout's theorem for tropical curves.\n\nIn the first talk we explai
n what we mean by the "quadratic enrichment"\, that is we define the neces
sary notions of enumerative geometry over arbitrary fields valued in the G
rothendieck-Witt ring of quadratic forms over k.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo Puentes (Universität Duisburg-Essen)
DTSTART:20221125T143000Z
DTEND:20221125T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/45
DESCRIPTION:Title: Quadratically enriched tropical intersections 2\nby Andrés Jaram
illo Puentes (Universität Duisburg-Essen) as part of Tropical Geometry in
Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nTropical geometry has been proven to
be a powerful computational tool in enumerative geometry over the complex
and real numbers. Results from motivic homotopy theory allow to study que
stions in enumerative geometry over an arbitrary field k.\nIn these two ta
lks we present one of the first examples of how to use tropical geometry f
or questions in enuemrative geometry over k\, namely a proof of the quadra
tically enriched Bézout's theorem for tropical curves. \n\nIn the second
talk we define the quadratically enriched multiplicity at an intersection
point of two tropical curves and show that it can be computed combinatoria
lly. We will use this new approach to prove an enriched version of the Bé
zout theorem and of the Bernstein–Kushnirenko theorem\, both for enriche
d tropical curves.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schröter (Goethe-Universität Frankfurt)
DTSTART:20221125T154500Z
DTEND:20221125T164000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/46
DESCRIPTION:Title: Valuative invariants for large classes of matroids\nby Benjamin S
chröter (Goethe-Universität Frankfurt) as part of Tropical Geometry in F
rankfurt/Zoom TGiF/Z\n\n\nAbstract\nValuations on polytopes are maps that
combine the geometry of polytopes with relations in a group. It turns out
that many important invariants of matroids are valuative on the collection
of matroid base polytopes\, e.g.\, the Tutte polynomial and its specializ
ations or the Hilbert–Poincaré series of the Chow ring of a matroid.\n\
nIn this talk I will present a framework that allows us to compute such in
variants on large classes of matroids\, e.g.\, sparse paving and elementar
y split matroids\, explicitly. The concept of split matroids introduced by
Joswig and myself is relatively new. However\, this class appears natural
ly in this context. Moreover\, (sparse) paving matroids are split. I will
demonstrate the framework by looking at Ehrhart polynomials\, relations in
Chow rings of combinatorial geometries\, and further examples.\n\nThis ta
lk is based on the preprint `Valuative invariants for large classes of mat
roids' which is joint work with Luis Ferroni.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Schleis (Universität Tübingen)
DTSTART:20230203T130000Z
DTEND:20230203T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/47
DESCRIPTION:Title: Linear degenerate tropical flag matroids\nby Victoria Schleis (Un
iversität Tübingen) as part of Tropical Geometry in Frankfurt/Zoom TGiF/
Z\n\n\nAbstract\nGrassmannians and flag varieties are important moduli spa
ces in algebraic geometry. Their\nlinear degenerations arise in representa
tion theory as they describe quiver representations\nand their irreducible
modules. As linear degenerations of flag varieties are difficult to\nanal
yze algebraically\, we describe them in a combinatorial setting and furthe
r investigate\ntheir tropical counterparts.\n\nIn this talk\, I will intro
duce matroidal\, polyhedral and tropical analoga and descriptions of linea
r degenerate flags and their varieties obtained in joint work with Alessio
Borzì. To this end\, we introduce and study morphisms of valuated matroi
ds. Using techniques from matroid theory\, polyhedral geometry and linear
tropical geometry\, we use the correspondences between the different descr
iptions to gain insight on the structure of linear degeneration. Further\,
we analyze the structure of linear degenerate flag varieties in all three
settings\, and provide some cover relations on the poset of degenerations
. For small examples\, we relate the observations on cover relations to th
e flat irreducible locus studied in representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Monin (Universität Leipzig)
DTSTART:20230203T143000Z
DTEND:20230203T153000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/48
DESCRIPTION:Title: Polyhedral models for K-theory\nby Leonid Monin (Universität Lei
pzig) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\
nOne can associate a commutative\, graded algebra which satisfies \nPoinca
re duality to a homogeneous polynomial f on a vector space V. One \npartic
ularly interesting example of this construction is when f is the volume \n
polynomial on a suitable space of (virtual) polytopes. In this case the al
gebra \nA_f recovers cohomology rings of toric or flag varieties. \n\nIn m
y talk I will explain these results and present their recent generalizatio
ns. \nIn particular\, I will explain how to associate an algebra with Gore
nstein duality \nto any function g on a lattice L. In the case when g is t
he Ehrhart function on \na lattice of integer (virtual) polytopes\, this c
onstruction recovers K-theory of \ntoric and full flag varieties.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou (Queen Mary University of London)
DTSTART:20230203T154500Z
DTEND:20230203T164500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/49
DESCRIPTION:Title: Universality for tropical maps.\nby Navid Nabijou (Queen Mary Uni
versity of London) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n
\n\nAbstract\nI will discuss recent work concerning maps from tropical cur
ves to orthants. A “combinatorial type” of such map is the data of an
abstract graph together with slope vectors along the edges. To each such c
ombinatorial type there is an associated moduli space\, which parametrises
metric enhancements of the graph compatible with the given slopes. This m
oduli space is a rational polyhedral cone\, giving rise to an affine toric
variety.\n\nOur main result shows that every rational polyhedral cone app
ears as the moduli space associated to some combinatorial type of tropical
map. This establishes universality (also known as Murphy’s law) for tro
pical maps. The proof is constructive and extremely concrete\, as I will d
emonstrate. Combined with insights from logarithmic geometry\, our result
implies that every toric singularity appears as a virtual singularity on a
moduli space of stable logarithmic maps.\n\nThis is joint work with Gabri
el Corrigan and Dan Simms.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (ENS)
DTSTART:20230505T120000Z
DTEND:20230505T130000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/50
DESCRIPTION:Title: The SYZ conjecture for families of hypersurfaces\nby Léonard Pil
le-Schneider (ENS) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n
\n\nAbstract\nLet $X \\to D^*$ be a polarized family of complex Calabi-Yau
manifolds\, whose\ncomplex structure degenerates in the worst possible wa
y. The SYZ\nconjecture predicts that the fibers $X_t$\, as $t \\to 0$\, de
generate to a\ntropical object\; and in particular the program of Kontsevi
ch and Soibelman\nrelates it to the Berkovich analytification of $X$\, vie
wed as a variety over\nthe non-archimedean field of complex Laurent series
.\nI will explain the ideas of this program and some recent progress in th
e\ncase of hypersurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loujean Cobigo (Universität Tübingen)
DTSTART:20230505T133000Z
DTEND:20230505T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/51
DESCRIPTION:Title: Tropical spin Hurwitz numbers\nby Loujean Cobigo (Universität T
übingen) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstr
act\nClassical Hurwitz numbers count the number of branched covers of a fi
xed target curve that exhibit a certain ramification behaviour. It is an e
numerative problem deeply rooted in mathematical history. \n A modern twis
t: Spin Hurwitz numbers were introduced by Eskin-Okounkov-Pandharipande fo
r certain computations in the moduli space of differentials on a Riemann s
urface.\n Similarly to Hurwitz numbers they are defined as a weighted coun
t of branched coverings of a smooth algebraic curve with fixed degree and
branching profile. In addition\,\n they include information about the lift
of a theta characteristic of fixed parity on the base curve. \n\nIn this
talk we investigate them from a tropical point of view. We start by defini
ng tropical spin Hurwitz numbers as result of an algebraic degeneration pr
ocedure\,\nbut soon notice that these have a natural place in the tropical
world as tropical covers with tropical theta characteristics on source an
d target curve. \nOur main results are two correspondence theorems stating
the equality of the tropical spin Hurwitz number with the classical one.\
n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Ducros (Sorbonne Université)
DTSTART:20230505T144500Z
DTEND:20230505T154500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/52
DESCRIPTION:Title: Tropical functions on skeletons: a finiteness result\nby Antoine
Ducros (Sorbonne Université) as part of Tropical Geometry in Frankfurt/Zo
om TGiF/Z\n\n\nAbstract\nSkeletons are subsets of non-archimedean spaces (
in the sense of Berkovich) that inherit from the ambiant space a natural P
L (piecewise-linear) structure\, and if $S$ is such a skeleton\, for every
invertible holomorphic function $f$ defined in a neighborhood of $S$\, th
e restriction of $\\log |f|$ to $S$ is PL. \nIn this talk\, I will present
a joint work with E.Hrushovski F. Loeser and J. Ye in which we consider a
n irreducible algebraic variety $X$ over an algebraically closed\, non-tri
vially valued and complete non-archimedean field $k$\, and a skeleton $S$
of the analytification of $X$ defined using only algebraic functions\, and
consisting of Zariski-generic points. If $f$ is a non-zero rational funct
ion on $X$ then $\\log |f|$ induces a PL function on $S$\, and if we denot
e by $E$ the group of all\nPL functions on $S$ that are of this form\, we
prove the following finiteness result on the group $E$: it is stable under
min and max\, and there exist finitely many non-zero rational functions $
f_1\,\\ldots\,f_m$ on $X$ such that $E$ is generated\, as a group\nequippe
d with min and max operators\, by the $\\log |f_i|$ and the constants $|a|
$ for $a$ in $k^*$. Our proof makes a crucial use of Hrushovski-Loeser’s
model-theoretic approach of Berkovich spaces.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Gualdi (University of Regensburg)
DTSTART:20230707T130000Z
DTEND:20230707T140000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/54
DESCRIPTION:Title: From amoebas to arithmetics\nby Roberto Gualdi (University of Reg
ensburg) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstra
ct\nMotivated by the computation of the integral of a piecewise linear fun
c- tion on the amoeba of the line (x1 + x2 + 1 = 0)\, we will show how tro
pical objects play a role in arithmetics.\n\nThis will bring us to an excu
rsion into the Arakelov geometry of toric varieties\; in this framework\,
we will use our tropical computation to predict the arithmetic complexity
of the intersection of a projective planar line with its translate by a to
rsion point. This is a joint work with Martín Sombra.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattias Jonsson (University of Michigan)
DTSTART:20230707T144500Z
DTEND:20230707T154500Z
DTSTAMP:20260404T094341Z
UID:TGiZ/55
DESCRIPTION:Title: A tropical Monge-Ampere equation and the SYZ conjecture\nby Matti
as Jonsson (University of Michigan) as part of Tropical Geometry in Frankf
urt/Zoom TGiF/Z\n\n\nAbstract\nA celebrated result of Yau says that every
compact Kähler manifold with trivial canonical bundle admits a Ricci flat
metric in any given Kähler class. The proof amounts to solving a complex
Monge-Ampère equation. I will discuss joint work with Hultgren\, Mazzon\
, and McCleerey\, where we solve a "tropical" Monge--Ampère equation\, on
the boundary of simplex. Through recent work of Yang Li\, this has applic
ations to the SYZ conjecture\, on degenerations of Calabi-Yau manifolds.\
n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Afandi (Universität Münster)
DTSTART:20231214T133000Z
DTEND:20231214T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/56
DESCRIPTION:Title: Stationary Descendents and the Discriminant Modular Form\nby Adam
Afandi (Universität Münster) as part of Tropical Geometry in Frankfurt/
Zoom TGiF/Z\n\n\nAbstract\nBy using the Gromov-Witten/Hurwitz corresponden
ce\, Okounkov and Pandharipande showed that certain generating functions o
f stationary descendent Gromov-Witten invariants of a smooth elliptic curv
e are quasimodular forms. In this talk\, I will discuss the various ways o
ne can express the discriminant modular form in terms of these generating
functions. The motivation behind this calculation is to provide a new pers
pective on tackling a longstanding conjecture of Lehmer from the middle of
the 20th century\; Lehmer posited that the Ramanujan tau function (i.e. t
he Fourier coefficients of the discriminant modular form) never vanishes.
The connection with Gromov-Witten invariants allows one to translate Lehme
r's conjecture into a combinatorial problem involving characters of the sy
mmetric group and shifted symmetric functions.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajith Urundolil-Kumaran (University of Cambridge)
DTSTART:20231214T150000Z
DTEND:20231214T160000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/57
DESCRIPTION:Title: Refined tropical curve counting with descendants\nby Ajith Urundo
lil-Kumaran (University of Cambridge) as part of Tropical Geometry in Fran
kfurt/Zoom TGiF/Z\n\n\nAbstract\nWe introduce the enumerative geometry of
curves in the algebraic torus (C*)^2. We show that a certain class of inva
riants associated with moduli spaces of curves in (C*)^2 can be calculated
explicitly using a refined tropical correspondence theorem. If time permi
ts we will explain how the proof relies on higher double ramification cycl
es and work of Buryak-Rossi on integrable systems on the moduli space of c
urves. This is joint work with Patrick Kennedy-Hunt and Qaasim Shafi.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Bernig (Goethe-Universität Frankfurt)
DTSTART:20240202T150000Z
DTEND:20240202T160000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/58
DESCRIPTION:Title: Hard Lefschetz theorem and Hodge-Riemann relations for convex valuati
ons\nby Andreas Bernig (Goethe-Universität Frankfurt) as part of Trop
ical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe hard Lefschetz t
heorem and the Hodge-Riemann relations have their origin in the cohomology
theory of compact Kähler manifolds. In recent years it has become clear
that similar results hold in many different settings\, in particular in al
gebraic geometry and combinatorics (work by Adiprasito\, Huh and others).
In a recent joint work with Jan Kotrbatý and Thomas Wannerer\, we prove t
he hard Lefschetz theorem and Hodge-Riemann relations for valuations on co
nvex bodies. These results can be translated into an array of quadratic in
equalities for mixed volumes of smooth convex bodies\, giving a smooth ana
logue of the quadratic inequalities in McMullen's polytope algebra. Surpri
nsingly\, these inequalities fail for general convex bodies. Our proof use
s elliptic operators and perturbation theory of unbounded operators.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manoel Zanoelo Jarra (Universität Groningen)
DTSTART:20240202T133000Z
DTEND:20240202T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/59
DESCRIPTION:Title: Category of matroids with coefficients\nby Manoel Zanoelo Jarra (
Universität Groningen) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nMatroids are combinatorial abstractions of the concept
of independence in linear algebra. There is a way back: when representing
a matroid over a field we get a linear subspace. Another algebraic object
for which we can represent matroids is the semifield of tropical numbers\,
which gives us valuated matroids. In this talk we introduce Baker-Bowler'
s theory of matroids with coefficients\, which recovers both classical and
valuated matroids\, as well linear subspaces\, and we show how to give a
categorical treatment to these objects that respects matroidal constructio
ns\, as minors and duality. This is a joint work with Oliver Lorscheid and
Eduardo Vital.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Schaller (Freie Universität Berlin)
DTSTART:20240503T123000Z
DTEND:20240503T133000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/60
DESCRIPTION:Title: NObodies are perfect\, semigroups are not\nby Karin Schaller (Fre
ie Universität Berlin) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nNewton-Okounkov bodies are asymptotic limits of certain
valuation semigroups. Their construction depends on a given flag of subva
rieties. We investigate toric surfaces together with non-toric flags and d
etermine when the associated valuation semigroups are finitely generated.
This is a joint work with K. Altmann\, C. Haase\, A. Küronya\, and L. Wal
ter.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Kühne (Universität Bielefeld)
DTSTART:20240503T140000Z
DTEND:20240503T150000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/61
DESCRIPTION:Title: The realization space of a matroid\nby Lukas Kühne (Universität
Bielefeld) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbs
tract\nA matroid is a fundamental and widely studied object in combinatori
cs. Following a brief introduction to matroids\, I will showcase parts of
a new OSCAR module for matroids using several examples. My emphasis will b
e on the computation of the realization space of a matroid\, which is the
space of all hyperplane arrangements that have the given matroid as their
intersection lattice.\n\nIn the second part\, I will discuss an applicatio
n in the realm of algebraic geometry\, namely a novel connection between m
atroid realization spaces and the elliptic modular surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pim Spelier (Leiden University)
DTSTART:20240614T123000Z
DTEND:20240614T133000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/62
DESCRIPTION:Title: The log tautological ring of the moduli space of curves\nby Pim S
pelier (Leiden University) as part of Tropical Geometry in Frankfurt/Zoom
TGiF/Z\n\n\nAbstract\nThe tautological ring of Mgn-bar has been a crucial
object in the study of the intersection theory of the moduli space of curv
es. Recently\, there has been more focus on the logarithmic enumerative ge
ometry of Mgn-bar\, with interesting classes coming from e.g. log double r
amification cycles. We present a definition of the log tautological ring o
f Mgn-bar\, together with a log decorated strata algebra\, and prove sever
al structure results. The main new tools are the notions of cone stacks wi
th boundary and homological piecewise polynomials\, that capture the tropi
calisation of strata of log smooth stacks and the combinatorial part of th
eir intersection theory.\nThis is joint work with Rahul Pandharipande\, Dh
ruv Ranganathan and Johannes Schmitt.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Gierczak (Institut Polytechnique de Paris)
DTSTART:20240614T140000Z
DTEND:20240614T150000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/63
DESCRIPTION:Title: Counting Weierstrass points on degenerating algebraic curves\nby
Lucas Gierczak (Institut Polytechnique de Paris) as part of Tropical Geome
try in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWeierstrass points on algebrai
c curves are special points of high importance in algebraic geometry and a
rithmetic geometry. In this talk\, we study how those special points behav
e when the algebraic curve degenerates to a nodal curve. To this end\, we
first explain why tropical geometry is a relevant formalism for studying d
egeneration questions. We then define a tropical analogue on metric graphs
(seen as tropical curves) for Weierstrass points\, and explore the proper
ties of the so-called “tropical Weierstrass locus". We also associate in
trinsic weights to the connected components of this locus\, and show that
their total sum for a given metric graph and divisor is a function of few
combinatorial parameters (degree and rank of the divisor\, genus of the me
tric graph). Finally\, in the case the divisor on the metric graph comes f
rom the tropicalization of a divisor on an algebraic curve\, we specify th
e compatibility between the Weierstrass loci.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giusi Capobianco (Roma Tor Vergata)
DTSTART:20250117T133000Z
DTEND:20250117T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/64
DESCRIPTION:Title: The tropical 1-fold Abel-Prym map\nby Giusi Capobianco (Roma Tor
Vergata) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstra
ct\nThe algebraic Abel-Prym map relates the geometry of a double cover of
algebraic curves with their corresponding Prym varieties. Birkenhake and L
ange proved that the map has degree 2 if and only if the cover curve is hy
perelliptic.\nIn the talk I will present joint work with Yoav Len\, in whi
ch we investigate the 1-fold Abel-Prym map in the tropical setting and pro
ve similar results. I will describe a new combinatorial construction of hy
perelliptic double covers of metric graphs and prove that the tropical Abe
l-Prym map is a harmonic morphism of degree 2. Furthermore\, we will see
that the Jacobian of the image of this map is isomorphic\, as pptav\, to t
he Prym variety of the cover. When the double cover is not hyperelliptic h
owever\, contrary to the algebraic result\, the tropical Abel-Prym map is
almost never injective. I will provide counterexamples and discuss its ima
ge.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shelby Cox (MPI Leipzig)
DTSTART:20250117T140000Z
DTEND:20250117T150000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/65
DESCRIPTION:Title: Tree spaces in tropical geometry\nby Shelby Cox (MPI Leipzig) as
part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe spac
e of phylogenetic trees on n leaves arises naturally in tropical geometry
through the tropical Grassmannian trop Gr(2\,n). The space of equidistant
trees on n leaves is the tropicalization of M_{0\,n}\, which is tropically
convex. In this talk\, I will present recent work using tropical tree spa
ces for phylogenetic statistics and inference (joint with Curiel\, Sabol\,
Talbut\, and Yoshida). I will also discuss a conjectural analogue of the
space of equidistant trees for type C (joint with Igor Makhlin)\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Balla (MPI Leipzig)
DTSTART:20250207T133000Z
DTEND:20250207T143000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/66
DESCRIPTION:Title: Regular subdivisions and bounds on initial ideals\nby George Ball
a (MPI Leipzig) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\
nAbstract\nWe extend two known constructions that relate regular subdivisi
ons to initial degenerations of projective toric varieties and Grassmannia
ns. We associate a point configuration A with any homogeneous ideal I. We
obtain upper and lower bounds on each initial ideal of I in terms of regul
ar subdivisions of A. We also investigate when these bounds are exact\, fo
r example\, the lower bound is exact for every initial ideal of the Plück
er ideal I(2\,n) with respect to points in the tropicalization. This talk
is based on joint work with Dan Corey\, Igor Makhlin\, and Victoria Schlei
s.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Crumplin (Universität Heidelberg)
DTSTART:20250207T150000Z
DTEND:20250207T160000Z
DTSTAMP:20260404T094341Z
UID:TGiZ/67
DESCRIPTION:Title: Moduli spaces of twisted maps to smooth pairs\nby Robert Crumplin
(Universität Heidelberg) as part of Tropical Geometry in Frankfurt/Zoom
TGiF/Z\n\n\nAbstract\nThe question of counting maps from marked curves wit
h fixed tangency conditions to a divisor in the target has been studied ex
tensively over the past 15 years. One way of formulating these enumerative
problems is via twisted maps to a root stack. I will describe the geometr
y of moduli spaces of twisted maps using tropical techniques\, in particul
ar giving new understanding to universal structural results of orbifold Gr
omov–Witten invariants. If time permits\, I will talk about upcoming wor
k with Sam Johnston which relates these moduli spaces to their logarithmic
counterparts and provides a splitting of the virtual class in terms of th
e aforementioned tropical data.\n
LOCATION:https://stable.researchseminars.org/talk/TGiZ/67/
END:VEVENT
END:VCALENDAR