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BEGIN:VEVENT
SUMMARY:Yoav Len (University of St Andrews)
DTSTART;VALUE=DATE-TIME:20200710T140000Z
DTEND;VALUE=DATE-TIME:20200710T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/1
DESCRIPTION:Title: Brill--Noether theory of Prym varieties\nby Yoav Len (University of S
t Andrews) as part of (LAGARTOS) Latin American Real and Tropical Geometry
Seminar\n\n\nAbstract\nI will discuss combinatorial aspects of Prym varie
ties\, a class of Abelian varieties that shows up in the presence of doubl
e covers of curves. Pryms have deep connections with torsion points of Jac
obians\, bi-tangent lines\, and spin structures. As I will explain\, probl
ems concerning Pryms may be reduced\, via tropical geometry\, to combinato
rial games on graphs. Consequently we obtain new results in the geometry o
f special algebraic curves and bounds on dimensions of certain Brill–Noe
ther loci.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenii Shustin (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200724T140000Z
DTEND;VALUE=DATE-TIME:20200724T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/2
DESCRIPTION:Title: Expressive curves\nby Eugenii Shustin (Tel Aviv University) as part o
f (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstra
ct\nThe talk is devoted to a class of real plane algebraic curves\nwhich w
e call expressive.\nThese are the curves whose defining polynomial has the
smallest\nnumber of critical points allowed by the topology of the real
point set.\nThis concept can be viewed as a global version of the notion o
f\na real morsification of an isolated real plane curve singularity.\nWe p
rovide a characterization of expressive curves and describe several\nconst
ructions that produce a large number of example of expressive\ncurves. Fin
ally\, we discuss further potential developments\ntowards combinatorics of
divides\, topology of links at infinity\,\nmutations of quivers etc.\nJoi
nt work with Sergey Fomin.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (Impa)
DTSTART;VALUE=DATE-TIME:20200807T140000Z
DTEND;VALUE=DATE-TIME:20200807T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/3
DESCRIPTION:Title: Towards a cohomological understanding of the tropical Riemann--Roch theor
em\nby Oliver Lorscheid (Impa) as part of (LAGARTOS) Latin American Re
al and Tropical Geometry Seminar\n\n\nAbstract\nIn this talk\, we outline
a program of developing a cohomological\nunderstanding of the tropical Rie
mann--Roch theorem and discuss the first\nestablished steps in detail. In
particular\, we highlight the role of the\ntropical hyperfield and explain
why ordered blue schemes provide a\nsatisfying framework for tropical sch
eme theory.\n\nIn the last part of the talk\, we turn to the notion of mat
roid bundles\,\nwhich we hope to be the right tool to set up sheaf cohomol
ogy for\ntropical schemes. This is based on a joint work with Matthew Bake
r.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sally Andria (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20200821T140000Z
DTEND;VALUE=DATE-TIME:20200821T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/4
DESCRIPTION:Title: Abel maps for nodal curves via tropical geometry\nby Sally Andria (Un
iversidade Federal Fluminense) as part of (LAGARTOS) Latin American Real a
nd Tropical Geometry Seminar\n\n\nAbstract\nLet $\\pi\\colon \\mathcal{C}\
\rightarrow B$ be a regular smoothing of a nodal curve with smooth compone
nts and a section $\\sigma$ of $\\pi$ through its smooth locus. \nLet $\\
mu$ and $\\mathcal{L}$ be a polarization and an invertible\nsheaf of degre
e $k$ on $\\mathcal{C}/B$. The Abel map $\\alpha^{d}_{\\mathcal{L}}$ is th
e rational map \n$\\alpha^{d}_{\\mathcal{L}}\\colon \\mathcal{C}^d \\dashr
ightarrow \\overline{\\mathcal{J}}_{\\mu}^{\\sigma}$ taking a tuple \nof p
oints $(Q_1\,\\dots\,Q_d)$ on a fiber $C_b$ of $\\pi$ to the sheaf $\\math
cal{O}_{C_b}(Q_1+\\dots+Q_d-d\\sigma(b))\\otimes \\mathcal{L}|_{C_b}$. Her
e $\\overline{\\mathcal{J}}_{\\mu}^{\\sigma}$ denotes Esteves compactified
Jacobian.\nAn interesting question is to find an explicit resolution of t
he map $\\alpha^{d}_{\\mathcal{L}}$.\nWe translate this problem into an ex
plicit combinatorial problem by means of tropical and toric geometry. The
solution of the combinatorial problem gives rise to an explicit resolutio
n of the Abel map. We are able to use this technique to construct all the
degree-$1$ Abel maps and give a resolution of the degree-$2$ Abel-Jacobi m
ap.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang He (Hebrew University)
DTSTART;VALUE=DATE-TIME:20200904T140000Z
DTEND;VALUE=DATE-TIME:20200904T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/5
DESCRIPTION:Title: A tropical approach to the Severi problem\nby Xiang He (Hebrew Univer
sity) as part of (LAGARTOS) Latin American Real and Tropical Geometry Semi
nar\n\n\nAbstract\nSeveri varieties parameterize reduced irreducible curve
s of given geometric genus in a given linear system on an algebraic surfac
e. The irreducibility of Severi varieties is established firstly by Harris
in 1986 for the projective plane in characteristic zero. In this talk\, I
will give a brief overview of the ideas involved\, and describe a tropica
l approach to studying degererations of plane curves\, which leads to a ne
w proof of the irreducibility that also works in positive characteristic.
This is joint work with Karl Christ and Ilya Tyomkin.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Rincón (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20200918T140000Z
DTEND;VALUE=DATE-TIME:20200918T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/6
DESCRIPTION:Title: Tropical ideals\nby Felipe Rincón (Queen Mary University of London)
as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\
n\nAbstract\nTropical ideals are combinatorial objects introduced with the
aim of giving tropical geometry a solid algebraic foundation. They can be
thought of as combinatorial generalizations of the possible collections o
f subsets arising as the supports of all polynomials in an ideal. In gener
al\, their structure is dictated by a sequence of 'compatible' matroids. I
n this talk I will introduce and motivate the notion of tropical ideals\,
and I will discuss work studying some of their main properties and their p
ossible associated varieties.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Sturmfels (MPI-Leipzig)
DTSTART;VALUE=DATE-TIME:20201002T140000Z
DTEND;VALUE=DATE-TIME:20201002T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/7
DESCRIPTION:Title: Theta surfaces\nby Bernd Sturmfels (MPI-Leipzig) as part of (LAGARTOS
) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nA theta
surface in affine 3-space is the zero set of a Riemann theta function in
genus 3. This includes surfaces arising from special plane quartics that a
re singular or reducible. Lie and Poincaré showed that theta surfaces are
precisely the surfaces of double translation\, i.e. obtained as the Minko
wski sum of two space curves in two different ways. These curves are param
etrized by abelian integrals\, so they are usually not algebraic. We prese
nt a new view on this classical topic through the lens of computation. We
discuss practical tools for passing between quartic curves and their theta
surfaces\, and we develop the numerical algebraic geometry of degeneratio
ns of theta functions. This is joint work with Daniele Agostini\, Turku Ce
lik and Julia Struwe.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Giansiracusa (Swansea University)
DTSTART;VALUE=DATE-TIME:20201016T140000Z
DTEND;VALUE=DATE-TIME:20201016T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/8
DESCRIPTION:Title: A general theory of tropical differential equations\nby Jeffrey Gians
iracusa (Swansea University) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nA few years ago Grigoriev introd
uced a theory of tropical differential equations and how to tropicalize al
gebraic ODEs over a trivially valued field. In his setup\, one looks at f
ormal power series solutions\, and tropicalizing is taking the support.
I will describe work with Stefano Mereta towards building a theory of sign
ificantly more general scope with potential applications to p-adic differe
ntial equations. I will describe analogues of valuations\, Berkovich anal
ytification\, and tropicalization\, for algebraic differential equations o
ver a differential field with a non-trivial valuation. The theory is built
in the language of idempotent semirings.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fuensanta Aroca (UNAM)
DTSTART;VALUE=DATE-TIME:20201030T140000Z
DTEND;VALUE=DATE-TIME:20201030T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/9
DESCRIPTION:Title: Tropical geometry in higher rank\nby Fuensanta Aroca (UNAM) as part o
f (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstra
ct\nA valuation \nThe link between algebraic geometry and tropical geometr
y is given by a valuation from the field to the real numbers. A valuation
over the reals is a valuation of rank one. In commutative algebra valuatio
ns are defined over totally ordered groups.\nThe tropical semiring is the
semiring ${\\displaystyle (\\mathbb{R} \\cup \\{+\\infty \\}\,\\oplus \,\\
otimes)}$\, with the operations $x\\oplus y=\\min\\{x\,y\\}\,\nx\\otimes y
=x+y$. These operations may be defined for any totally ordered group G.\nW
hat is the notion of convexity in $G^n$? Are the tropical varieties easy t
o describe?\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (U. Tübingen)
DTSTART;VALUE=DATE-TIME:20201113T150000Z
DTEND;VALUE=DATE-TIME:20201113T160000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/10
DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arithmetic\nby Hannah Markwig (U. Tübingen) as part of (LAGARTOS) Latin American
Real and Tropical Geometry Seminar\n\n\nAbstract\nA smooth plane quartic d
efined over the complex numbers has precisely\n28 bitangents. This result
goes back to Pluecker. In the tropical world\,\nthe situation is different
. One can define equivalence classes of\ntropical bitangents of which ther
e are seven\, and each has 4 lifts over\nthe complex numbers. Over the rea
ls\, we can have 4\, 8\, 16 or 28\nbitangents. The avoidance locus of a re
al quartic is the set in the dual\nplane consisting of all lines which do
not meet the quartic. Every\nconnected component of the avoidance locus ha
s precisely 4 bitangents in its closure. For any field k of characteristic
not equal to 2 and\nwith a non-Archimedean valuation which allows us to t
ropicalize\, 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 which exis
ts\ntropically and over the reals is intimately connected: roughly\, tropi
cal\nbitangent classes can be viewed as tropicalizations of closures of\n
connected components of the avoidance locus. Arithmetic counts offer a\nb
ridge connecting real and complex counts\, and we investigate how\ntropic
al geometry can be used to study this bridge.\n\nThis talk is based on joi
nt work with Maria Angelica Cueto\, and on joint\nwork in progress with Sa
m Payne and Kristin Shaw.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Loho (U. Kassel)
DTSTART;VALUE=DATE-TIME:20201204T140000Z
DTEND;VALUE=DATE-TIME:20201204T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/11
DESCRIPTION:Title: Oriented matroids from triangulations of products of simplices\nby G
eorg Loho (U. Kassel) as part of (LAGARTOS) Latin American Real and Tropic
al Geometry Seminar\n\n\nAbstract\nClassically\, there is a rich theory in
algebraic combinatorics\nsurrounding the various objects associated with
a generic real matrix.\nExamples include regular triangulations of the pro
duct of two simplices\,\ncoherent matching fields\, and realizable oriente
d matroids.\nIn this talk\, we will extend the theory by skipping the matr
ix and\nstarting with an arbitrary triangulation of the product of two sim
plices\ninstead. In particular\, we show that every polyhedral matching fi
eld\ninduces oriented matroids. The oriented matroid is composed of\ncompa
tible chirotopes on the cells in a matroid subdivision of the\nhypersimple
x. Furthermore\, we give a corresponding topological\nconstruction using V
iro’s patchworking. This allows to derive a\nrepresentation of the orien
ted matroid as a pseudosphere arrangement\nfrom a fine mixed subdivision.\
nThis is joint work with Marcel Celaya and Chi-Ho Yuen.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Yun (Brown U.)
DTSTART;VALUE=DATE-TIME:20201211T140000Z
DTEND;VALUE=DATE-TIME:20201211T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/13
DESCRIPTION:Title: The S_n-equivariant rational homology of the tropical moduli spaces \\De
lta_{2\,n}.\nby Claudia Yun (Brown U.) as part of (LAGARTOS) Latin Ame
rican Real and Tropical Geometry Seminar\n\n\nAbstract\nThe tropical modul
i space \\Delta_{g\,n} is a topological space that parametrizes isomorphis
m 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-representa
tions induced by permuting markings. In this talk\, we focus on \\Delta_{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-complex\, a c
oncept introduced by Chan\, Glatius\, and Payne. The computation is done i
n SageMath.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20210115T140000Z
DTEND;VALUE=DATE-TIME:20210115T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/14
DESCRIPTION:Title: The tropical Hodge conjecture\nby Omid Amini (École Polytechnique)
as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\
n\nAbstract\nI will present the proof of the tropical Hodge conjecture for
smooth projective tropical varieties which admit a rational triangulation
. This in particular includes those which come from tropicalization of smo
oth projective varieties over the field of Puiseux series over any base fi
eld.\n\nThe talk is based on joint works with Matthieu Piquerez (Ecole Pol
ytechnique).\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin Shaw (U. Oslo)
DTSTART;VALUE=DATE-TIME:20210129T140000Z
DTEND;VALUE=DATE-TIME:20210129T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/15
DESCRIPTION:Title: Real phase structures on tropical varieties\nby Kristin Shaw (U. Osl
o) 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 s
tructures on\ntropical varieties. I’ll explain that when the tropical va
riety is a\nmatroid fan\, specifying a real phase structure is cryptomorph
ic to\nproviding an orientation of the underlying matroid.\n\nI’ll defin
e the real part of a tropical variety with a real phase\nstructure. This d
etermines a closed chain in an appropriate homology\ntheory. In the case w
hen the tropical variety is non-singular\, the real\npart is a PL-manifold
. Moreover\, for tropical manifolds equipped with\nreal phase structures w
e can apply the same spectral sequence for\nhypersurfaces\, obtained by Re
naudineau and myself\, and bound the Betti\nnumbers of the real part by th
e dimensions of the tropical homology groups.\n\nThis is joint work in pro
gress with Johannes Rau and Arthur Renaudineau.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugallé (U. Nantes)
DTSTART;VALUE=DATE-TIME:20210212T150000Z
DTEND;VALUE=DATE-TIME:20210212T160000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/16
DESCRIPTION:Title: Polynomial properties of tropical refined invariants\nby Erwan Bruga
llé (U. Nantes) as part of (LAGARTOS) Latin American Real and Tropical Ge
ometry Seminar\n\n\nAbstract\nTropical geometry is a useful tool in the en
umeration of complex or real algebraic curves. Around 10 years ago Block a
nd Göttsche proposed a kind of quantification of tropical enumerative inv
ariants\, which are Laurent\npolynomial interpolating between complex and
real enumerative\ninvariants. In this talk I will review these tropical re
fined invariants\nand their relation with classical enumerative geometry.
I will then\nexplain some curious polynomial behavior of the coefficients
of these\nrefined invariants\, providing in particular a surprising resurg
ence\, in\na dual setting\, of the so-called node polynomials and Göttsch
e conjecture.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucía López de Medrano (UNAM)
DTSTART;VALUE=DATE-TIME:20210226T140000Z
DTEND;VALUE=DATE-TIME:20210226T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/17
DESCRIPTION:Title: Topology of tropical varieties\nby Lucía López de Medrano (UNAM) a
s part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n
\nAbstract\nIt was recently shown that the top Betti number of tropical va
rieties can exceed the upper bounds of those of complex varieties of the s
ame dimension and degree.\nThis is because\, unlike complex varieties\, th
e upper bounds of the top Betti numbers for tropical varieties also depend
on the codimension.\n\nIn this talk\, we will recall the maximal construc
tions known so far and show that in the case of cubic tropical curves\, th
is construction is maximally optimal.\n\nThis is a joint work with Benoit
Bretrand and Erwan Brugallé.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (U. Buenos Aires)
DTSTART;VALUE=DATE-TIME:20210319T140000Z
DTEND;VALUE=DATE-TIME:20210319T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/18
DESCRIPTION:Title: Optimal Descartes rule of signs for polynomial systems supported on circ
uits\nby Alicia Dickenstein (U. Buenos Aires) as part of (LAGARTOS) La
tin American Real and Tropical Geometry Seminar\n\n\nAbstract\nDescartes'
rule of signs for univariate real polynomials is a beautifully simple uppe
r bound for the number of positive real roots. Moreover\, it gives the exa
ct 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 elusive.
I will recall the few known multivariate cases and will present a new opt
imal Descartes rule for polynomials supported on circuits\, obtained in co
llaboration with Frédéric Bihan and Jens Forsgård. If time permits\, I
will talk a bit about lower bounds.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (U. Roma Tre)
DTSTART;VALUE=DATE-TIME:20210326T140000Z
DTEND;VALUE=DATE-TIME:20210326T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/19
DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian varieties\nby Margarida Melo (U. Roma Tre) as part of (LAGARTOS) Latin American Re
al and Tropical Geometry Seminar\n\n\nAbstract\nThe moduli space of abelia
n varieties Ag admits well behaved toroidal compactifications whose dual c
omplex can be given a tropical interpretation.\nTherefore\, one can use th
e techniques recently developed by Chan-Galatius-Payne in order to underst
and part of the topology of Ag via tropical geometry.\nIn this talk\, whic
h is based in joint work with Madeleine Brandt\, Juliette Bruce\, Melody C
han\, Gwyneth Moreland and Corey Wolfe\, I will explain how to use this se
tup\, and in particular computations in the perfect cone compactification
of Ag\, in order to describe its top weight cohomology for g up to 7.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Esterov (HSE Moscow)
DTSTART;VALUE=DATE-TIME:20210409T140000Z
DTEND;VALUE=DATE-TIME:20210409T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/20
DESCRIPTION:Title: Tropical characteristic classes\nby Alex Esterov (HSE Moscow) as par
t of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbs
tract\nTo every affine algebraic variety one can assign its tropical fan\,
which remembers a lot about the intersection theory of the variety. Moreo
ver\, to every k-dimensional variety one can associate its tropical charac
teristic classes (a tuple of tropical fans of dimensions from 0 to k)\, wh
ich remember much more. I will introduce tropical characteristic classes\,
discuss how to compute them\, point out their relations to some other obj
ects of similar nature (such as CSM classes of matroids and refined tropic
alizations)\, and tell about some applications to enumerative geometry and
singularity theory.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20210423T140000Z
DTEND;VALUE=DATE-TIME:20210423T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/21
DESCRIPTION:Title: Tropical ideals of projective hypersurfaces\nby Alex Fink (Queen Mar
y University of London) as part of (LAGARTOS) Latin American Real and Trop
ical Geometry Seminar\n\n\nAbstract\nA "tropical ideal"\, defined by Macla
gan and Rincon\, is an ideal in the tropical polynomial semiring that is a
lso a tropical linear space (on each finite set of monomials). A tropical
ideal cuts out a tropical variety. But already for projective tropical h
ypersurfaces there can be a large family of tropical ideal structures\, mu
ch larger even than the set of tropicalisations of classical ideals. This
talk will be centred on a collection of examples\, including a non-realis
able ideal structure on a large set of tropical hypersurfaces\, and the cl
assification of ideals of double points on the line.\n\nThis is based on j
oint work with Jeff and Noah Giansiracusa.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lionel Lang (Gävle University)
DTSTART;VALUE=DATE-TIME:20210507T140000Z
DTEND;VALUE=DATE-TIME:20210507T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/22
DESCRIPTION:Title: Patchworking the Log-critical locus of planar curves\nby Lionel Lang
(Gävle University) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nWe will report on a recent work in colla
boration with A. Renaudineau in which we studied the critical locus for th
e amoeba map along families of curves defined by Viro polynomials. \nRecal
l that for real curves\, this locus is a superset of the real part. In gen
eral\, this locus gives informations on how the curve sits in the plane. U
nfortunately\, not much is known on its topology besides some bounds on it
s Betti numbers.\nWe will see that the Log-critical locus admits a Patchwo
rking theorem. We will discuss some constructions and address the sharpnes
s of the bounds mentioned above.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Manzaroli (U. Tübingen)
DTSTART;VALUE=DATE-TIME:20210521T140000Z
DTEND;VALUE=DATE-TIME:20210521T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/23
DESCRIPTION:Title: Real fibered morphisms of real del Pezzo surfaces\nby Matilde Manzar
oli (U. Tübingen) as part of (LAGARTOS) Latin American Real and Tropical
Geometry Seminar\n\n\nAbstract\nA morphism of smooth varieties of the same
dimension is called \nreal fibered if the inverse image of the real part
of the target is the \nreal part of the source. It goes back to Ahlfors th
at a real algebraic \ncurve admits a real fibered morphism to the projecti
ve line if and only \nif the real part of the curve disconnects its comple
x part. Inspired by \nthis result\, in a joint work with Mario Kummer and
Cédric Le Texier\, we \nare interested in characterising real algebraic v
arieties of dimension n \nadmitting real fibered morphisms to the n-dimens
ional projective space. \nWe present a criterion to construct real fibered
morphisms that arise as \nfinite surjective linear projections from an em
bedded variety\; this \ncriterion relies on topological linking numbers. W
e address special \nattention to real algebraic surfaces. We classify all
real fibered \nmorphisms from real del Pezzo surfaces to the projective pl
ane and \ndetermine when such morphisms arise as the composition of a proj
ective \nembedding with a linear projection.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Mazzon (MPI Bonn)
DTSTART;VALUE=DATE-TIME:20210604T140000Z
DTEND;VALUE=DATE-TIME:20210604T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/24
DESCRIPTION:Title: Tropical affine manifolds in mirror symmetry and Berkovich geometry\
nby Enrica Mazzon (MPI Bonn) as part of (LAGARTOS) Latin American Real 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 share int
eresting geometrical properties.\n\nIn this talk\, I will introduce some n
otions relating mirror symmetry to tropical geometry\, inspired by the wor
k of Kontsevich-Soibelman and Gross-Siebert. In particular\, I will focus
on the construction of a so-called “tropical affine manifold” using me
thods of non-archimedean geometry\, and the guiding example will be the ca
se of K3 surfaces and some hyper-Kähler varieties. This is based on a joi
nt work with Morgan Brown and a work in progress with Léonard Pille-Schne
ider.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (U. Cambridge)
DTSTART;VALUE=DATE-TIME:20210618T140000Z
DTEND;VALUE=DATE-TIME:20210618T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/25
DESCRIPTION:Title: Piecewise polynomials and the moduli space of curves\nby Dhruv Ranga
nathan (U. Cambridge) as part of (LAGARTOS) Latin American Real and Tropic
al Geometry Seminar\n\n\nAbstract\nTropical geometry selects natural “pr
incipal contributions” in an intersection of two varieties inside a thir
d\, provided the three objects are equipped with a tropicalization (also k
nown as a logarithmic structure). When one is working inside the moduli sp
ace of curves\, these contributions are geometrically meaningful. I’ll t
ry to explain both why they are interesting (via joint work with Renzo Cav
alieri and Hannah Markwig) and how to understand them conceptually (via jo
int work with Sam Molcho). The main protagonist in the story is the ring o
f piecewise polynomial functions on the tropicalization of the moduli spac
e of curves.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (U. Bern)
DTSTART;VALUE=DATE-TIME:20210702T140000Z
DTEND;VALUE=DATE-TIME:20210702T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/26
DESCRIPTION:Title: The geometry of GL-varieties\nby Jan Draisma (U. Bern) as part of (L
AGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\n
A GL-variety is an infinite-dimensional variety equipped with\na suitable
action of the infinite-dimensional general linear group.\nGL-varieties ari
se naturally in the study of properties of polynomials\n(and more general
tensors) that do not depend on their number of\nvariables\, a research the
me that is attracting attention in diverse\nareas of mathematics. I will r
eport on joint work with Arthur Bik\,\nAlessandro Danelon\, Rob Eggermont\
, and Andrew Snowden\, in which we\nestablish GL-analogues of several fund
amental theorems on\nfinite-dimensional varieties.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20210716T140000Z
DTEND;VALUE=DATE-TIME:20210716T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/27
DESCRIPTION:Title: Lift theorems for representations of matroids over pastures\nby Matt
Baker (Georgia Tech) as part of (LAGARTOS) Latin American Real and Tropic
al Geometry Seminar\n\n\nAbstract\nGiven a partial field P\, the Lift Theo
rem of Pendavingh and van Zwam produces a partial field L(P) and a homomor
phism L(P) -> P with the property that if a matroid is representable over
P then it is also representable over L(P). We will formulate a generalizat
ion of the Pendavingh-van Zwam Lift Theorem to pastures\, which generalize
both partial fields and hyperfields\, and explore some of its combinatori
al implications. For certain restricted classes of matroids (e.g. ternary
matroids)\, we obtain a stronger lift theorem which is essentially sharp.
Even in the case of partial fields\, our method of proof is different from
that of Pendavingh and van Zwam and we're able to prove some new results.
This is joint work with Oliver Lorscheid.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington U. in St Louis)
DTSTART;VALUE=DATE-TIME:20210910T140000Z
DTEND;VALUE=DATE-TIME:20210910T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/28
DESCRIPTION:Title: Wall-crossing phenomenon for Newton--Okounkov bodies\nby Laura Escob
ar (Washington U. in St Louis) as part of (LAGARTOS) Latin American Real a
nd Tropical Geometry Seminar\n\n\nAbstract\nA Newton-Okounkov body is a co
nvex set associated to a projective variety\, equipped with a valuation. T
hese bodies generalize the theory of Newton polytopes and the corresponden
ce between polytopes and projective toric varieties. Work of Kaveh-Manon g
ives an explicit link between tropical geometry and Newton-Okounkov bodies
. We use this link to describe a wall-crossing phenomenon for Newton-Okoun
kov bodies. As an example\, we describe wall-crossing formula in the case
of the Grassmannian Gr(2\,m). This is joint work with Megumi Harada.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion U.)
DTSTART;VALUE=DATE-TIME:20210924T140000Z
DTEND;VALUE=DATE-TIME:20210924T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/29
DESCRIPTION:Title: Tropicalizations of families of curves and applications\nby Ilya Tyo
mkin (Ben-Gurion U.) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nIn my talk I’ll discuss tropicalizatio
n construction for one-parameter\nfamilies of curves\, and the properties
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 positi
ve characteristic.\nJoint with Karl Christ and Xiang He.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farbod Shokrieh (U. Washington)
DTSTART;VALUE=DATE-TIME:20211008T140000Z
DTEND;VALUE=DATE-TIME:20211008T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/30
DESCRIPTION:Title: Heights of abelian varieties\, and tropical geometry\nby Farbod Shok
rieh (U. Washington) as part of (LAGARTOS) Latin American Real and Tropica
l Geometry Seminar\n\n\nAbstract\nWe give a formula which\, for a principa
lly polarized abelian\nvariety $(A\,\\lambda)$ over the field of algebraic
numbers\, relates the\nstable Faltings height of $A$ with the N\\'eron-Ta
te height of a\nsymmetric theta divisor on $A$. Our formula involves invar
iants\narising from tropical geometry. We also discuss the case of Jacobia
ns\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://researchseminars.org/talk/LAGARTOS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Najera (UNAM-Oaxaca)
DTSTART;VALUE=DATE-TIME:20211022T140000Z
DTEND;VALUE=DATE-TIME:20211022T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/31
DESCRIPTION:Title: Cluster algebras\, deformation theory and beyond\nby Alfredo Najera
(UNAM-Oaxaca) as part of (LAGARTOS) Latin American Real and Tropical Geome
try Seminar\n\n\nAbstract\nThe purpose of this talk is to explain a fruitf
ul interaction of ideas/constructions coming from the theory of cluster
algebras\, representation theory of quivers and deformation theory.\n\nTh
e representation theory of quivers is a well developed branch of mathemat
ics that has been very active for nearly 50 years. The theory of cluster
algebras is much younger\, it was initiated by Fomin and Zelevinsky in 20
01. Various important developments in these theories have emerged in the
last 15 years thanks to the deep relation that exists in between them. A
fter a gentle introduction to this circle of ideas I will recall the cons
truction of a simplicial complex K(A) -- the tau-tilting complex-- associa
ted to a finite dimensional path algebra A. Then I will report on one asp
ect of work-in-progress with Nathan Ilten and Hipólito Treffinger. We sh
ow that if K(A) is a cluster complex of finite type then the associated
cluster algebra with universal coefficients is equal to a canonically ide
ntified subfamily of the semiuniversal family for the Stanley-Reisner rin
g of K(A). Time permitting\, and depending on the audience's preference\,
I will elaborate either on some aspects of the "non-cluster" case (name
ly\, when K(A) is not a cluster complex) or on the interpretation of thes
e results from the point of view of tropical geometry.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Katz (Ohio State University)
DTSTART;VALUE=DATE-TIME:20211105T140000Z
DTEND;VALUE=DATE-TIME:20211105T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/32
DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Katz (Ohio
State University) as part of (LAGARTOS) Latin American Real and Tropical
Geometry Seminar\n\n\nAbstract\nHow do you integrate a 1-form on an algebr
aic curve over the p-adic numbers? One can integrate locally\, but because
the topology is totally disconnected\, it's not possible to perform analy
tic continuation. For good reduction curves\, this question was answered b
y Coleman who introduced analytic continuation by Frobenius. For bad reduc
tion 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 nu
mber theoretic applications. We discuss the relationship between these int
egration theories\, concentrating on the p-adic analogue of Chen's iterate
d integration which is important for the non-Abelian Chabauty method. We e
xplain how to use combinatorial ideas\, informed by tropical geometry and
Hodge theory\, to compare the two integration theories and outline an expl
icit approach to computing these integrals. This is joint work with Daniel
Litt.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mounir Nisse (Xiamen University Malaysia)
DTSTART;VALUE=DATE-TIME:20211119T140000Z
DTEND;VALUE=DATE-TIME:20211119T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/33
DESCRIPTION:Title: On the topology of phase tropical varieties and beyond\nby Mounir Ni
sse (Xiamen University Malaysia) as part of (LAGARTOS) Latin American Real
and Tropical Geometry Seminar\n\n\nAbstract\nTropical geometry is a recen
t area of mathematics that can be seen as a limiting aspect (or "degenera
tion") of algebraic geometry. For example complex curves viewed as Riema
nn surfaces turn to metric graphs (one dimensional combinatorial object)
\, and $n$-dimensional complex varieties turn to $n$-dimensional polyhe
dral complexes with some properties. \n\nI will first give an overview\,
and I will recall the definition of phase tropical varieties\, their amo
ebas and coamoebas. After that\, I will focus on non-singular algebraic c
urves in $(\\mathbb{C}^*)^n$ with $n\\geq 2$ and explain how they degenera
te onto phase tropical curves that are topological manifolds. Such proper
ties 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 $k$-dimensional p
hase tropical variety in $(\\mathbb{C}^*)^{2k}$\, and I will ask some inte
resting questions.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anh Thi Ngoc Nguyen (U. Nantes)
DTSTART;VALUE=DATE-TIME:20211203T140000Z
DTEND;VALUE=DATE-TIME:20211203T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/34
DESCRIPTION:Title: Complex and real enumerative geometry in three-dimensional del Pezzo var
ieties\nby Anh Thi Ngoc Nguyen (U. Nantes) as part of (LAGARTOS) Latin
American Real and Tropical Geometry Seminar\n\n\nAbstract\nThe enumerativ
e problems with respect to counting (resp. real) algebraic curves passing
through certain (resp. real) configurations in (resp. real) algebraic vari
eties are usually known as Gromov-Witten invariants (resp. Welschinger in
variants).\n\nIn my talk\, I will present some interesting relaions betwee
n genus-0 Gromov-Witten-Welschinger invariants of some three-dimensional d
el Pezzo varieties and that of del Pezzo surfaces.\n\nThis is a generaliza
tion of a result by Brugallé and Georgieva in 2016.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattias Jonsson (U. Michigan)
DTSTART;VALUE=DATE-TIME:20220114T140000Z
DTEND;VALUE=DATE-TIME:20220114T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/35
DESCRIPTION:Title: Potential theory in non-Archimedean geometry\nby Mattias Jonsson (U.
Michigan) as part of (LAGARTOS) Latin American Real and Tropical Geometry
Seminar\n\n\nAbstract\nNon-Archimedean geometry is an analogue of complex
geometry when the complex numbers are replaced by a non-Archimedean field
. A. Thuillier and others have developed potential theory on Berkovich spa
ces as a non-Archimedean analogue of classical potential theory in the com
plex plane. I will give a gentle introduction to joint work with S. Boucks
om\, where we develop a higher-dimensional version of this theory. Convexi
ty and piecewise linear structures play an important role in our study. Ti
me permitting\, I will also describe some applications.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (TU Braunschweig)
DTSTART;VALUE=DATE-TIME:20220211T140000Z
DTEND;VALUE=DATE-TIME:20220211T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/36
DESCRIPTION:Title: The tropical discriminant of a polynomial map on the plane\nby Boulo
s El Hilany (TU Braunschweig) as part of (LAGARTOS) Latin American Real an
d 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.\nApproximat
ing $D(f)$ presents a fruitful insight for solving numerous problems in ma
thematics.\nHowever\, standard methods for achieving this rely on eliminat
ion techniques which can be excessively inefficient.\n\nI will present a p
urely combinatorial procedure for computing the tropical curve in $\\mathb
b{R}^2$ of the discriminant of a polynomial map on the plane satisfying so
me mild genericity conditions. Thanks to the advances in tropical geometry
in the last 20 years\, this new procedure gives rise to a more efficient
algorithm for approximating $D(f)$\, and for working out its geometrical/t
opological invariants.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Angélica Cueto (Ohio State U.)
DTSTART;VALUE=DATE-TIME:20220225T140000Z
DTEND;VALUE=DATE-TIME:20220225T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/37
DESCRIPTION:Title: Splice type surface singularities and their local tropicalizations\n
by Maria Angélica Cueto (Ohio State U.) as part of (LAGARTOS) Latin Ameri
can Real and Tropical Geometry Seminar\n\n\nAbstract\nSplice type surface
singularities were introduced by Neumann and Wahl as a generalization of t
he class of Pham-Brieskorn-Hamm complete intersections of dimension two. T
heir construction depends on a weighted graph with no loops called a splic
e 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 the
se singularities via tropical methods\, reproving some of Neumann and Wahl
's earlier results on these singularities\, and showings that splice type
surface singularities are Newton non-degenerate in the sense of Khovanskii
.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Le Texier (U. Toulouse)
DTSTART;VALUE=DATE-TIME:20220408T140000Z
DTEND;VALUE=DATE-TIME:20220408T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/38
DESCRIPTION:Title: Hyperbolic plane curves near the non-singular tropical limit\nby Cé
dric Le Texier (U. Toulouse) as part of (LAGARTOS) Latin American Real and
Tropical Geometry Seminar\n\n\nAbstract\nWe determine necessary and suffi
cient conditions for real algebraic curves near the non-singular tropical
limit to be hyperbolic with respect to a point\, thus generalising Speyer'
s classification of stable curves near the tropical limit.\nIn order to ob
tain the conditions\, we develop tools of real tropical intersection theor
y. \nWe introduce the tropical hyperbolicity locus and the signed tropica
l hyperbolicity locus of a real algebraic curve near the non-singular trop
ical limit\, and show that it satisfies a real tropical analogue of convex
ity.\nIn the case of honeycombs\, we characterise the tropical hyperbolici
ty locus in terms of the set of twisted edges on the tropical limit.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farhad Babaee (U. Bristol)
DTSTART;VALUE=DATE-TIME:20220311T140000Z
DTEND;VALUE=DATE-TIME:20220311T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/39
DESCRIPTION:Title: Dynamic tropicalisation\nby Farhad Babaee (U. Bristol) as part of (L
AGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\n
It is well-known that not every tropical variety can be lifted to an algeb
raic subvariety of the complex torus. However\, any tropical variety can b
e lifted to a current to obtain the associated complex tropical current. C
omplex tropical currents have proved to be useful in complex geometry\, an
d they can also appear as certain limits in complex dynamics. This dynamic
s provides a natural picture of tropicalisation (with respect to the trivi
al valuation)\, which we explain in this talk.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edvard Aksnes (U. Oslo)
DTSTART;VALUE=DATE-TIME:20220325T140000Z
DTEND;VALUE=DATE-TIME:20220325T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/40
DESCRIPTION:Title: Tropical Poincaré duality spaces\nby Edvard Aksnes (U. Oslo) as par
t of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbs
tract\nItenberg\, Katzarkov\, Mikhalkin and Zharkov introduced tropical ho
mology and\ncohomology groups for tropical varieties. These groups are rel
ated by a cap product\nmap. When this cap product is an isomorphism\, the
tropical variety is called a\nTropical Poincaré duality (TPD) space. Berg
man fans of matroids are TPD spaces\nby a result of Jell\, Smacka and Shaw
. In this talk\, we give criteria for when a fan is\na TPD space at all it
s faces. Such spaces are called smooth in recent work of Amini\nand Piquer
ez\, and satisfy certain cohomological restrictions. We also classify TPD\
nspaces of dimension one. We will conclude with some examples and open que
stions.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Kummer (TU Dresden)
DTSTART;VALUE=DATE-TIME:20220422T140000Z
DTEND;VALUE=DATE-TIME:20220422T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/41
DESCRIPTION:Title: A signed count of 2-torsion points on real abelian varieties\nby Mar
io Kummer (TU Dresden) as part of (LAGARTOS) Latin American Real and Tropi
cal Geometry Seminar\n\n\nAbstract\nWhile the number of 2-torsion points o
n an abelian variety of dimension\ng over the complex numbers is always eq
ual 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 real princ
ipally polarized abelian\nvariety such that the sum over all signs is alwa
ys 2^g. I will give an\ninterpretation of this count in the case when the
abelian variety is the\nJacobian of a curve and I will speculate about gen
eralizations to\narbitrary ground fields.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (UPMC Paris)
DTSTART;VALUE=DATE-TIME:20220506T140000Z
DTEND;VALUE=DATE-TIME:20220506T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/42
DESCRIPTION:Title: Planes in cubic fourfolds\nby Ilia Itenberg (UPMC Paris) as part of
(LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract
\nWe discuss possible numbers of 2-planes in a smooth cubic hypersurface i
n the 5-dimensional projective space. We show that\, in the complex case\,
the maximal number of planes is 405\, the maximum being realized by the F
ermat cubic. In the real case\, the maximal number of planes is 357. The p
roofs deal with the period spaces of cubic hypersurfaces in the 5-dimensio
nal complex projective space and are based on the global Torelli theorem a
nd the surjectivity of the period map for these hypersurfaces\, as well as
on Nikulin's theory of discriminant forms. Joint work with Alex Degtyarev
and John Christian Ottem.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Alexander Helminck (Durham U.)
DTSTART;VALUE=DATE-TIME:20220520T140000Z
DTEND;VALUE=DATE-TIME:20220520T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/43
DESCRIPTION:Title: Generic root counts and flatness in tropical geometry\nby Paul Alexa
nder Helminck (Durham U.) as part of (LAGARTOS) Latin American Real and Tr
opical Geometry Seminar\n\n\nAbstract\nIn this talk\, we give new generic
root counts of square polynomial systems using methods from tropical and n
on-archimedean geometry. The main theoretical ingredient is a generalizati
on of a famous theorem by Bernstein\, Kushnirenko and Khovanskii\, which n
ow says that the behavior of a single well-behaved zero-dimensional tropic
al fiber spreads to an open dense subset. We use this theorem on modificat
ions of the universal polynomial system to obtain generic root counts of d
eterminantal subvarieties of the universal parameter space.\nAn important
role in these generalizations is played by the notion of tropical flatness
\, which allows us to link a single tropical fiber to fibers over an open
dense subset. We also prove a tropical analogue of Grothendieck's generic
flatness theorem\, saying that a given morphism is tropically flat over a
dense open subset.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo-Puentes (U. Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20220603T140000Z
DTEND;VALUE=DATE-TIME:20220603T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/44
DESCRIPTION:Title: Enriched tropical intersection\nby Andrés Jaramillo-Puentes (U. Dui
sburg-Essen) as part of (LAGARTOS) Latin American Real and Tropical Geomet
ry Seminar\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. In this talk we present an example of a quadratic refinement of thi
s tool\, namely a proof of the quadratically refined Bézout’s theorem f
or tropical curves. We recall the necessary notions of enumerative geometr
y over arbitrary fields valued in the Grothendieck-Witt ring. We will ment
ion the Viro’s patchworking method that served as inspiration to our con
struction based on the duality of the tropical curves and the refined Newt
on polytope associated to its defining polynomial. We will prove that the
quadratically refined multiplicity of an intersection point of two tropica
l curves can be computed combinatorially. We will use this new approach to
prove an enriched version of the Bézout theorem and of the Bernstein–K
ushnirenko theorem\, both for enriched tropical curves. Based on a joint w
ork with S. Pauli.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (UFF)
DTSTART;VALUE=DATE-TIME:20220617T140000Z
DTEND;VALUE=DATE-TIME:20220617T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/45
DESCRIPTION:Title: On moduli spaces of roots in algebraic and tropical geometry\nby Ale
x Abreu (UFF) as part of (LAGARTOS) Latin American Real and Tropical Geome
try 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 relation
with Jarvis' moduli space of net of limit roots on stable curves.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Manon (U. Kentucky)
DTSTART;VALUE=DATE-TIME:20220909T140000Z
DTEND;VALUE=DATE-TIME:20220909T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/46
DESCRIPTION:Title: Toric vector bundles and tropical geometry\nby Christopher Manon (U.
Kentucky) as part of (LAGARTOS) Latin American Real and Tropical Geometry
Seminar\n\n\nAbstract\nI’ll give an overview of some recent work on the
geometry of projectivized toric\nvector bundles. A toric vector bundle is
a vector bundle over a toric variety equipped\nwith an action by the defi
ning torus of the base. As a source of examples\, toric\nvector bundles an
d their projectivizations provide a rich class of spaces that still\nmanag
e to admit a combinatorial characterization. I’ll begin with a recent cl
assification result which shows that a toric vector bundle can be captured
by an\narrangement of points on the Bergman fan of a matroid defined by D
iRocco\, Jabbusch\, and Smith in their work on ”the parliament of polyto
pes” of a vector bundle.\nThen I’ll describe how to extract geometric
information of the projectivization of\nthe toric vector bundle when 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. Then I
’ll describe how these properties interact with natural operations on\nt
oric vector bundles. This involves the geometry of the closely related cla
ss of toric\nflag bundles and tropical flag varieties. This is joint work
with Kiumars Kaveh and\nCourtney George.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Hicks (U. Edinburgh)
DTSTART;VALUE=DATE-TIME:20220923T140000Z
DTEND;VALUE=DATE-TIME:20220923T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/47
DESCRIPTION:Title: Realizability criteria in tropical geometry from symplectic geometry
\nby Jeffrey Hicks (U. Edinburgh) as part of (LAGARTOS) Latin American Rea
l and Tropical Geometry Seminar\n\n\nAbstract\nThe realizability problem a
sks if a given tropical subvariety is the tropicalization of some algebrai
c 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\, Mates
si\, Mikhalkin\, and I show that for many examples of tropcial subvarieti
es in $\\mathbb {R}^n$ there exists a Lagrangian lift. This is a Lagrangia
n submanifold of $(\\mathbb {C}^*)^n$ whose image under the moment map app
roximates a given tropical subvariety. In particular\, every smooth tropic
al curve in $\\mathbb {R}^n$ can be lifted to a Lagrangian submanifold (in
contrast to the algebraic setting!)\n\n \n\nIn this talk\, I'll discuss w
hat it means to be a Lagrangian lift of a tropical curve. We will then loo
k at what symplectic conditions on the resulting Lagrangian detect realiza
bility of the underlying tropical curve. As an application\, we will prove
that every tropical curve in a tropical abelian surface has a rigid-analy
tic realization.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilson Zúñiga-Galindo (U. Texas Rio Grande Valley)
DTSTART;VALUE=DATE-TIME:20221007T140000Z
DTEND;VALUE=DATE-TIME:20221007T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/48
DESCRIPTION:Title: Graphs\, local zeta functions\, log-Coulomb gases\, and phase transition
s at finite temperature\nby Wilson Zúñiga-Galindo (U. Texas Rio Gran
de Valley) as part of (LAGARTOS) Latin American Real and Tropical Geometry
Seminar\n\n\nAbstract\nThe talk aims to present some connections between
local zeta functions and physics. The first part of the talk is dedicated
to reviewing some basic results about local zeta functions. The second par
t aims to present some connections between local zeta functions attached t
o graphs and Coulomb gases. The talk is based on the paper: Zúñiga-Galin
do W. A.\, Zambrano-Luna B. A.\, León-Cardenal E.\, Graphs\, local zeta f
unctions\, log-Coulomb gases\, and phase transitions at finite temperature
\, J. Math. Phys. 63 (2022)\, no. 1\, Paper No. 013506\, 21 pp.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20221118T140000Z
DTEND;VALUE=DATE-TIME:20221118T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/49
DESCRIPTION:Title: The non-Archimedean Monge-Ampère operator\nby Léonard Pille-Schnei
der (École Polytechnique) as part of (LAGARTOS) Latin American Real and T
ropical Geometry Seminar\n\n\nAbstract\nLet $(X\, L)$ be a polarized varie
ty over a non-archimedean field K. In this\ntalk I will explain how to def
ine a notion of semi-positive metric on L on\nthe Berkovich analytificatio
n $X^{\\text{an}}$ of $X$\, and how to define the\nnon-archimedean Monge-A
mpère measure associated to such a metric.\nIf time permits I will explai
n how the non-archimedean Monge-Ampère\noperator can be related to the re
al MA operator on skeleta in some\nexamples.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nicaise (Imperial College/KU Leuven)
DTSTART;VALUE=DATE-TIME:20221202T140000Z
DTEND;VALUE=DATE-TIME:20221202T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/50
DESCRIPTION:Title: Tropical degenerations and irrationality of hypersurfaces in products of
projective spaces\nby Johannes Nicaise (Imperial College/KU Leuven) a
s part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n
\nAbstract\nThe specialization map for stable birational types associates
with every strictly toroidal one-parameter degeneration an obstruction to
the stable rationality of a very general fiber. In many applications\, sui
table 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 description
in terms of regular subdivisions of Newton polytopes. I will illustrate t
his technique for hypersurfaces in products of projective spaces. This is
based on joint work with John Christian Ottem.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard U.)
DTSTART;VALUE=DATE-TIME:20220113T140000Z
DTEND;VALUE=DATE-TIME:20220113T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/51
DESCRIPTION:Title: Circles of Apollonius two ways\nby Stephen McKean (Harvard U.) as pa
rt of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKean (Harvard U.)
DTSTART;VALUE=DATE-TIME:20230113T140000Z
DTEND;VALUE=DATE-TIME:20230113T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/52
DESCRIPTION:Title: Circles of Apollonius two ways\nby Stephen McKean (Harvard U.) as pa
rt of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAb
stract\nThere are eight circles tangent to a given trio of circles\, provi
ded that one works over the complex numbers. Over the reals\, some of thes
e tangent circles can go missing. In order to obtain an invariant count of
tangent circles\, one needs to count each tangent circle with an appropri
ate weight. I will talk about two geometric characterizations of such coun
ting weights\, as well as how to use these counting weights over any field
of characteristic not 2.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Rabinoff (Duke U.)
DTSTART;VALUE=DATE-TIME:20230127T140000Z
DTEND;VALUE=DATE-TIME:20230127T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/53
DESCRIPTION:Title: Weakly smooth forms and Dolbeault cohomology of curves\nby Joe Rabin
off (Duke U.) as part of (LAGARTOS) Latin American Real and Tropical Geome
try Seminar\n\n\nAbstract\nGubler and I work out a theory of weakly smooth
forms on non-Archimedean analytic spaces closely following the constructi
on of Chambert-Loir and Ducros\, but in which harmonic functions are force
d to be smooth. We call such forms "weakly smooth". We compute the Dolbe
ault cohomology groups of rig-smooth\, compact non-Archimedean curves with
respect to this theory\, and show that they have the expected dimensions
and satisfy Poincaré duality. We carry out this computation by giving an
alternative characterization of weakly smooth forms on curves as pullback
s of certain "smooth forms" on a skeleton of the curve. This yields an is
omorphism between the Dolbeault cohomology of the skeleton\, which can be
computed using standard combinatorial methods\, and the Dolbeault cohomolo
gy of the curve.\n\nThis work is joint with Walter Gubler.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Gross (U. Frankfurt)
DTSTART;VALUE=DATE-TIME:20230210T140000Z
DTEND;VALUE=DATE-TIME:20230210T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/54
DESCRIPTION:Title: Vector bundles in tropical geometry\nby Andreas Gross (U. Frankfurt)
as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n
\n\nAbstract\nAlthough tropical vector bundles have been introduced by All
ermann ten years ago\, very little has been said about their structure and
their relation to vector bundles on algebraic varieties. I will present r
ecent work with Martin Ulirsch and Dmitry Zakharov that changes exactly th
is in the case of curves: we prove analogues of the Weil-Riemann-Roch theo
rem 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 isomorphic t
o a certain component of the moduli space of semistable tropical vector bu
ndles on its dual metric graph. Time permitting I will also report on work
in progress with Inder Kaur\, Martin Ulirsch\, and Annette Werner and exp
lain some of the difficulties that arise when generalizing beyond the case
of curves to Abelian varieties of arbitrary dimension.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Fevola (MPI Leipzig)
DTSTART;VALUE=DATE-TIME:20230324T140000Z
DTEND;VALUE=DATE-TIME:20230324T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/55
DESCRIPTION:Title: KP solutions from tropical limits\nby Claudia Fevola (MPI Leipzig) a
s part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n
\nAbstract\nThe study of solutions to the The Kadomtsev-Petviashvili (KP)
equation yields\ninteresting connections between integrable systems and al
gebraic curves. In this\ntalk\, I will discuss solutions to the KP equatio
n whose underlying algebraic curves\nundergo tropical degenerations. In th
ese cases\, Riemann’s theta function becomes\na finite exponential sum s
upported on a Delaunay polytope. I will introduce the\nHirota variety whic
h parametrizes KP solutions arising from such a sum. This talk\nis based o
n joint works with Daniele Agostini\, Yelena Mandelshtam\, and Bernd\nStur
mfels.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Degtyarev (Bilkent U.)
DTSTART;VALUE=DATE-TIME:20230310T140000Z
DTEND;VALUE=DATE-TIME:20230310T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/56
DESCRIPTION:Title: Singular real plane sextic curves without real points\nby Alex Degty
arev (Bilkent U.) as part of (LAGARTOS) Latin American Real and Tropical G
eometry Seminar\n\n\nAbstract\nIt is a common understanding that any reaso
nable geometric question about\nK3-surfaces can be restated and solved in
purely arithmetical terms\, by\nmeans of an appropriately defined homologi
cal type. For example\, this works\nwell in the study of singular complex
sextic curves or quartic surfaces\, as well as in that of smooth real ones
. However\, when\nthe two are combined (singular real curves or surfaces)\
, the approach fails as\nthe obvious concept of homological type does not
fully reflect the geometry.\nWe show that the situation can be repaired if
the curves in question have\nempty real part or\, more generally\, have n
o real singular points\; then\, one can\nindeed confine oneself to the hom
ological types consisting of the exceptional\ndivisors\, polarization\, an
d real structure. Still\, the resulting arithmetical\nproblem is not quite
straightforward\, but we manage to solve it in the case\nof empty real pa
rt.\nThis project was conceived and partially completed during our joint s
tay at\nthe Max-Planck-Institut für Mathematik\, Bonn.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Mereta (MPI-Leipzig)
DTSTART;VALUE=DATE-TIME:20230421T140000Z
DTEND;VALUE=DATE-TIME:20230421T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/57
DESCRIPTION:Title: The Fundamental theorem of tropical differential algebra over nontrivial
ly valued fields\nby Stefano Mereta (MPI-Leipzig) as part of (LAGARTOS
) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nWe will
discuss a fundamental theorem for tropical differential equations analogu
e of the fundamental theorem of tropical geometry in this context. We exte
nd results from Aroca et al. and from Fink and Toghani\, working only in t
he case of trivial valuation as introduced by Grigoriev\, to differential
equations with power series coefficients over any valued field. To do so\,
a crucial ingredient is the framework for tropical differential equations
introduced by Giansiracusa and Mereta. As a corollary of the fundamental
theorem\, the radius of convergence of solutions of a differential equatio
n over a nontrivially valued field can be computed tropically.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Eggleston (U. Osnabrück)
DTSTART;VALUE=DATE-TIME:20230505T140000Z
DTEND;VALUE=DATE-TIME:20230505T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/58
DESCRIPTION:Title: The amoeba dimension of a linear space\nby Sarah Eggleston (U. Osnab
rück) as part of (LAGARTOS) Latin American Real and Tropical Geometry Sem
inar\n\n\nAbstract\nGiven a complex vector subspace $V$ of $\\mathbb{C}^n$
\, the dimension of the amoeba of $V \\cap (\\mathbb{C}^∗)^n$ depends on
ly on the matroid of $V$. Here we prove that this dimension is given by th
e minimum of a certain function over all partitions $P_1\,\\dots\,P_k$ of
the ground set into nonempty parts $P_i$\, as previously conjectured by Jo
hannes Rau. We also prove that this formula can be evaluated in polynomial
time. This is joint work with Jan Draisma\, Rudi Pendavingh\, Johannes Ra
u\, and Chi Ho Yuen.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Vargas (U. Frankfurt)
DTSTART;VALUE=DATE-TIME:20230519T140000Z
DTEND;VALUE=DATE-TIME:20230519T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/59
DESCRIPTION:Title: Valuated matroids\, tropicalized linear spaces and the affine building o
f PGL_{r+1}(K)\nby Alejandro Vargas (U. Frankfurt) as part of (LAGARTO
S) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nValuat
ed matroids were introduced by Dress and Wenzel in the 90s to\ncombinatori
ally 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 introduced by
Bruhat and Tits in the 70s as highly\nsymmetric simplicial complexes to ex
tract the combinatorics of algebraic\ngroups.\nThe affine building associa
ted to the projective linear group\n$PGL_{r+1}(K)$ admits a description vi
a norms\, and by work of Werner a\ncompactification via semi-norms.\nInspi
red by Payne's result that the Berkovich analytification is the\nlimit 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$\\iota : \
\mathbb{P}^r\\hookrightarrow\\mathbb{P}^n$ and prove a faithful\ntropical
ization result for compactified linear spaces.\nThus\, under a suitable hy
pothesis on the non-Archimedean field $K$\, the\npunchline is that the ran
k-$(r+1)$ $K$-realizable valuated matroids\napproximate the compactificati
on of the affine building of\n$PGL_{r+1}(K)$ in a precise manner\, and thi
s can be regarded as the\ntropical linear space associated to a universal
$K$-realizable valuated\nmatroid.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristhian Garay López (CIMAT (Guanajuato))
DTSTART;VALUE=DATE-TIME:20230602T140000Z
DTEND;VALUE=DATE-TIME:20230602T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T144444Z
UID:LAGARTOS/60
DESCRIPTION:Title: Infinite matroids in tropical differential algebra\nby Cristhian Gar
ay López (CIMAT (Guanajuato)) as part of (LAGARTOS) Latin American Real a
nd Tropical Geometry Seminar\n\n\nAbstract\nGiven a set $\\Sigma\\subset
K[x_1\,\\ldots\,x_n]$ of homogeneous linear polynomials\, a classical res
ult in tropical algebraic geometry states that the tropicalization (with r
espect 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 $E=[n]$ ass
ociated to the ideal $(\\Sigma)$. Moreover\, this set is tropically convex
in the sense that it is closed under tropical linear combinations. \
n\n\nWe discuss an analogue of this result in the context of tropical diff
erential algebraic geometry\, namely\, if $\\Sigma\\subset K[\\![t_1\,\\l
dots\,t_m]\\!][x_{1\,J}\,\\ldots\,x_{n\,J}\\::\\:J\\in\\mathbb{N}^m]$ is c
ertain type of set of homogeneous linear differential polynomials with coe
fficients in $K[\\![t_1\,\\ldots\,t_m]\\!]$\, then the tropicalization (wi
th respect to the trivial valuation) of the set of formal solutions $Sol(\
\Sigma)\\subset K[\\![t_1\,\\ldots\,t_m]\\!]^n$ is a matroid $B(Sol(\\S
igma))$ over the set of labels $E=\\mathbb{N}^{mn}$\, where $m\,n$ are po
sitive integers. Moreover\, this set is tropically convex in the sense tha
t it is closed under boolean linear combinations\, i.e.\, it is a com
mutative and idempotent monoid.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/60/
END:VEVENT
END:VCALENDAR