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BEGIN:VEVENT
SUMMARY:Yoav Len (University of St Andrews)
DTSTART:20200710T140000Z
DTEND:20200710T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/1
DESCRIPTION:Title: Brill--Noether theory of Prym varieties\nby Yoav Len (Universi
ty of St Andrews) as part of (LAGARTOS) Latin American Real and Tropical G
eometry Seminar\n\n\nAbstract\nI will discuss combinatorial aspects of Pry
m varieties\, a class of Abelian varieties that shows up in the presence o
f double covers of curves. Pryms have deep connections with torsion points
of Jacobians\, bi-tangent lines\, and spin structures. As I will explain\
, problems concerning Pryms may be reduced\, via tropical geometry\, to co
mbinatorial games on graphs. Consequently we obtain new results in the geo
metry of special algebraic curves and bounds on dimensions of certain Bril
l–Noether loci.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenii Shustin (Tel Aviv University)
DTSTART:20200724T140000Z
DTEND:20200724T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/2
DESCRIPTION:Title: Expressive curves\nby Eugenii Shustin (Tel Aviv University) as
part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\
nAbstract\nThe talk is devoted to a class of real plane algebraic curves\n
which we call expressive.\nThese are the curves whose defining polynomial
has the smallest\nnumber of critical points allowed by the topology of th
e real point set.\nThis concept can be viewed as a global version of the n
otion of\na real morsification of an isolated real plane curve singularity
.\nWe provide a characterization of expressive curves and describe several
\nconstructions that produce a large number of example of expressive\ncurv
es. Finally\, we discuss further potential developments\ntowards combinato
rics of divides\, topology of links at infinity\,\nmutations of quivers et
c.\nJoint work with Sergey Fomin.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (Impa)
DTSTART:20200807T140000Z
DTEND:20200807T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/3
DESCRIPTION:Title: Towards a cohomological understanding of the tropical Riemann--Roc
h theorem\nby Oliver Lorscheid (Impa) as part of (LAGARTOS) Latin Amer
ican Real and Tropical Geometry Seminar\n\n\nAbstract\nIn this talk\, we o
utline a program of developing a cohomological\nunderstanding of the tropi
cal Riemann--Roch theorem and discuss the first\nestablished steps in deta
il. In particular\, we highlight the role of the\ntropical hyperfield and
explain why ordered blue schemes provide a\nsatisfying framework for tropi
cal scheme theory.\n\nIn the last part of the talk\, we turn to the notion
of matroid bundles\,\nwhich we hope to be the right tool to set up sheaf
cohomology for\ntropical schemes. This is based on a joint work with Matth
ew Baker.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sally Andria (Universidade Federal Fluminense)
DTSTART:20200821T140000Z
DTEND:20200821T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/4
DESCRIPTION:Title: Abel maps for nodal curves via tropical geometry\nby Sally And
ria (Universidade Federal Fluminense) as part of (LAGARTOS) Latin American
Real and Tropical Geometry Seminar\n\n\nAbstract\nLet $\\pi\\colon \\math
cal{C}\\rightarrow B$ be a regular smoothing of a nodal curve with smooth
components and a section $\\sigma$ of $\\pi$ through its smooth locus. \n
Let $\\mu$ and $\\mathcal{L}$ be a polarization and an invertible\nsheaf o
f degree $k$ on $\\mathcal{C}/B$. The Abel map $\\alpha^{d}_{\\mathcal{L}}
$ is the rational map \n$\\alpha^{d}_{\\mathcal{L}}\\colon \\mathcal{C}^d
\\dashrightarrow \\overline{\\mathcal{J}}_{\\mu}^{\\sigma}$ taking a tuple
\nof points $(Q_1\,\\dots\,Q_d)$ on a fiber $C_b$ of $\\pi$ to the sheaf
$\\mathcal{O}_{C_b}(Q_1+\\dots+Q_d-d\\sigma(b))\\otimes \\mathcal{L}|_{C_b
}$. Here $\\overline{\\mathcal{J}}_{\\mu}^{\\sigma}$ denotes Esteves compa
ctified Jacobian.\nAn interesting question is to find an explicit resoluti
on of the map $\\alpha^{d}_{\\mathcal{L}}$.\nWe translate this problem int
o an explicit combinatorial problem by means of tropical and toric geomet
ry. The solution of the combinatorial problem gives rise to an explicit re
solution of the Abel map. We are able to use this technique to construct a
ll the degree-$1$ Abel maps and give a resolution of the degree-$2$ Abel-J
acobi map.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang He (Hebrew University)
DTSTART:20200904T140000Z
DTEND:20200904T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/5
DESCRIPTION:Title: A tropical approach to the Severi problem\nby Xiang He (Hebrew
University) as part of (LAGARTOS) Latin American Real and Tropical Geomet
ry Seminar\n\n\nAbstract\nSeveri varieties parameterize reduced irreducibl
e curves of given geometric genus in a given linear system on an algebraic
surface. The irreducibility of Severi varieties is established firstly by
Harris in 1986 for the projective plane in characteristic zero. In this t
alk\, I will give a brief overview of the ideas involved\, and describe a
tropical approach to studying degererations of plane curves\, which leads
to a new proof of the irreducibility that also works in positive character
istic. This is joint work with Karl Christ and Ilya Tyomkin.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Rincón (Queen Mary University of London)
DTSTART:20200918T140000Z
DTEND:20200918T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/6
DESCRIPTION:Title: Tropical ideals\nby Felipe Rincón (Queen Mary University of L
ondon) as part of (LAGARTOS) Latin American Real and Tropical Geometry Sem
inar\n\n\nAbstract\nTropical ideals are combinatorial objects introduced w
ith the aim of giving tropical geometry a solid algebraic foundation. They
can be thought of as combinatorial generalizations of the possible collec
tions of subsets arising as the supports of all polynomials in an ideal. I
n general\, their structure is dictated by a sequence of 'compatible' matr
oids. In this talk I will introduce and motivate the notion of tropical id
eals\, and I will discuss work studying some of their main properties and
their possible associated varieties.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Sturmfels (MPI-Leipzig)
DTSTART:20201002T140000Z
DTEND:20201002T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/7
DESCRIPTION:Title: Theta surfaces\nby Bernd Sturmfels (MPI-Leipzig) as part of (L
AGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\n
A theta surface in affine 3-space is the zero set of a Riemann theta funct
ion in genus 3. This includes surfaces arising from special plane quartics
that are singular or reducible. Lie and Poincaré showed that theta surfa
ces are precisely the surfaces of double translation\, i.e. obtained as th
e Minkowski sum of two space curves in two different ways. These curves ar
e parametrized by abelian integrals\, so they are usually not algebraic. W
e present a new view on this classical topic through the lens of computati
on. We discuss practical tools for passing between quartic curves and thei
r theta surfaces\, and we develop the numerical algebraic geometry of dege
nerations of theta functions. This is joint work with Daniele Agostini\, T
urku Celik and Julia Struwe.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Giansiracusa (Swansea University)
DTSTART:20201016T140000Z
DTEND:20201016T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/8
DESCRIPTION:Title: A general theory of tropical differential equations\nby Jeffre
y Giansiracusa (Swansea University) as part of (LAGARTOS) Latin American R
eal and Tropical Geometry Seminar\n\n\nAbstract\nA few years ago Grigoriev
introduced a theory of tropical differential equations and how to tropica
lize algebraic ODEs over a trivially valued field. In his setup\, one loo
ks at formal power series solutions\, and tropicalizing is taking the supp
ort. I will describe work with Stefano Mereta towards building a theory
of significantly more general scope with potential applications to p-adic
differential equations. I will describe analogues of valuations\, Berkovi
ch analytification\, and tropicalization\, for algebraic differential equa
tions over a differential field with a non-trivial valuation. The theory i
s built in the language of idempotent semirings.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fuensanta Aroca (UNAM)
DTSTART:20201030T140000Z
DTEND:20201030T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/9
DESCRIPTION:Title: Tropical geometry in higher rank\nby Fuensanta Aroca (UNAM) as
part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\
nAbstract\nA valuation \nThe link between algebraic geometry and tropical
geometry is given by a valuation from the field to the real numbers. A val
uation over the reals is a valuation of rank one. In commutative algebra v
aluations are defined over totally ordered groups.\nThe tropical semiring
is the semiring ${\\displaystyle (\\mathbb{R} \\cup \\{+\\infty \\}\,\\opl
us \,\\otimes)}$\, with the operations $x\\oplus y=\\min\\{x\,y\\}\,\nx\\o
times y=x+y$. These operations may be defined for any totally ordered grou
p G.\nWhat is the notion of convexity in $G^n$? Are the tropical varieties
easy to describe?\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (U. Tübingen)
DTSTART:20201113T150000Z
DTEND:20201113T160000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/10
DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arith
metic\nby Hannah Markwig (U. Tübingen) as part of (LAGARTOS) Latin Am
erican Real and Tropical Geometry Seminar\n\n\nAbstract\nA smooth plane qu
artic defined over the complex numbers has precisely\n28 bitangents. This
result goes back to Pluecker. In the tropical world\,\nthe situation is di
fferent. One can define equivalence classes of\ntropical bitangents of whi
ch there are seven\, and each has 4 lifts over\nthe complex numbers. Over
the reals\, we can have 4\, 8\, 16 or 28\nbitangents. The avoidance locus
of a real quartic is the set in the dual\nplane consisting of all lines wh
ich do not meet the quartic. Every\nconnected component of the avoidance l
ocus has precisely 4 bitangents in its closure. For any field k of charact
eristic not equal to 2 and\nwith a non-Archimedean valuation which allows
us to tropicalize\, we\nshow that a tropical bitangent class of a quartic
either has 0 or 4\nlifts over k. This way of grouping into sets of 4 whi
ch exists\ntropically and over the reals is intimately connected: roughly\
, tropical\nbitangent classes can be viewed as tropicalizations of closur
es of\nconnected components of the avoidance locus. Arithmetic counts off
er a\nbridge connecting real and complex counts\, and we investigate how\
ntropical geometry can be used to study this bridge.\n\nThis talk is based
on joint work with Maria Angelica Cueto\, and on joint\nwork in progress
with Sam Payne and Kristin Shaw.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Loho (U. Kassel)
DTSTART:20201204T140000Z
DTEND:20201204T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/11
DESCRIPTION:Title: Oriented matroids from triangulations of products of simplices\nby Georg Loho (U. Kassel) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nClassically\, there is a rich th
eory in algebraic combinatorics\nsurrounding the various objects associate
d with a generic real matrix.\nExamples include regular triangulations of
the product of two simplices\,\ncoherent matching fields\, and realizable
oriented matroids.\nIn this talk\, we will extend the theory by skipping t
he matrix and\nstarting with an arbitrary triangulation of the product of
two simplices\ninstead. In particular\, we show that every polyhedral matc
hing field\ninduces oriented matroids. The oriented matroid is composed of
\ncompatible chirotopes on the cells in a matroid subdivision of the\nhype
rsimplex. Furthermore\, we give a corresponding topological\nconstruction
using Viro’s patchworking. This allows to derive a\nrepresentation of th
e oriented matroid as a pseudosphere arrangement\nfrom a fine mixed subdiv
ision.\nThis is joint work with Marcel Celaya and Chi-Ho Yuen.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Yun (Brown U.)
DTSTART:20201211T140000Z
DTEND:20201211T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/13
DESCRIPTION:Title: The S_n-equivariant rational homology of the tropical moduli spac
es \\Delta_{2\,n}.\nby Claudia Yun (Brown U.) as part of (LAGARTOS) La
tin American Real and Tropical Geometry Seminar\n\n\nAbstract\nThe tropica
l moduli space \\Delta_{g\,n} is a topological space that parametrizes iso
morphism classes of n-marked stable tropical curves of genus g with total
volume 1. Its reduced rational homology has a natural structure of S_n-rep
resentations induced by permuting markings. In this talk\, we focus on \\D
elta_{2\,n} and compute the characters of these S_n-representations for n
up to 8. We use the fact that \\Delta_{2\,n} is a symmetric \\Delta-comple
x\, a concept introduced by Chan\, Glatius\, and Payne. The computation is
done in SageMath.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (École Polytechnique)
DTSTART:20210115T140000Z
DTEND:20210115T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/14
DESCRIPTION:Title: The tropical Hodge conjecture\nby Omid Amini (École Polytech
nique) as part of (LAGARTOS) Latin American Real and Tropical Geometry Sem
inar\n\n\nAbstract\nI will present the proof of the tropical Hodge conject
ure for smooth projective tropical varieties which admit a rational triang
ulation. This in particular includes those which come from tropicalization
of smooth projective varieties over the field of Puiseux series over any
base field.\n\nThe talk is based on joint works with Matthieu Piquerez (Ec
ole Polytechnique).\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin Shaw (U. Oslo)
DTSTART:20210129T140000Z
DTEND:20210129T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/15
DESCRIPTION:Title: Real phase structures on tropical varieties\nby Kristin Shaw
(U. Oslo) as part of (LAGARTOS) Latin American Real and Tropical Geometry
Seminar\n\n\nAbstract\nIn this talk\, I will propose a definition of real
phase structures on\ntropical varieties. I’ll explain that when the trop
ical variety is a\nmatroid fan\, specifying a real phase structure is cryp
tomorphic to\nproviding an orientation of the underlying matroid.\n\nI’l
l define the real part of a tropical variety with a real phase\nstructure.
This determines a closed chain in an appropriate homology\ntheory. In the
case when the tropical variety is non-singular\, the real\npart is a PL-m
anifold. Moreover\, for tropical manifolds equipped with\nreal phase struc
tures we can apply the same spectral sequence for\nhypersurfaces\, obtaine
d by Renaudineau and myself\, and bound the Betti\nnumbers of the real par
t by the dimensions of the tropical homology groups.\n\nThis is joint work
in progress with Johannes Rau and Arthur Renaudineau.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugallé (U. Nantes)
DTSTART:20210212T150000Z
DTEND:20210212T160000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/16
DESCRIPTION:Title: Polynomial properties of tropical refined invariants\nby Erwa
n Brugallé (U. Nantes) as part of (LAGARTOS) Latin American Real and Trop
ical Geometry Seminar\n\n\nAbstract\nTropical geometry is a useful tool in
the enumeration of complex or real algebraic curves. Around 10 years ago
Block and Göttsche proposed a kind of quantification of tropical enumerat
ive invariants\, which are Laurent\npolynomial interpolating between compl
ex and real enumerative\ninvariants. In this talk I will review these trop
ical refined invariants\nand their relation with classical enumerative geo
metry. I will then\nexplain some curious polynomial behavior of the coeffi
cients of these\nrefined invariants\, providing in particular a surprising
resurgence\, in\na dual setting\, of the so-called node polynomials and G
öttsche conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucía López de Medrano (UNAM)
DTSTART:20210226T140000Z
DTEND:20210226T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/17
DESCRIPTION:Title: Topology of tropical varieties\nby Lucía López de Medrano (
UNAM) as part of (LAGARTOS) Latin American Real and Tropical Geometry Semi
nar\n\n\nAbstract\nIt was recently shown that the top Betti number of trop
ical varieties can exceed the upper bounds of those of complex varieties o
f the same dimension and degree.\nThis is because\, unlike complex varieti
es\, the upper bounds of the top Betti numbers for tropical varieties also
depend on the codimension.\n\nIn this talk\, we will recall the maximal c
onstructions known so far and show that in the case of cubic tropical curv
es\, this construction is maximally optimal.\n\nThis is a joint work with
Benoit Bretrand and Erwan Brugallé.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (U. Buenos Aires)
DTSTART:20210319T140000Z
DTEND:20210319T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/18
DESCRIPTION:Title: Optimal Descartes rule of signs for polynomial systems supported
on circuits\nby Alicia Dickenstein (U. Buenos Aires) as part of (LAGAR
TOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nDesc
artes' rule of signs for univariate real polynomials is a beautifully simp
le upper bound for the number of positive real roots. Moreover\, it gives
the exact number of positive real roots when the polynomial is real rooted
\, for instance\, for characteristic polynomials of symmetric matrices. A
general multivariate Descartes rule is certainly more complex and still el
usive. I will recall the few known multivariate cases and will present a
new optimal Descartes rule for polynomials supported on circuits\, obtaine
d in collaboration with Frédéric Bihan and Jens Forsgård. If time permi
ts\, I will talk a bit about lower bounds.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (U. Roma Tre)
DTSTART:20210326T140000Z
DTEND:20210326T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/19
DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian varie
ties\nby Margarida Melo (U. Roma Tre) as part of (LAGARTOS) Latin Amer
ican Real and Tropical Geometry Seminar\n\n\nAbstract\nThe moduli space of
abelian varieties Ag admits well behaved toroidal compactifications whose
dual complex can be given a tropical interpretation.\nTherefore\, one can
use the techniques recently developed by Chan-Galatius-Payne in order to
understand part of the topology of Ag via tropical geometry.\nIn this talk
\, which is based in joint work with Madeleine Brandt\, Juliette Bruce\, M
elody Chan\, Gwyneth Moreland and Corey Wolfe\, I will explain how to use
this setup\, and in particular computations in the perfect cone compactifi
cation of Ag\, in order to describe its top weight cohomology for g up to
7.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Esterov (HSE Moscow)
DTSTART:20210409T140000Z
DTEND:20210409T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/20
DESCRIPTION:Title: Tropical characteristic classes\nby Alex Esterov (HSE Moscow)
as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n
\n\nAbstract\nTo every affine algebraic variety one can assign its tropica
l fan\, which remembers a lot about the intersection theory of the variety
. Moreover\, to every k-dimensional variety one can associate its tropical
characteristic classes (a tuple of tropical fans of dimensions from 0 to
k)\, which remember much more. I will introduce tropical characteristic cl
asses\, discuss how to compute them\, point out their relations to some ot
her objects of similar nature (such as CSM classes of matroids and refined
tropicalizations)\, and tell about some applications to enumerative geome
try and singularity theory.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART:20210423T140000Z
DTEND:20210423T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/21
DESCRIPTION:Title: Tropical ideals of projective hypersurfaces\nby Alex Fink (Qu
een Mary University of London) as part of (LAGARTOS) Latin American Real a
nd Tropical Geometry Seminar\n\n\nAbstract\nA "tropical ideal"\, defined b
y Maclagan and Rincon\, is an ideal in the tropical polynomial semiring th
at is also a tropical linear space (on each finite set of monomials). A t
ropical ideal cuts out a tropical variety. But already for projective tro
pical hypersurfaces there can be a large family of tropical ideal structur
es\, much larger even than the set of tropicalisations of classical ideals
. This talk will be centred on a collection of examples\, including a non
-realisable ideal structure on a large set of tropical hypersurfaces\, and
the classification of ideals of double points on the line.\n\nThis is bas
ed on joint work with Jeff and Noah Giansiracusa.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lionel Lang (Gävle University)
DTSTART:20210507T140000Z
DTEND:20210507T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/22
DESCRIPTION:Title: Patchworking the Log-critical locus of planar curves\nby Lion
el Lang (Gävle University) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nWe will report on a recent work i
n collaboration with A. Renaudineau in which we studied the critical locus
for the amoeba map along families of curves defined by Viro polynomials.
\nRecall that for real curves\, this locus is a superset of the real part.
In general\, this locus gives informations on how the curve sits in the p
lane. Unfortunately\, not much is known on its topology besides some bound
s on its Betti numbers.\nWe will see that the Log-critical locus admits a
Patchworking theorem. We will discuss some constructions and address the s
harpness of the bounds mentioned above.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Manzaroli (U. Tübingen)
DTSTART:20210521T140000Z
DTEND:20210521T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/23
DESCRIPTION:Title: Real fibered morphisms of real del Pezzo surfaces\nby Matilde
Manzaroli (U. Tübingen) as part of (LAGARTOS) Latin American Real and Tr
opical Geometry Seminar\n\n\nAbstract\nA morphism of smooth varieties of t
he same dimension is called \nreal fibered if the inverse image of the rea
l part of the target is the \nreal part of the source. It goes back to Ahl
fors that a real algebraic \ncurve admits a real fibered morphism to the p
rojective line if and only \nif the real part of the curve disconnects its
complex part. Inspired by \nthis result\, in a joint work with Mario Kumm
er and Cédric Le Texier\, we \nare interested in characterising real alge
braic varieties of dimension n \nadmitting real fibered morphisms to the n
-dimensional projective space. \nWe present a criterion to construct real
fibered morphisms that arise as \nfinite surjective linear projections fro
m an embedded variety\; this \ncriterion relies on topological linking num
bers. We address special \nattention to real algebraic surfaces. We classi
fy all real fibered \nmorphisms from real del Pezzo surfaces to the projec
tive plane and \ndetermine when such morphisms arise as the composition of
a projective \nembedding with a linear projection.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Mazzon (MPI Bonn)
DTSTART:20210604T140000Z
DTEND:20210604T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/24
DESCRIPTION:Title: Tropical affine manifolds in mirror symmetry and Berkovich geomet
ry\nby Enrica Mazzon (MPI Bonn) as part of (LAGARTOS) Latin American R
eal and Tropical Geometry Seminar\n\n\nAbstract\nMirror symmetry is a fast
-moving research area at the boundary between mathematics and theoretical
physics. Originated from observations in string theory\, it suggests that
certain geometrical objects (complex Calabi-Yau manifolds) should come in
pairs\, in the sense that each of them has a mirror partner and the two sh
are interesting geometrical properties.\n\nIn this talk\, I will introduce
some notions relating mirror symmetry to tropical geometry\, inspired by
the work of Kontsevich-Soibelman and Gross-Siebert. In particular\, I will
focus on the construction of a so-called “tropical affine manifold” u
sing methods of non-archimedean geometry\, and the guiding example will be
the case of K3 surfaces and some hyper-Kähler varieties. This is based o
n a joint work with Morgan Brown and a work in progress with Léonard Pill
e-Schneider.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (U. Cambridge)
DTSTART:20210618T140000Z
DTEND:20210618T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/25
DESCRIPTION:Title: Piecewise polynomials and the moduli space of curves\nby Dhru
v Ranganathan (U. Cambridge) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nTropical geometry selects natura
l “principal contributions” in an intersection of two varieties inside
a third\, provided the three objects are equipped with a tropicalization
(also known as a logarithmic structure). When one is working inside the mo
duli space of curves\, these contributions are geometrically meaningful. I
’ll try to explain both why they are interesting (via joint work with Re
nzo Cavalieri and Hannah Markwig) and how to understand them conceptually
(via joint work with Sam Molcho). The main protagonist in the story is the
ring of piecewise polynomial functions on the tropicalization of the modu
li space of curves.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (U. Bern)
DTSTART:20210702T140000Z
DTEND:20210702T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/26
DESCRIPTION:Title: The geometry of GL-varieties\nby Jan Draisma (U. Bern) as par
t of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbs
tract\nA GL-variety is an infinite-dimensional variety equipped with\na su
itable action of the infinite-dimensional general linear group.\nGL-variet
ies arise naturally in the study of properties of polynomials\n(and more g
eneral tensors) that do not depend on their number of\nvariables\, a resea
rch theme that is attracting attention in diverse\nareas of mathematics. I
will report on joint work with Arthur Bik\,\nAlessandro Danelon\, Rob Egg
ermont\, and Andrew Snowden\, in which we\nestablish GL-analogues of sever
al fundamental theorems on\nfinite-dimensional varieties.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Tech)
DTSTART:20210716T140000Z
DTEND:20210716T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/27
DESCRIPTION:Title: Lift theorems for representations of matroids over pastures\n
by Matt Baker (Georgia Tech) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nGiven a partial field P\, the Li
ft Theorem of Pendavingh and van Zwam produces a partial field L(P) and a
homomorphism L(P) -> P with the property that if a matroid is representabl
e over P then it is also representable over L(P). We will formulate a gene
ralization of the Pendavingh-van Zwam Lift Theorem to pastures\, which gen
eralize both partial fields and hyperfields\, and explore some of its comb
inatorial implications. For certain restricted classes of matroids (e.g. t
ernary matroids)\, we obtain a stronger lift theorem which is essentially
sharp. Even in the case of partial fields\, our method of proof is differe
nt from that of Pendavingh and van Zwam and we're able to prove some new r
esults. This is joint work with Oliver Lorscheid.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington U. in St Louis)
DTSTART:20210910T140000Z
DTEND:20210910T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/28
DESCRIPTION:Title: Wall-crossing phenomenon for Newton--Okounkov bodies\nby Laur
a Escobar (Washington U. in St Louis) as part of (LAGARTOS) Latin American
Real and Tropical Geometry Seminar\n\n\nAbstract\nA Newton-Okounkov body
is a convex set associated to a projective variety\, equipped with a valua
tion. These bodies generalize the theory of Newton polytopes and the corre
spondence between polytopes and projective toric varieties. Work of Kaveh-
Manon gives an explicit link between tropical geometry and Newton-Okounkov
bodies. We use this link to describe a wall-crossing phenomenon for Newto
n-Okounkov bodies. As an example\, we describe wall-crossing formula in th
e case of the Grassmannian Gr(2\,m). This is joint work with Megumi Harada
.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion U.)
DTSTART:20210924T140000Z
DTEND:20210924T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/29
DESCRIPTION:Title: Tropicalizations of families of curves and applications\nby I
lya Tyomkin (Ben-Gurion U.) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nIn my talk I’ll discuss tropica
lization construction for one-parameter\nfamilies of curves\, and the prop
erties of the associated map from the\ntropicalization of the base to the
moduli space of tropical curves. I\nwill explain how these can be used to
obtain irreducibility results for\nSeveri varieties and Hurwitz schemes in
positive characteristic.\nJoint with Karl Christ and Xiang He.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farbod Shokrieh (U. Washington)
DTSTART:20211008T140000Z
DTEND:20211008T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/30
DESCRIPTION:Title: Heights of abelian varieties\, and tropical geometry\nby Farb
od Shokrieh (U. Washington) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nWe give a formula which\, for a p
rincipally polarized abelian\nvariety $(A\,\\lambda)$ over the field of al
gebraic numbers\, relates the\nstable Faltings height of $A$ with the N\\'
eron-Tate height of a\nsymmetric theta divisor on $A$. Our formula involve
s invariants\narising from tropical geometry. We also discuss the case of
Jacobians\nin some detail\, where graphs and electrical networks will play
a key\nrole.\n(Based on joint works with Robin de Jong.)\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Najera (UNAM-Oaxaca)
DTSTART:20211022T140000Z
DTEND:20211022T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/31
DESCRIPTION:Title: Cluster algebras\, deformation theory and beyond\nby Alfredo
Najera (UNAM-Oaxaca) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nThe purpose of this talk is to explain a
fruitful interaction of ideas/constructions coming from the theory of c
luster algebras\, representation theory of quivers and deformation theory
.\n\nThe representation theory of quivers is a well developed branch of m
athematics that has been very active for nearly 50 years. The theory of c
luster algebras is much younger\, it was initiated by Fomin and Zelevinsk
y in 2001. Various important developments in these theories have emerged
in the last 15 years thanks to the deep relation that exists in between
them. After a gentle introduction to this circle of ideas I will recall t
he construction of a simplicial complex K(A) -- the tau-tilting complex--
associated to a finite dimensional path algebra A. Then I will report on
one aspect of work-in-progress with Nathan Ilten and Hipólito Treffinger
. We show that if K(A) is a cluster complex of finite type then the asso
ciated cluster algebra with universal coefficients is equal to a canonica
lly identified subfamily of the semiuniversal family for the Stanley-Reis
ner ring of K(A). Time permitting\, and depending on the audience's prefe
rence\, I will elaborate either on some aspects of the "non-cluster" cas
e (namely\, when K(A) is not a cluster complex) or on the interpretation
of these results from the point of view of tropical geometry.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Katz (Ohio State University)
DTSTART:20211105T140000Z
DTEND:20211105T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/32
DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Kat
z (Ohio State University) as part of (LAGARTOS) Latin American Real and Tr
opical Geometry Seminar\n\n\nAbstract\nHow do you integrate a 1-form on an
algebraic curve over the p-adic numbers? One can integrate locally\, but
because the topology is totally disconnected\, it's not possible to perfor
m analytic continuation. For good reduction curves\, this question was ans
wered by Coleman who introduced analytic continuation by Frobenius. For ba
d reduction curves\, there are two notions of integration: a local theory
that is easy to compute\; and a global single-valued theory that is useful
for number theoretic applications. We discuss the relationship between th
ese integration theories\, concentrating on the p-adic analogue of Chen's
iterated integration which is important for the non-Abelian Chabauty metho
d. We explain how to use combinatorial ideas\, informed by tropical geomet
ry and Hodge theory\, to compare the two integration theories and outline
an explicit approach to computing these integrals. This is joint work with
Daniel Litt.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mounir Nisse (Xiamen University Malaysia)
DTSTART:20211119T140000Z
DTEND:20211119T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/33
DESCRIPTION:Title: On the topology of phase tropical varieties and beyond\nby Mo
unir Nisse (Xiamen University Malaysia) as part of (LAGARTOS) Latin Americ
an Real and Tropical Geometry Seminar\n\n\nAbstract\nTropical geometry is
a recent area of mathematics that can be seen as a limiting aspect (or "d
egeneration") of algebraic geometry. For example complex curves viewed as
Riemann surfaces turn to metric graphs (one dimensional combinatorial
object)\, and $n$-dimensional complex varieties turn to $n$-dimensional
polyhedral complexes with some properties. \n\nI will first give an over
view\, and I will recall the definition of phase tropical varieties\, th
eir amoebas and coamoebas. After that\, I will focus on non-singular alge
braic curves in $(\\mathbb{C}^*)^n$ with $n\\geq 2$ and explain how they d
egenerate onto phase tropical curves that are topological manifolds. Such
properties were conjectured in a talk by O. Viro in a workshop at MSRI in
2009 (Viro's conjecture is very general). \n\nThen\, I will discuss and
explain how we show this fact\, under certain conditions\, for $k$-dimens
ional phase tropical variety in $(\\mathbb{C}^*)^{2k}$\, and I will ask so
me interesting questions.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anh Thi Ngoc Nguyen (U. Nantes)
DTSTART:20211203T140000Z
DTEND:20211203T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/34
DESCRIPTION:Title: Complex and real enumerative geometry in three-dimensional del Pe
zzo varieties\nby Anh Thi Ngoc Nguyen (U. Nantes) as part of (LAGARTOS
) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nThe enu
merative problems with respect to counting (resp. real) algebraic curves p
assing through certain (resp. real) configurations in (resp. real) algebra
ic varieties are usually known as Gromov-Witten invariants (resp. Welschi
nger invariants).\n\nIn my talk\, I will present some interesting relaions
between genus-0 Gromov-Witten-Welschinger invariants of some three-dimens
ional del Pezzo varieties and that of del Pezzo surfaces.\n\nThis is a gen
eralization of a result by Brugallé and Georgieva in 2016.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattias Jonsson (U. Michigan)
DTSTART:20220114T140000Z
DTEND:20220114T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/35
DESCRIPTION:Title: Potential theory in non-Archimedean geometry\nby Mattias Jons
son (U. Michigan) as part of (LAGARTOS) Latin American Real and Tropical G
eometry Seminar\n\n\nAbstract\nNon-Archimedean geometry is an analogue of
complex geometry when the complex numbers are replaced by a non-Archimedea
n field. A. Thuillier and others have developed potential theory on Berkov
ich spaces as a non-Archimedean analogue of classical potential theory in
the complex plane. I will give a gentle introduction to joint work with S.
Boucksom\, where we develop a higher-dimensional version of this theory.
Convexity and piecewise linear structures play an important role in our st
udy. Time permitting\, I will also describe some applications.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (TU Braunschweig)
DTSTART:20220211T140000Z
DTEND:20220211T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/36
DESCRIPTION:Title: The tropical discriminant of a polynomial map on the plane\nb
y Boulos El Hilany (TU Braunschweig) as part of (LAGARTOS) Latin American
Real and Tropical Geometry Seminar\n\n\nAbstract\nThe discriminant\, $D(f)
$\, of a map $f:X\\to Y$ is the set of images of its critical points.\nApp
roximating $D(f)$ presents a fruitful insight for solving numerous problem
s in mathematics.\nHowever\, standard methods for achieving this rely on e
limination techniques which can be excessively inefficient.\n\nI will pres
ent a purely combinatorial procedure for computing the tropical curve in $
\\mathbb{R}^2$ of the discriminant of a polynomial map on the plane satisf
ying some mild genericity conditions. Thanks to the advances in tropical g
eometry in the last 20 years\, this new procedure gives rise to a more eff
icient algorithm for approximating $D(f)$\, and for working out its geomet
rical/topological invariants.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Angélica Cueto (Ohio State U.)
DTSTART:20220225T140000Z
DTEND:20220225T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/37
DESCRIPTION:Title: Splice type surface singularities and their local tropicalization
s\nby Maria Angélica Cueto (Ohio State U.) as part of (LAGARTOS) Lati
n American Real and Tropical Geometry Seminar\n\n\nAbstract\nSplice type s
urface singularities were introduced by Neumann and Wahl as a generalizati
on of the class of Pham-Brieskorn-Hamm complete intersections of dimension
two. Their construction depends on a weighted graph with no loops called
a splice diagram. In this talk\, I will report on joint work with Patrick
Popescu-Pampu and Dmitry Stepanov (arXiv: 2108.05912) that sheds new light
on these singularities via tropical methods\, reproving some of Neumann a
nd Wahl's earlier results on these singularities\, and showings that splic
e type surface singularities are Newton non-degenerate in the sense of Kho
vanskii.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Le Texier (U. Toulouse)
DTSTART:20220408T140000Z
DTEND:20220408T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/38
DESCRIPTION:Title: Hyperbolic plane curves near the non-singular tropical limit\
nby Cédric Le Texier (U. Toulouse) as part of (LAGARTOS) Latin American R
eal and Tropical Geometry Seminar\n\n\nAbstract\nWe determine necessary an
d sufficient conditions for real algebraic curves near the non-singular tr
opical limit to be hyperbolic with respect to a point\, thus generalising
Speyer's classification of stable curves near the tropical limit.\nIn orde
r to obtain the conditions\, we develop tools of real tropical intersectio
n theory. \nWe introduce the tropical hyperbolicity locus and the signed
tropical hyperbolicity locus of a real algebraic curve near the non-singul
ar tropical limit\, and show that it satisfies a real tropical analogue of
convexity.\nIn the case of honeycombs\, we characterise the tropical hype
rbolicity locus in terms of the set of twisted edges on the tropical limit
.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farhad Babaee (U. Bristol)
DTSTART:20220311T140000Z
DTEND:20220311T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/39
DESCRIPTION:Title: Dynamic tropicalisation\nby Farhad Babaee (U. Bristol) as par
t of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbs
tract\nIt is well-known that not every tropical variety can be lifted to a
n algebraic subvariety of the complex torus. However\, any tropical variet
y can be lifted to a current to obtain the associated complex tropical cur
rent. Complex tropical currents have proved to be useful in complex geomet
ry\, and they can also appear as certain limits in complex dynamics. This
dynamics provides a natural picture of tropicalisation (with respect to th
e trivial valuation)\, which we explain in this talk.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edvard Aksnes (U. Oslo)
DTSTART:20220325T140000Z
DTEND:20220325T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/40
DESCRIPTION:Title: Tropical Poincaré duality spaces\nby Edvard Aksnes (U. Oslo)
as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n
\n\nAbstract\nItenberg\, Katzarkov\, Mikhalkin and Zharkov introduced trop
ical homology and\ncohomology groups for tropical varieties. These groups
are related by a cap product\nmap. When this cap product is an isomorphism
\, the tropical variety is called a\nTropical Poincaré duality (TPD) spac
e. Bergman fans of matroids are TPD spaces\nby a result of Jell\, Smacka a
nd Shaw. In this talk\, we give criteria for when a fan is\na TPD space at
all its faces. Such spaces are called smooth in recent work of Amini\nand
Piquerez\, and satisfy certain cohomological restrictions. We also classi
fy TPD\nspaces of dimension one. We will conclude with some examples and o
pen questions.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Kummer (TU Dresden)
DTSTART:20220422T140000Z
DTEND:20220422T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/41
DESCRIPTION:Title: A signed count of 2-torsion points on real abelian varieties\
nby Mario Kummer (TU Dresden) as part of (LAGARTOS) Latin American Real an
d Tropical Geometry Seminar\n\n\nAbstract\nWhile the number of 2-torsion p
oints on an abelian variety of dimension\ng over the complex numbers is al
ways equal to 4^g\, the number of real\n2-torsion points varies between 2^
g and 4^g. I will assign a sign ±1 to\neach real 2-torsion point on a rea
l principally polarized abelian\nvariety such that the sum over all signs
is always 2^g. I will give an\ninterpretation of this count in the case wh
en the abelian variety is the\nJacobian of a curve and I will speculate ab
out generalizations to\narbitrary ground fields.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (UPMC Paris)
DTSTART:20220506T140000Z
DTEND:20220506T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/42
DESCRIPTION:Title: Planes in cubic fourfolds\nby Ilia Itenberg (UPMC Paris) as p
art of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nA
bstract\nWe discuss possible numbers of 2-planes in a smooth cubic hypersu
rface in the 5-dimensional projective space. We show that\, in the complex
case\, the maximal number of planes is 405\, the maximum being realized b
y the Fermat cubic. In the real case\, the maximal number of planes is 357
. The proofs deal with the period spaces of cubic hypersurfaces in the 5-d
imensional complex projective space and are based on the global Torelli th
eorem and the surjectivity of the period map for these hypersurfaces\, as
well as on Nikulin's theory of discriminant forms. Joint work with Alex De
gtyarev and John Christian Ottem.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Alexander Helminck (Durham U.)
DTSTART:20220520T140000Z
DTEND:20220520T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/43
DESCRIPTION:Title: Generic root counts and flatness in tropical geometry\nby Pau
l Alexander Helminck (Durham U.) as part of (LAGARTOS) Latin American Real
and Tropical Geometry Seminar\n\n\nAbstract\nIn this talk\, we give new g
eneric root counts of square polynomial systems using methods from tropica
l and non-archimedean geometry. The main theoretical ingredient is a gener
alization of a famous theorem by Bernstein\, Kushnirenko and Khovanskii\,
which now says that the behavior of a single well-behaved zero-dimensional
tropical fiber spreads to an open dense subset. We use this theorem on mo
difications of the universal polynomial system to obtain generic root coun
ts of determinantal subvarieties of the universal parameter space.\nAn imp
ortant role in these generalizations is played by the notion of tropical f
latness\, which allows us to link a single tropical fiber to fibers over a
n open dense subset. We also prove a tropical analogue of Grothendieck's g
eneric flatness theorem\, saying that a given morphism is tropically flat
over a dense open subset.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo-Puentes (U. Duisburg-Essen)
DTSTART:20220603T140000Z
DTEND:20220603T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/44
DESCRIPTION:Title: Enriched tropical intersection\nby Andrés Jaramillo-Puentes
(U. Duisburg-Essen) as part of (LAGARTOS) Latin American Real and Tropical
Geometry Seminar\n\n\nAbstract\nTropical geometry has been proven to be a
powerful computational tool in enumerative geometry over the complex and
real numbers. In this talk we present an example of a quadratic refinement
of this tool\, namely a proof of the quadratically refined Bézout’s th
eorem for tropical curves. We recall the necessary notions of enumerative
geometry over arbitrary fields valued in the Grothendieck-Witt ring. We wi
ll mention the Viro’s patchworking method that served as inspiration to
our construction based on the duality of the tropical curves and the refin
ed Newton polytope associated to its defining polynomial. We will prove th
at the quadratically refined multiplicity of an intersection point of two
tropical curves can be computed combinatorially. We will use this new appr
oach to prove an enriched version of the Bézout theorem and of the Bernst
ein–Kushnirenko theorem\, both for enriched tropical curves. Based on a
joint work with S. Pauli.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (UFF)
DTSTART:20220617T140000Z
DTEND:20220617T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/45
DESCRIPTION:Title: On moduli spaces of roots in algebraic and tropical geometry\
nby Alex Abreu (UFF) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nIn this talk we will construct a topical
moduli space of roots of divisors on stable tropical curves and see its r
elation with Jarvis' moduli space of net of limit roots on stable curves.\
n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Manon (U. Kentucky)
DTSTART:20220909T140000Z
DTEND:20220909T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/46
DESCRIPTION:Title: Toric vector bundles and tropical geometry\nby Christopher Ma
non (U. Kentucky) as part of (LAGARTOS) Latin American Real and Tropical G
eometry Seminar\n\n\nAbstract\nI’ll give an overview of some recent work
on the geometry of projectivized toric\nvector bundles. A toric vector bu
ndle is a vector bundle over a toric variety equipped\nwith an action by t
he defining torus of the base. As a source of examples\, toric\nvector bun
dles and their projectivizations provide a rich class of spaces that still
\nmanage to admit a combinatorial characterization. I’ll begin with a re
cent classification result which shows that a toric vector bundle can be c
aptured by an\narrangement of points on the Bergman fan of a matroid defin
ed by DiRocco\, Jabbusch\, and Smith in their work on ”the parliament of
polytopes” of a vector bundle.\nThen I’ll describe how to extract geo
metric information of the projectivization of\nthe toric vector bundle whe
n this data is nice. I will focus primarily on the Cox\nring of the bundle
\, and the question of whether or not the bundle is a Mori dream\nspace. T
hen I’ll describe how these properties interact with natural operations
on\ntoric vector bundles. This involves the geometry of the closely relate
d class of toric\nflag bundles and tropical flag varieties. This is joint
work with Kiumars Kaveh and\nCourtney George.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Hicks (U. Edinburgh)
DTSTART:20220923T140000Z
DTEND:20220923T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/47
DESCRIPTION:Title: Realizability criteria in tropical geometry from symplectic geome
try\nby Jeffrey Hicks (U. Edinburgh) as part of (LAGARTOS) Latin Ameri
can Real and Tropical Geometry Seminar\n\n\nAbstract\nThe realizability pr
oblem asks if a given tropical subvariety is the tropicalization of some a
lgebraic subvariety. Realizability is already an interesting question for
curves in $\\mathbb {R}^3$\, where Mikhalkin exhibited a tropical curve of
genus 1 which is non-realizable. In recent independent work\, Mak-Ruddat\
, Matessi\, Mikhalkin\, and I show that for many examples of tropcial sub
varieties in $\\mathbb {R}^n$ there exists a Lagrangian lift. This is a La
grangian submanifold of $(\\mathbb {C}^*)^n$ whose image under the moment
map approximates a given tropical subvariety. In particular\, every smooth
tropical curve in $\\mathbb {R}^n$ can be lifted to a Lagrangian submanif
old (in contrast to the algebraic setting!)\n\n \n\nIn this talk\, I'll di
scuss what it means to be a Lagrangian lift of a tropical curve. We will t
hen look at what symplectic conditions on the resulting Lagrangian detect
realizability of the underlying tropical curve. As an application\, we wil
l prove that every tropical curve in a tropical abelian surface has a rigi
d-analytic realization.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilson Zúñiga-Galindo (U. Texas Rio Grande Valley)
DTSTART:20221007T140000Z
DTEND:20221007T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/48
DESCRIPTION:Title: Graphs\, local zeta functions\, log-Coulomb gases\, and phase tra
nsitions at finite temperature\nby Wilson Zúñiga-Galindo (U. Texas R
io Grande Valley) as part of (LAGARTOS) Latin American Real and Tropical G
eometry Seminar\n\n\nAbstract\nThe talk aims to present some connections b
etween local zeta functions and physics. The first part of the talk is ded
icated to reviewing some basic results about local zeta functions. The sec
ond part aims to present some connections between local zeta functions att
ached to graphs and Coulomb gases. The talk is based on the paper: Zúñig
a-Galindo W. A.\, Zambrano-Luna B. A.\, León-Cardenal E.\, Graphs\, local
zeta functions\, log-Coulomb gases\, and phase transitions at finite temp
erature\, J. Math. Phys. 63 (2022)\, no. 1\, Paper No. 013506\, 21 pp.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (École Polytechnique)
DTSTART:20221118T140000Z
DTEND:20221118T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/49
DESCRIPTION:Title: The non-Archimedean Monge-Ampère operator\nby Léonard Pille
-Schneider (École Polytechnique) as part of (LAGARTOS) Latin American Rea
l and Tropical Geometry Seminar\n\n\nAbstract\nLet $(X\, L)$ be a polarize
d variety over a non-archimedean field K. In this\ntalk I will explain how
to define a notion of semi-positive metric on L on\nthe Berkovich analyti
fication $X^{\\text{an}}$ of $X$\, and how to define the\nnon-archimedean
Monge-Ampère measure associated to such a metric.\nIf time permits I will
explain how the non-archimedean Monge-Ampère\noperator can be related to
the real MA operator on skeleta in some\nexamples.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nicaise (Imperial College/KU Leuven)
DTSTART:20221202T140000Z
DTEND:20221202T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/50
DESCRIPTION:Title: Tropical degenerations and irrationality of hypersurfaces in prod
ucts of projective spaces\nby Johannes Nicaise (Imperial College/KU Le
uven) as part of (LAGARTOS) Latin American Real and Tropical Geometry Semi
nar\n\n\nAbstract\nThe specialization map for stable birational types asso
ciates with every strictly toroidal one-parameter degeneration an obstruct
ion to the stable rationality of a very general fiber. In many application
s\, suitable degenerations can be constructed by hand\, but there are also
cases where the complexity gets too high to write down explicit equations
\, and one needs to rely on tropical geometry to give a combinatorial desc
ription in terms of regular subdivisions of Newton polytopes. I will illus
trate this technique for hypersurfaces in products of projective spaces. T
his is based on joint work with John Christian Ottem.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard U.)
DTSTART:20220113T140000Z
DTEND:20220113T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/51
DESCRIPTION:Title: Circles of Apollonius two ways\nby Stephen McKean (Harvard U.
) as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard U.)
DTSTART:20230113T140000Z
DTEND:20230113T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/52
DESCRIPTION:Title: Circles of Apollonius two ways\nby Stephen McKean (Harvard U.
) as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\
n\n\nAbstract\nThere are eight circles tangent to a given trio of circles\
, provided that one works over the complex numbers. Over the reals\, some
of these tangent circles can go missing. In order to obtain an invariant c
ount of tangent circles\, one needs to count each tangent circle with an a
ppropriate weight. I will talk about two geometric characterizations of su
ch counting weights\, as well as how to use these counting weights over an
y field of characteristic not 2.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Rabinoff (Duke U.)
DTSTART:20230127T140000Z
DTEND:20230127T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/53
DESCRIPTION:Title: Weakly smooth forms and Dolbeault cohomology of curves\nby Jo
e Rabinoff (Duke U.) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nGubler and I work out a theory of weakly
smooth forms on non-Archimedean analytic spaces closely following the con
struction of Chambert-Loir and Ducros\, but in which harmonic functions ar
e forced to be smooth. We call such forms "weakly smooth". We compute th
e Dolbeault cohomology groups of rig-smooth\, compact non-Archimedean curv
es with respect to this theory\, and show that they have the expected dime
nsions and satisfy Poincaré duality. We carry out this computation by gi
ving an alternative characterization of weakly smooth forms on curves as p
ullbacks of certain "smooth forms" on a skeleton of the curve. This yield
s an isomorphism between the Dolbeault cohomology of the skeleton\, which
can be computed using standard combinatorial methods\, and the Dolbeault c
ohomology of the curve.\n\nThis work is joint with Walter Gubler.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Gross (U. Frankfurt)
DTSTART:20230210T140000Z
DTEND:20230210T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/54
DESCRIPTION:Title: Vector bundles in tropical geometry\nby Andreas Gross (U. Fra
nkfurt) as part of (LAGARTOS) Latin American Real and Tropical Geometry Se
minar\n\n\nAbstract\nAlthough tropical vector bundles have been introduced
by Allermann ten years ago\, very little has been said about their struct
ure and their relation to vector bundles on algebraic varieties. I will pr
esent recent work with Martin Ulirsch and Dmitry Zakharov that changes exa
ctly this in the case of curves: we prove analogues of the Weil-Riemann-Ro
ch theorem and the Narasimhan-Seshadri correspondence for tropical vector
bundles on tropical curves. We also show that the non-Archimedean skeleton
of the moduli space of semistable vector bundles on a Tate curve is isomo
rphic to a certain component of the moduli space of semistable tropical ve
ctor bundles on its dual metric graph. Time permitting I will also report
on work in progress with Inder Kaur\, Martin Ulirsch\, and Annette Werner
and explain some of the difficulties that arise when generalizing beyond t
he case of curves to Abelian varieties of arbitrary dimension.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Fevola (MPI Leipzig)
DTSTART:20230324T140000Z
DTEND:20230324T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/55
DESCRIPTION:Title: KP solutions from tropical limits\nby Claudia Fevola (MPI Lei
pzig) as part of (LAGARTOS) Latin American Real and Tropical Geometry Semi
nar\n\n\nAbstract\nThe study of solutions to the The Kadomtsev-Petviashvil
i (KP) equation yields\ninteresting connections between integrable systems
and algebraic curves. In this\ntalk\, I will discuss solutions to the KP
equation whose underlying algebraic curves\nundergo tropical degenerations
. In these cases\, Riemann’s theta function becomes\na finite exponentia
l sum supported on a Delaunay polytope. I will introduce the\nHirota varie
ty which parametrizes KP solutions arising from such a sum. This talk\nis
based on joint works with Daniele Agostini\, Yelena Mandelshtam\, and Bern
d\nSturmfels.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Degtyarev (Bilkent U.)
DTSTART:20230310T140000Z
DTEND:20230310T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/56
DESCRIPTION:Title: Singular real plane sextic curves without real points\nby Ale
x Degtyarev (Bilkent U.) as part of (LAGARTOS) Latin American Real and Tro
pical Geometry Seminar\n\n\nAbstract\nIt is a common understanding that an
y reasonable geometric question about\nK3-surfaces can be restated and sol
ved in purely arithmetical terms\, by\nmeans of an appropriately defined h
omological type. For example\, this works\nwell in the study of singular c
omplex sextic curves or quartic surfaces\, as well as in that of smooth re
al ones. However\, when\nthe two are combined (singular real curves or sur
faces)\, the approach fails as\nthe obvious concept of homological type do
es not fully reflect the geometry.\nWe show that the situation can be repa
ired if the curves in question have\nempty real part or\, more generally\,
have no real singular points\; then\, one can\nindeed confine oneself to
the homological types consisting of the exceptional\ndivisors\, polarizati
on\, and real structure. Still\, the resulting arithmetical\nproblem is no
t quite straightforward\, but we manage to solve it in the case\nof empty
real part.\nThis project was conceived and partially completed during our
joint stay at\nthe Max-Planck-Institut für Mathematik\, Bonn.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Mereta (MPI-Leipzig)
DTSTART:20230421T140000Z
DTEND:20230421T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/57
DESCRIPTION:Title: The Fundamental theorem of tropical differential algebra over non
trivially valued fields\nby Stefano Mereta (MPI-Leipzig) as part of (L
AGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\n
We will discuss a fundamental theorem for tropical differential equations
analogue of the fundamental theorem of tropical geometry in this context.
We extend results from Aroca et al. and from Fink and Toghani\, working on
ly in the case of trivial valuation as introduced by Grigoriev\, to differ
ential equations with power series coefficients over any valued field. To
do so\, a crucial ingredient is the framework for tropical differential eq
uations introduced by Giansiracusa and Mereta. As a corollary of the funda
mental theorem\, the radius of convergence of solutions of a differential
equation over a nontrivially valued field can be computed tropically.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Eggleston (U. Osnabrück)
DTSTART:20230505T140000Z
DTEND:20230505T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/58
DESCRIPTION:Title: The amoeba dimension of a linear space\nby Sarah Eggleston (U
. Osnabrück) as part of (LAGARTOS) Latin American Real and Tropical Geome
try Seminar\n\n\nAbstract\nGiven a complex vector subspace $V$ of $\\mathb
b{C}^n$\, the dimension of the amoeba of $V \\cap (\\mathbb{C}^∗)^n$ dep
ends only on the matroid of $V$. Here we prove that this dimension is give
n by the minimum of a certain function over all partitions $P_1\,\\dots\,P
_k$ of the ground set into nonempty parts $P_i$\, as previously conjecture
d by Johannes Rau. We also prove that this formula can be evaluated in pol
ynomial time. This is joint work with Jan Draisma\, Rudi Pendavingh\, Joha
nnes Rau\, and Chi Ho Yuen.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Vargas (U. Frankfurt)
DTSTART:20230519T140000Z
DTEND:20230519T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/59
DESCRIPTION:Title: Valuated matroids\, tropicalized linear spaces and the affine bui
lding of PGL_{r+1}(K)\nby Alejandro Vargas (U. Frankfurt) as part of (
LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\
nValuated matroids were introduced by Dress and Wenzel in the 90s to\ncomb
inatorially study metric spaces that arise naturally in $p$-adic\ngeometry
and in phylogenetics.\nIn tropical geometry\, they encode the information
of the tropicalization\nof a linear space.\nAffine buildings were introdu
ced by Bruhat and Tits in the 70s as highly\nsymmetric simplicial complexe
s to extract the combinatorics of algebraic\ngroups.\nThe affine building
associated to the projective linear group\n$PGL_{r+1}(K)$ admits a descrip
tion via norms\, and by work of Werner a\ncompactification via semi-norms.
\nInspired by Payne's result that the Berkovich analytification is the\nli
mit of all tropicalizations\, we show that the space of seminorms on\n$(K^
{r+1})^*$ is the limit of all tropicalized \\emph{linear} embeddings\n$\\i
ota : \\mathbb{P}^r\\hookrightarrow\\mathbb{P}^n$ and prove a faithful\nt
ropicalization result for compactified linear spaces.\nThus\, under a suit
able hypothesis on the non-Archimedean field $K$\, the\npunchline is that
the rank-$(r+1)$ $K$-realizable valuated matroids\napproximate the compact
ification of the affine building of\n$PGL_{r+1}(K)$ in a precise manner\,
and this can be regarded as the\ntropical linear space associated to a uni
versal $K$-realizable valuated\nmatroid.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristhian Garay López (CIMAT (Guanajuato))
DTSTART:20230602T140000Z
DTEND:20230602T150000Z
DTSTAMP:20260404T110744Z
UID:LAGARTOS/60
DESCRIPTION:Title: Infinite matroids in tropical differential algebra\nby Cristh
ian Garay López (CIMAT (Guanajuato)) as part of (LAGARTOS) Latin American
Real and Tropical Geometry Seminar\n\n\nAbstract\nGiven a set $\\Sigma\\
subset K[x_1\,\\ldots\,x_n]$ of homogeneous linear polynomials\, a classi
cal result in tropical algebraic geometry states that the tropicalization
(with respect to the trivial valuation) of the corresponding variety $V(\\
Sigma)\\subset K^n$ is a fan $B(V(\\Sigma))\\subset(\\mathbb{R}\\cup\\{-\
\infty\\})^n$ that depends only on the matroid over the set of labels $E=[
n]$ associated to the ideal $(\\Sigma)$. Moreover\, this set is tropically
convex in the sense that it is closed under tropical linear combinat
ions. \n\n\nWe discuss an analogue of this result in the context of tropic
al differential algebraic geometry\, namely\, if $\\Sigma\\subset K[\\![t
_1\,\\ldots\,t_m]\\!][x_{1\,J}\,\\ldots\,x_{n\,J}\\::\\:J\\in\\mathbb{N}^m
]$ is certain type of set of homogeneous linear differential polynomials w
ith coefficients in $K[\\![t_1\,\\ldots\,t_m]\\!]$\, then the tropicalizat
ion (with respect to the trivial valuation) of the set of formal solutions
$Sol(\\Sigma)\\subset K[\\![t_1\,\\ldots\,t_m]\\!]^n$ is a matroid $B(
Sol(\\Sigma))$ over the set of labels $E=\\mathbb{N}^{mn}$\, where $m\,n$
are positive integers. Moreover\, this set is tropically convex in the se
nse that it is closed under boolean linear combinations\, i.e.\, it i
s a commutative and idempotent monoid.\n
LOCATION:https://stable.researchseminars.org/talk/LAGARTOS/60/
END:VEVENT
END:VCALENDAR