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BEGIN:VEVENT
SUMMARY:Marta Panizzut (Universität Osnabrück)
DTSTART;VALUE=DATE-TIME:20200424T120000Z
DTEND;VALUE=DATE-TIME:20200424T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/1
DESCRIPTION:Title: Tro
pical cubic surfaces and their lines\nby Marta Panizzut (Universität
Osnabrück) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (Universität Bern)
DTSTART;VALUE=DATE-TIME:20200424T131500Z
DTEND;VALUE=DATE-TIME:20200424T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/2
DESCRIPTION:Title: Cat
alan-many morphisms to trees-Part I\nby Jan Draisma (Universität Bern
) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Vargas (Universität Bern)
DTSTART;VALUE=DATE-TIME:20200424T143000Z
DTEND;VALUE=DATE-TIME:20200424T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/3
DESCRIPTION:Title: Cat
alan-many morphisms to trees-Part II\nby Alejandro Vargas (Universitä
t Bern) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Smith (University of Manchester)
DTSTART;VALUE=DATE-TIME:20200529T120000Z
DTEND;VALUE=DATE-TIME:20200529T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/4
DESCRIPTION:Title: Fac
es of tropical polyhedra - cancelled\nby Ben Smith (University of Manc
hester) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yue Ren (Swansea University)
DTSTART;VALUE=DATE-TIME:20200529T131500Z
DTEND;VALUE=DATE-TIME:20200529T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/5
DESCRIPTION:Title: Tro
pical varieties of neural networks\nby Yue Ren (Swansea University) as
part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (University of Tuebingen)
DTSTART;VALUE=DATE-TIME:20200529T143000Z
DTEND;VALUE=DATE-TIME:20200529T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/6
DESCRIPTION:Title: The
combinatorics and real lifting of tropical bitangents to plane quartics
a>\nby Hannah Markwig (University of Tuebingen) as part of Tropical Geomet
ry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200626T120000Z
DTEND;VALUE=DATE-TIME:20200626T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/7
DESCRIPTION:Title: Glu
ing log Gromov-Witten invariants\nby Mark Gross (University of Cambrid
ge) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nI
will give a progress report on joint work with Abramovich\, Chen and Sieb
ert aiming to understand gluing formulae for log Gromov-Witten invariants\
, generalizing the Li/Ruan and Jun Li gluing formulas for relative Gromov-
Witten invariants.\n
LOCATION:https://researchseminars.org/talk/TGiZ/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Battistella (University of Heidelberg)
DTSTART;VALUE=DATE-TIME:20200626T131500Z
DTEND;VALUE=DATE-TIME:20200626T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/8
DESCRIPTION:Title: A s
mooth compactification of genus two curves in projective space\nby Luc
a Battistella (University of Heidelberg) as part of Tropical Geometry in F
rankfurt/Zoom TGiF/Z\n\n\nAbstract\nQuestions of enumerative geometry can
often be translated into problems of intersection theory on a compact modu
li space of curves in projective space. Kontsevich's stable maps work extr
aordinarily well when the curves are rational\, but in higher genus the bu
rden of degenerate contributions is heavily felt\, as the moduli space acq
uires several boundary components. The closure of the locus of maps with s
mooth source curve is interesting but troublesome\, for its functor of poi
nts interpretation is most often unclear\; on the other hand\, after the w
ork of Li--Vakil--Zinger and Ranganathan--Santos-Parker--Wise in genus one
\, points in the boundary correspond to maps that admit a nice factorisati
on through some curve with Gorenstein singularities (morally\, contracting
any higher genus subcurve on which the map is constant). The question bec
omes how to construct such a universal family of Gorenstein curves. In joi
nt work with F. Carocci\, we construct one such family in genus two over a
logarithmic modification of the space of admissible covers. I will focus
on how tropical geometry determines this logarithmic modification via trop
ical canonical divisors.\n
LOCATION:https://researchseminars.org/talk/TGiZ/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Yale University)
DTSTART;VALUE=DATE-TIME:20200626T143000Z
DTEND;VALUE=DATE-TIME:20200626T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/9
DESCRIPTION:Title: Pri
me tropical ideals\nby Kalina Mincheva (Yale University) as part of Tr
opical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nIn the recent year
s\, there has been a lot of effort dedicated to developing the necessary t
ools for commutative algebra using different frameworks\, among which prim
e congruences\, tropical ideals\, tropical schemes. These approaches allow
s for the exploration of the properties of tropicalized spaces without ty
ing them up to the original varieties and working with geometric structure
s inherently defined in characteristic one (that is\, additively idempoten
t) semifields. In this talk we explore the relationship between tropical i
deals and congruences to conclude that the variety of a non-zero prime (tr
opical) ideal is either empty or consists of a single point.\n
LOCATION:https://researchseminars.org/talk/TGiZ/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fang (Universität Köln)
DTSTART;VALUE=DATE-TIME:20201204T130000Z
DTEND;VALUE=DATE-TIME:20201204T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/10
DESCRIPTION:Title: Tr
opical flag varieties - a Lie theoretic approach\nby Xin Fang (Univers
ität Köln) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAb
stract\nIn this talk I will explain how to use Lie theory to describe the
facets of a maximal prime cone in a type A tropical complete flag variety.
The face lattice of this cone encodes degeneration structures in Lie alge
bra\, quiver Grassmannians and module categories of quivers. This talk bas
es on different joint works with (subsets of) G. Cerulli-Irelli\, E. Feigi
n\, G. Fourier\, M. Gorsky\, P. Littelmann\, I. Makhlin and M. Reineke\, a
s well as some work in progress.\n
LOCATION:https://researchseminars.org/talk/TGiZ/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai Cheung (Harvard University)
DTSTART;VALUE=DATE-TIME:20201204T141500Z
DTEND;VALUE=DATE-TIME:20201204T151500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/11
DESCRIPTION:Title: Po
lytopes\, wall crossings\, and cluster varieties\nby Man-Wai Cheung (H
arvard University) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n
\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are a u
nion of algebraic tori glued by birational "mutation" maps. Partial comp
actifications of the varieties\, studied by Gross\, Hacking\, Keel\, and K
ontsevich\, generalize the polytope construction of toric varieties. Howev
er\, it is not clear from the definitions how to characterize the polytope
s giving compactifications of cluster varieties. We will show how to descr
ibe the compactifications easily by broken line convexity. As an applicati
on\, we will see the non-integral vertex in the Newton Okounkov body of Gr
(3\,6) comes from broken line convexity. Further\, we will also see certai
n positive polytopes will give us hints about the Batyrev mirror in the cl
uster setting. The mutations of the polytopes will be related to the almos
t toric fibration from the symplectic point of view. Finally\, we can see
how to extend the idea of gluing of tori in Floer theory which then ended
up with the Family Floer Mirror for the del Pezzo surfaces of degree 5 and
6. The talk will be based on a series of joint works with Bossinger\, Lin
\, Magee\, Najera-Chavez\, and Vianna.\n
LOCATION:https://researchseminars.org/talk/TGiZ/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca)
DTSTART;VALUE=DATE-TIME:20201204T153000Z
DTEND;VALUE=DATE-TIME:20201204T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/12
DESCRIPTION:Title: Tr
opical geometry of Grassmannians and their cluster structure\nby Lara
Bossinger (UNAM Oaxaca) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nThe Grassmannain\, or more precisely its homogeneous co
ordinate ring with respect to the Plücker embedding\, was found to be a c
luster algebra by Scott in the early years of cluster theory. Since then\,
this cluster structure was studied from many different perspectives by a
number of mathematicians. As the whole subject of cluster algebras broadly
speaking divides into two main perspectives\, algebraic and geometric\, s
o do the results regarding Grassmannian. Geometrically\, the Grassmannian
contains two open subschemes that are dual cluster varieties.\n\nInteresti
ngly\, we can find tropical geometry in both directions: from the algebrai
c point of view\, we discover relations between maximal cones in the tropi
calization of the defining ideal (what Speyer and Sturmfels call the tropi
cal Grassmannian) and seeds of the cluster algebra. From the geometric poi
nt of view\, due to work of Fock--Goncharov followed by work of Gross--Hac
king--Keel--Kontsevich we know that the scheme theoretic tropical points o
f the cluster varieties parametrize functions on the Grassmannian.\n\nIn t
his talk I aim to explain the interaction of tropical geometry with the cl
uster structure for the Grassmannian from the algebraic and the geometric
point of view.\n
LOCATION:https://researchseminars.org/talk/TGiZ/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alheydis Geiger (Universität Tübingen)
DTSTART;VALUE=DATE-TIME:20210122T130000Z
DTEND;VALUE=DATE-TIME:20210122T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/13
DESCRIPTION:Title: De
formations of bitangent classes of tropical quartic curves\nby Alheydi
s Geiger (Universität Tübingen) as part of Tropical Geometry in Frankfur
t/Zoom TGiF/Z\n\n\nAbstract\nOver an algebraically closed field a smooth q
uartic curve has 28 bitangent lines. Plücker proved that over the real nu
mbers we have either 4\, 8\, 16 or 28 real bitangents to a real quartic cu
rve. A tropical smooth quartic curve has exactly 7 bitangent classes which
each lift either 0 or 4 times over the real numbers. The shapes of these
bitangent classes have been classified by Markwig and Cueto in 2020\, who
also determined their real lifting conditions.\nHowever\, for a fixed unim
odular triangulation different choices of coefficients imply different edg
e lengths of the quartic and these can change the shape of the 7 bitangent
classes and might therefore influence their real lifting conditions.\nIn
order to prove Plückers Theorem about the number of real bitangents tropi
cally\, we have to study these deformations of the bitangent shapes. In a
joint work with Marta Panizzut we develope a polymake extension\, which co
mputes the tropical bitangents. For this we determine two refinements of t
he secondary fan: one for which the bitangent shapes in each cone stay con
stant and one for which the lifting conditions in each cone stay constant.
\nThis is still work in progress\, but there will be a small software demo
nstration.\n
LOCATION:https://researchseminars.org/talk/TGiZ/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210122T141500Z
DTEND;VALUE=DATE-TIME:20210122T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/14
DESCRIPTION:Title: Pa
stures\, Polynomials\, and Matroids\nby Matt Baker (Georgia Institute
of Technology) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\n
Abstract\nA pasture is\, roughly speaking\, a field in which addition is a
llowed to be both multivalued and partially undefined. Pastures are natura
l objects from the point of view of F_1 geometry and Lorscheid’s theory
of ordered blueprints. I will describe a theorem about univariate polynomi
als over pastures which simultaneously generalizes Descartes’ Rule of Si
gns and the theory of NewtonPolygons. Conjecturally\, there should be a si
milar picture for several polynomials in several variables generalizing tr
opical intersection theory. I will also describe a novel approach to the t
heory of matroid representations which revolves around a canonical univers
al pasture called the “foundation” that one can attach to any matroid.
This is joint work with Oliver Lorscheid.\n
LOCATION:https://researchseminars.org/talk/TGiZ/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (University of Georgia)
DTSTART;VALUE=DATE-TIME:20210122T153000Z
DTEND;VALUE=DATE-TIME:20210122T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/15
DESCRIPTION:Title: Th
e tropical section conjecture\nby Daniel Litt (University of Georgia)
as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nGroth
endieck's section conjecture predicts that for a curve X of genus at least
2 over an arithmetically interesting field (say\, a number field or p-adi
c field)\, the étale fundamental group of X encodes all the information a
bout rational points on X. In this talk I will formulate a tropical analog
ue of the section conjecture and explain how to use methods from low-dimen
sional topology and moduli theory to prove many cases of it. As a byproduc
t\, I'll construct many examples of curves for which the section conjectur
e is true\, in interesting ways. For example\, I will explain how to prove
the section conjecture for the generic curve\, and for the generic curve
with a rational divisor class\, as well as how to construct curves over p-
adic fields which satisfy the section conjecture for geometric reasons. Th
is is joint work with Wanlin Li\, Nick Salter\, and Padma Srinivasan.\n
LOCATION:https://researchseminars.org/talk/TGiZ/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (University of Oslo)
DTSTART;VALUE=DATE-TIME:20210219T130000Z
DTEND;VALUE=DATE-TIME:20210219T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/16
DESCRIPTION:Title: Tr
opical degenerations and stable rationality\nby John Christian Ottem (
University of Oslo) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\
n\n\nAbstract\nI will explain how tropical degenerations and birational sp
ecialization techniques can be used in rationality problems. In particular
\, I will apply these techniques to study quartic fivefolds and complete i
ntersections of a quadric and a cubic in P^6. This is joint work with Joha
nnes Nicaise.\n
LOCATION:https://researchseminars.org/talk/TGiZ/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Pacini (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20210219T141500Z
DTEND;VALUE=DATE-TIME:20210219T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/17
DESCRIPTION:Title: A
universal tropical Jacobian over the moduli space of tropical curves\n
by Marco Pacini (Universidade Federal Fluminense) as part of Tropical Geom
etry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe introduce polystable divis
ors on a tropical curve\, which are the tropical analogue of polystable to
rsion-free rank-1 sheaves on a nodal curve. We show how to construct a uni
versal tropical Jacobian by means of polystable divisors on tropical curve
s. This space can be seen as a tropical counterpart of Caporaso universal
Picard scheme. This is a joint work with Abreu\, Andria\, and Taboada.\n
LOCATION:https://researchseminars.org/talk/TGiZ/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART;VALUE=DATE-TIME:20210219T153000Z
DTEND;VALUE=DATE-TIME:20210219T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/18
DESCRIPTION:Title: Wa
ll-crossing and Newton-Okounkov bodies\nby Laura Escobar (Washington U
niversity in St. Louis) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nA Newton-Okounkov body is a convex set associated to a
projective variety\, equipped with a valuation. These bodies generalize th
e theory of Newton polytopes. Work of Kaveh-Manon gives an explicit link b
etween tropical geometry and Newton-Okounkov bodies. In joint work with Me
gumi Harada we use this link to describe a wall-crossing phenomenon for Ne
wton-Okounkov bodies.\n
LOCATION:https://researchseminars.org/talk/TGiZ/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthea Monod (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210312T130000Z
DTEND;VALUE=DATE-TIME:20210312T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/19
DESCRIPTION:Title: Tr
opical geometry of phylogenetic tree spaces\nby Anthea Monod (Imperial
College London) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n
\nAbstract\nThe Billera-Holmes-Vogtmann (BHV) space is a well-studied modu
li space of phylogenetic trees that appears in many scientific disciplines
\, including computational biology\, computer vision\, combinatorics\, and
category theory. Speyer and Sturmfels identify a homeomorphism between BH
V space and a version of the Grassmannian using tropical geometry\, endowi
ng the space of phylogenetic trees with a tropical structure\, which turns
out to be advantageous for computational studies. In this talk\, I will p
resent the coincidence between BHV space and the tropical Grassmannian. I
will then give an overview of some recent work I have done that studies th
e tropical Grassmannian as a metric space and the practical implications o
f these results on probabilistic and statistical studies on real datasets
of phylogenetic trees.\n
LOCATION:https://researchseminars.org/talk/TGiZ/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia He Yun (Brown University)
DTSTART;VALUE=DATE-TIME:20210312T141500Z
DTEND;VALUE=DATE-TIME:20210312T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/20
DESCRIPTION:Title: Th
e $S_n$-equivariant rational homology of the tropical moduli spaces $\\Del
ta_{2\,n}$\nby Claudia He Yun (Brown University) as part of Tropical G
eometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe tropical moduli space
$\\Delta_{g\,n}$ is a topological space that parametrizes isomorphism clas
ses 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 $n$ u
p to 8. We use the fact that $\\Delta_{2\,n}$ is a symmetric $\\Delta$-com
plex\, a concept introduced by Chan\, Glatius\, and Payne. The computation
is done in SageMath.\n
LOCATION:https://researchseminars.org/talk/TGiZ/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Corey (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20210312T153000Z
DTEND;VALUE=DATE-TIME:20210312T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/21
DESCRIPTION:Title: Th
e Ceresa class: tropical\, topological\, and algebraic\nby Daniel Core
y (University of Wisconsin-Madison) as part of Tropical Geometry in Frankf
urt/Zoom TGiF/Z\n\n\nAbstract\nThe Ceresa cycle is an algebraic cycle atta
ched to a smooth algebraic curve. It is homologically trivial but not alge
braically equivalent to zero for a very general curve. In this sense\, it
is one of the simplest algebraic cycles that goes ``beyond homology.'' The
image of the Ceresa cycle under a certain cycle class map produces a clas
s in étale homology called the Ceresa class. We define the Ceresa class f
or a tropical curve and for a product of commuting Dehn twists on a topolo
gical surface. We relate these to the Ceresa class of a smooth algebraic c
urve over C((t)). Our main result is that the Ceresa class in each of thes
e settings is torsion. Nevertheless\, this class is readily computable\, f
requently nonzero\, and implies nontriviality of the Ceresa cycle when non
zero. This is joint work with Jordan Ellenberg and Wanlin Li.\n
LOCATION:https://researchseminars.org/talk/TGiZ/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Usatine (Brown University)
DTSTART;VALUE=DATE-TIME:20210430T131500Z
DTEND;VALUE=DATE-TIME:20210430T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/22
DESCRIPTION:Title: St
ringy invariants and toric Artin stacks\nby Jeremy Usatine (Brown Univ
ersity) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstrac
t\nStringy Hodge numbers are certain generalizations\, to the singular set
ting\, of Hodge numbers. Unlike usual Hodge numbers\, stringy Hodge number
s are not defined as dimensions of cohomology groups. Nonetheless\, an ope
n conjecture of Batyrev's predicts that stringy Hodge numbers are nonnegat
ive. In the special case of varieties with only quotient singularities\, Y
asuda proved Batyrev's conjecture by showing that the stringy Hodge number
s are given by orbifold cohomology. For more general singularities\, a sim
ilar cohomological interpretation remains elusive. I will discuss a conjec
tural framework\, proven in the toric case\, that relates stringy Hodge nu
mbers to motivic integration for Artin stacks\, and I will explain how thi
s framework applies to the search for a cohomological interpretation for s
tringy Hodge numbers. This talk is based on joint work with Matthew Satria
no.\n
LOCATION:https://researchseminars.org/talk/TGiZ/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART;VALUE=DATE-TIME:20210430T143000Z
DTEND;VALUE=DATE-TIME:20210430T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/23
DESCRIPTION:Title: To
pology of tropical moduli spaces of weighted stable curves in higher genus
\nby Shiyue Li (Brown University) as part of Tropical Geometry in Fran
kfurt/Zoom TGiF/Z\n\n\nAbstract\nThe space of tropical weighted curves of
genus g and volume 1 is the dual complex of the divisor of singular curves
in Hassett’s moduli space of weighted stable genus g curves. One can de
rive plenty of topological properties of the Hassett spaces by studying th
e topology of these dual complexes. In this talk\, we show that the spaces
of tropical weighted curves of genus g and volume 1 are simply-connected
for all genus greater than zero and all rational weights\, under the frame
work of symmetric Delta-complexes and via a result by Allcock-Corey-Payne
19. We also calculate the Euler characteristics of these spaces and the to
p weight Euler characteristics of the classical Hassett spaces in terms of
the combinatorics of the weights. I will also discuss some work in progre
ss on a geometric group approach to simple connectivity of these spaces. T
his is joint work with Siddarth Kannan\, Stefano Serpente\, and Claudia Yu
n.\n
LOCATION:https://researchseminars.org/talk/TGiZ/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Rincon (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20210430T120000Z
DTEND;VALUE=DATE-TIME:20210430T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/24
DESCRIPTION:Title: Tr
opical Ideals\nby Felipe Rincon (Queen Mary University of London) as p
art of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nTropical
ideals are ideals in the tropical polynomial semiring in which any bounded
-degree piece is “matroidal”. They were conceived as a sensible class
of objects for developing algebraic foundations in tropical geometry. In t
his talk I will introduce and motivate the notion of tropical ideals\, and
I will discuss work studying some of their main properties and their poss
ible associated varieties.\n
LOCATION:https://researchseminars.org/talk/TGiZ/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (University of Coimbra and University of Roma Tre)
DTSTART;VALUE=DATE-TIME:20210528T120000Z
DTEND;VALUE=DATE-TIME:20210528T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/25
DESCRIPTION:Title: On
the top weight cohomology of the moduli space of abelian varieties\nb
y Margarida Melo (University of Coimbra and University of Roma Tre) as par
t of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe moduli
space of abelian varieties Ag admits well behaved toroidal compactificatio
ns whose dual complex can be given a tropical interpretation. Therefore\,
one can use the techniques recently developed by Chan-Galatius-Payne in or
der to understand part of the topology of Ag via tropical geometry. In thi
s talk\, which is based in joint work with Madeleine Brandt\, Juliette Bru
ce\, Melody Chan\, Gwyneth Moreland and Corey Wolfe\, I will explain how t
o use this setup\, and in particular computations in the perfect cone comp
actification of Ag\, in order to describe its top weight cohomology for g
up to 7.\n
LOCATION:https://researchseminars.org/talk/TGiZ/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenia Tevelev (University of Massachusetts Amherst)
DTSTART;VALUE=DATE-TIME:20210528T143000Z
DTEND;VALUE=DATE-TIME:20210528T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/26
DESCRIPTION:Title: Co
mpactifications of moduli of points and lines in the (tropical) plane\
nby Jenia Tevelev (University of Massachusetts Amherst) as part of Tropica
l Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nProjective duality iden
tifies moduli spaces of points and lines in the projective plane. The latt
er space admits Kapranov's Chow quotient compactification\, studied also b
y Lafforgue\, Hacking-Keel-Tevelev\, and Alexeev\, which gives an example
of a KSBA moduli space of stable surfaces: it carries a family of reducibl
e degenerations of the projective plane with "broken lines". From the trop
ical perspective\, these degenerations are encoded in matroid decompositio
ns and tropical planes and their moduli space in the Dressian and the trop
ical Grasmannian. In 1991\, Gerritzen and Piwek proposed a dual perspectiv
e\, a compact moduli space parametrizing reducible degenerations of the pr
ojective plane with n smooth points. In a joint paper with Luca Schaffler\
, we investigate the extension of projective duality to degenerations\, an
swering a question of Kapranov.\n
LOCATION:https://researchseminars.org/talk/TGiZ/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baldur Sigurðsson (Vietnam Academy of Sciences and Technology)
DTSTART;VALUE=DATE-TIME:20210528T131500Z
DTEND;VALUE=DATE-TIME:20210528T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/27
DESCRIPTION:Title: Lo
cal tropical Cartier divisors and the multiplicity\nby Baldur Sigurðs
son (Vietnam Academy of Sciences and Technology) as part of Tropical Geome
try in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe consider the group of local
tropical cycles in the local\ntropicalization of the local analytic ring
of a toric variety\, in\nparticular\, Cartier divisors defined by a functi
on germ. We see a\nformula for the multiplicity\, a result which is motiva
ted by a classical\ntheorem of Wagreich for normal surface singularities.\
n
LOCATION:https://researchseminars.org/talk/TGiZ/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hülya Argüz (Université de Versailles)
DTSTART;VALUE=DATE-TIME:20210625T120000Z
DTEND;VALUE=DATE-TIME:20210625T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/28
DESCRIPTION:Title: Tr
opical enumeration of real log curves in toric varieties and log Welsching
er invariants\nby Hülya Argüz (Université de Versailles) as part of
Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWe give a new p
roof of a central theorem in real enumerative geometry: the Mikhalkin corr
espondence theorem for Welschinger invariants. The proof goes through tota
lly different techniques as the original proof of Mikhalkin and is an adap
tation to the real setting of the approach of Nishinou-Siebert to the comp
lex correspondence theorem. It uses log-geometry as a central tool. We wil
l discuss how this reinterpretation in terms of log-geometry may lead to n
ew developments\, as for example a real version of mirror symmetry. This i
s joint work with Pierrick Bousseau.\n
LOCATION:https://researchseminars.org/talk/TGiZ/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Mereta (Swansea University)
DTSTART;VALUE=DATE-TIME:20210625T131500Z
DTEND;VALUE=DATE-TIME:20210625T141500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/29
DESCRIPTION:Title: Tr
opical differential equations\nby Stefano Mereta (Swansea University)
as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nIn 20
15 Dimitri Grigoriev introduced a way to tropicalize differential equation
with coefficients in a power series ring and defined what a solution for
such a tropicalized equation should be. In 2016 Aroca\, Garay and Toghani
proved a fundamental theorem analogue to the fundamental theorem of tropic
al geometry for power series over a trivially valued field. In this talk I
will introduce the basic ideas moving then towards a functor of points ap
proach to the subject by means of the recently developed tropical scheme t
heory\, as introduced by Giansiracusa and Giansiracusa\, looking at soluti
ons to such equations as morphisms between so-called pairs. I will also gi
ve a generalisation to power series ring with non-trivially valued coeffic
ients and state a colimit theorem along the lines of Payne's inverse limit
theorem.\n
LOCATION:https://researchseminars.org/talk/TGiZ/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Katz (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210625T143000Z
DTEND;VALUE=DATE-TIME:20210625T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/30
DESCRIPTION:Title: Co
mbinatorial and p-adic iterated integrals\nby Eric Katz (Ohio State Un
iversity) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstr
act\nThe classical operations of algebraic geometry often have combinatori
al analogues. We will discuss the combinatorial analogue of Chen’s itera
ted integrals. These have a richer\, non-abelian structure than classical
integrals. We will describe the tropical analogue of the unipotent Torelli
theorem of Hain and Pulte and make connections between iterated integrals
and monodromy with applications to p-adic integration.\n
LOCATION:https://researchseminars.org/talk/TGiZ/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mima Stanojkovski (RWTH Aachen University)
DTSTART;VALUE=DATE-TIME:20220121T130000Z
DTEND;VALUE=DATE-TIME:20220121T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/31
DESCRIPTION:Title: Or
ders and polytropes: matrices from valuations\nby Mima Stanojkovski (R
WTH Aachen University) as part of Tropical Geometry in Frankfurt/Zoom TGiF
/Z\n\n\nAbstract\nLet K be a discretely valued field with ring of integers
R. To a d-by-d matrix M with integral coefficients one can associate an R
-module\, in K^{d x d}\, and a polytope\, in the Euclidean space of dimens
ion d-1. We will look at the interplay between these two objects\, from th
e point of view of tropical geometry and building on work of Plesken and Z
assenhaus. This is joint work with Y. El Maazouz\, M. A. Hahn\, G. Nebe\,
and B. Sturmfels.\n
LOCATION:https://researchseminars.org/talk/TGiZ/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben Gurioin University)
DTSTART;VALUE=DATE-TIME:20220121T141500Z
DTEND;VALUE=DATE-TIME:20220121T151500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/32
DESCRIPTION:Title: Ap
plications of tropical geometry to irreducibility problems in algebraic ge
ometry\nby Ilya Tyomkin (Ben Gurioin University) as part of Tropical G
eometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nIn my talk\, I will discus
s a novel tropical approach to classical irreducibility problems of Severi
varieties and of Hurwitz schemes. I will explain how to prove such irredu
cibility results by investigating the properties of tropicalizations of on
e-parameter families of curves and of the induced maps to the tropical mod
uli space of parametrized tropical curves. The talk is based on a series o
f joint works with Karl Christ and Xiang He.\n
LOCATION:https://researchseminars.org/talk/TGiZ/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harry Richman (University of Washington)
DTSTART;VALUE=DATE-TIME:20220121T153000Z
DTEND;VALUE=DATE-TIME:20220121T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/33
DESCRIPTION:Title: Un
iform bounds for torsion packets on tropical curves\nby Harry Richman
(University of Washington) as part of Tropical Geometry in Frankfurt/Zoom
TGiF/Z\n\n\nAbstract\nSay two points x\, y on an algebraic curve are in th
e same torsion packet if [x - y] is a torsion element of the Jacobian. In
genus 0 and 1\, torsion packets have infinitely many points. In higher gen
us\, a theorem of Raynaud states that all torsion packets are finite. It w
as long conjectured\, and only recently proven*\, that the size of a torsi
on packet is bounded uniformly in terms of the genus of the underlying cur
ve. We study the tropical analogue of this construction for a metric graph
. On a higher genus metric graph\, torsion packets are not always finite\,
but they are finite under an additional "genericity" assumption on the ed
ge lengths. Under this genericity assumption\, the torsion packets satisfy
a uniform bound in terms of the genus of the underlying graph. (*by Kuehn
e and Looper-Silverman-Wilmes in 2021)\n
LOCATION:https://researchseminars.org/talk/TGiZ/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Rau (Universidad de los Andes)
DTSTART;VALUE=DATE-TIME:20220218T130000Z
DTEND;VALUE=DATE-TIME:20220218T135000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/34
DESCRIPTION:Title: Pa
tchworks of real algebraic varieties in higher codimension\nby Johanne
s Rau (Universidad de los Andes) as part of Tropical Geometry in Frankfurt
/Zoom TGiF/Z\n\n\nAbstract\nI will present a combinatorial setup\, based o
n smooth tropical varieties and real phase structures\, which after "unfol
ding" produces a certain class of PL-manifolds (called patchworks). We hav
e two motivations in mind: Firstly\, in the spirit of Viro's combinatoria
l patchwoking for hypersurfaces\, these patchworks can be used to describe
the topology of real algebraic varieties close to the tropical limit. Sec
ondly\, even if not "realisable" by real algebraic varieties\, real phase
structures provide a geometric framework for combinatorial structures such
as oriented matroids. Joint work with Arthur Renaudineau and Kris Shaw.\n
LOCATION:https://researchseminars.org/talk/TGiZ/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Kannan (Brown University)
DTSTART;VALUE=DATE-TIME:20220218T141500Z
DTEND;VALUE=DATE-TIME:20220218T151500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/35
DESCRIPTION:Title: Cu
t-and-paste invariants of moduli spaces of relative stable maps to $\\math
bb{P}^1$\nby Siddharth Kannan (Brown University) as part of Tropical G
eometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nI will discuss ongoing wor
k studying moduli spaces of genus zero stable maps to $\\mathbb{P}^1$\, wi
th fixed ramification profiles over $0$ and infinity. I will describe a ch
amber decomposition of the space of ramification data such that the Grothe
ndieck class of the moduli space is constant on the chambers. Finally\, fo
r the sequence of ramification data corresponding to maximal ramification
over $0$ and no ramification over infinity\, I will describe a recursive a
lgorithm to compute the generating function for Euler characteristics of t
hese spaces.\n
LOCATION:https://researchseminars.org/talk/TGiZ/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rohini Ramadas (University of Warwick)
DTSTART;VALUE=DATE-TIME:20220218T153000Z
DTEND;VALUE=DATE-TIME:20220218T163000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/36
DESCRIPTION:Title: Th
e $S_n$ action on the homology groups of $\\overline{M}_{0\,n}$\nby Ro
hini Ramadas (University of Warwick) as part of Tropical Geometry in Frank
furt/Zoom TGiF/Z\n\n\nAbstract\nThe symmetric group on $n$ letters acts on
$\\overline{M}_{0\,n}$\, and thus on its (co-)homology groups. The induce
d actions on (co-)homology have been studied by\, eg.\, Getzler\, Bergstro
m-Minabe\, Castravet-Tevelev. We ask: does $H_{2k}(\\overline{M}_{0\,n})$
admit an equivariant basis\, i.e. one that is permuted by $S_n$? We descri
be progress towards answering this question. This talk includes joint work
with Rob Silversmith.\n
LOCATION:https://researchseminars.org/talk/TGiZ/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana María Botero (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20220513T130000Z
DTEND;VALUE=DATE-TIME:20220513T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/37
DESCRIPTION:Title: To
roidal b-divisors and Monge-Ampère measures\nby Ana María Botero (Un
iversity of Regensburg) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Ignacio Burgos Gil (Instituto de Ciencias Matemáticas)
DTSTART;VALUE=DATE-TIME:20220520T143000Z
DTEND;VALUE=DATE-TIME:20220520T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/38
DESCRIPTION:Title: Ch
ern-Weil theory and Hilbert-Samuel theorem for semi-positive singular toro
idal metrics on line bundles\nby José Ignacio Burgos Gil (Instituto d
e Ciencias Matemáticas) as part of Tropical Geometry in Frankfurt/Zoom TG
iF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jensen (University of Kentucky)
DTSTART;VALUE=DATE-TIME:20220610T130000Z
DTEND;VALUE=DATE-TIME:20220610T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/39
DESCRIPTION:Title: Br
ill-Noether Theory over the Hurwitz Space\nby David Jensen (University
of Kentucky) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nA
bstract\nBrill-Noether theory is the study of line bundles on algebraic cu
rves. A series of results in the 80's describe the varieties parameterizin
g line bundles with given invariants on a sufficiently general curve. Mor
e recently\, several mathematicians have turned their attention to the Bri
ll-Noether theory of general covers -- that is\, curves that are general i
n the Hurwitz space rather than in the moduli space of curves. We will su
rvey these recent results and\, time permitting\, some generalizations.\n
LOCATION:https://researchseminars.org/talk/TGiZ/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaelin Cook-Powell (Emory University)
DTSTART;VALUE=DATE-TIME:20220610T141500Z
DTEND;VALUE=DATE-TIME:20220610T151500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/40
DESCRIPTION:Title: Th
e combinatorics of the Brill-Noether Theory of general covers\nby Kael
in Cook-Powell (Emory University) as part of Tropical Geometry in Frankfur
t/Zoom TGiF/Z\n\n\nAbstract\nThe study of line bundles on algebraic curves
has historically had deep connections with combinatorics. For example\, s
tandard young tableaux have been used to study line bundles of sufficientl
y general curves. Recently a variation of tableaux\, known as k-uniform di
splacement tableaux\, have been used to study line bundles of general cove
rs -- that is curves general in the Hurwitz space. We will discuss how the
se displacement tableaux relate to line bundles of general covers and exam
ine how they are used to produce new results in Brill-Noether Theory.\n
LOCATION:https://researchseminars.org/talk/TGiZ/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Manzaroli (University of Tuebingen)
DTSTART;VALUE=DATE-TIME:20220708T120000Z
DTEND;VALUE=DATE-TIME:20220708T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/41
DESCRIPTION:Title: Tr
opical homology over discretely valued fields\nby Matilde Manzaroli (U
niversity of Tuebingen) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Corey (TU Berlin)
DTSTART;VALUE=DATE-TIME:20220708T133000Z
DTEND;VALUE=DATE-TIME:20220708T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/42
DESCRIPTION:Title: In
itial degenerations of flag varieties\nby Dan Corey (TU Berlin) as par
t of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Zakharov (Central Michigan University)
DTSTART;VALUE=DATE-TIME:20220708T144500Z
DTEND;VALUE=DATE-TIME:20220708T154500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/43
DESCRIPTION:Title: An
analogue of Kirchhoff's theorem for the tropical Prym variety\nby Dmi
try Zakharov (Central Michigan University) as part of Tropical Geometry in
Frankfurt/Zoom TGiF/Z\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TGiZ/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabrina Pauli (Universität Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20221125T130000Z
DTEND;VALUE=DATE-TIME:20221125T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/44
DESCRIPTION:Title: Qu
adratically enriched tropical intersections 1\nby Sabrina Pauli (Unive
rsität Duisburg-Essen) as part of Tropical Geometry in Frankfurt/Zoom TGi
F/Z\n\n\nAbstract\nTropical geometry has been proven to be a powerful comp
utational tool in enumerative geometry over the complex and real numbers.
Results from motivic homotopy theory allow to study questions in enumerati
ve geometry over an arbitrary field k.\nIn these two talks we present one
of the first examples of how to use tropical geometry for questions in enu
emrative geometry over k\, namely a proof of the quadratically enriched B
ézout's theorem for tropical curves.\n\nIn the first talk we explain what
we mean by the "quadratic enrichment"\, that is we define the necessary n
otions of enumerative geometry over arbitrary fields valued in the Grothen
dieck-Witt ring of quadratic forms over k.\n
LOCATION:https://researchseminars.org/talk/TGiZ/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo Puentes (Universität Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20221125T143000Z
DTEND;VALUE=DATE-TIME:20221125T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/45
DESCRIPTION:Title: Qu
adratically enriched tropical intersections 2\nby Andrés Jaramillo Pu
entes (Universität Duisburg-Essen) as part of Tropical Geometry in Frankf
urt/Zoom TGiF/Z\n\n\nAbstract\nTropical geometry has been proven to be a p
owerful computational tool in enumerative geometry over the complex and re
al numbers. Results from motivic homotopy theory allow to study questions
in enumerative geometry over an arbitrary field k.\nIn these two talks we
present one of the first examples of how to use tropical geometry for ques
tions in enuemrative geometry over k\, namely a proof of the quadratically
enriched Bézout's theorem for tropical curves. \n\nIn the second talk we
define the quadratically enriched multiplicity at an intersection point o
f two tropical curves and show that it can be computed combinatorially. We
will use this new approach to prove an enriched version of the Bézout th
eorem and of the Bernstein–Kushnirenko theorem\, both for enriched tropi
cal curves.\n
LOCATION:https://researchseminars.org/talk/TGiZ/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schröter (Goethe-Universität Frankfurt)
DTSTART;VALUE=DATE-TIME:20221125T154500Z
DTEND;VALUE=DATE-TIME:20221125T164000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/46
DESCRIPTION:Title: Va
luative invariants for large classes of matroids\nby Benjamin Schröte
r (Goethe-Universität Frankfurt) as part of Tropical Geometry in Frankfur
t/Zoom TGiF/Z\n\n\nAbstract\nValuations on polytopes are maps that combine
the geometry of polytopes with relations in a group. It turns out that ma
ny important invariants of matroids are valuative on the collection of mat
roid base polytopes\, e.g.\, the Tutte polynomial and its specializations
or the Hilbert–Poincaré series of the Chow ring of a matroid.\n\nIn thi
s talk I will present a framework that allows us to compute such invariant
s on large classes of matroids\, e.g.\, sparse paving and elementary split
matroids\, explicitly. The concept of split matroids introduced by Joswig
and myself is relatively new. However\, this class appears naturally in t
his context. Moreover\, (sparse) paving matroids are split. I will demonst
rate the framework by looking at Ehrhart polynomials\, relations in Chow r
ings of combinatorial geometries\, and further examples.\n\nThis talk is b
ased on the preprint `Valuative invariants for large classes of matroids'
which is joint work with Luis Ferroni.\n
LOCATION:https://researchseminars.org/talk/TGiZ/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Schleis (Universität Tübingen)
DTSTART;VALUE=DATE-TIME:20230203T130000Z
DTEND;VALUE=DATE-TIME:20230203T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/47
DESCRIPTION:Title: Li
near degenerate tropical flag matroids\nby Victoria Schleis (Universit
ät Tübingen) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\n
Abstract\nGrassmannians and flag varieties are important moduli spaces in
algebraic geometry. Their\nlinear degenerations arise in representation th
eory as they describe quiver representations\nand their irreducible module
s. As linear degenerations of flag varieties are difficult to\nanalyze alg
ebraically\, we describe them in a combinatorial setting and further inves
tigate\ntheir tropical counterparts.\n\nIn this talk\, I will introduce ma
troidal\, polyhedral and tropical analoga and descriptions of linear degen
erate flags and their varieties obtained in joint work with Alessio Borzì
. To this end\, we introduce and study morphisms of valuated matroids. Usi
ng techniques from matroid theory\, polyhedral geometry and linear tropica
l geometry\, we use the correspondences between the different descriptions
to gain insight on the structure of linear degeneration. Further\, we ana
lyze the structure of linear degenerate flag varieties in all three settin
gs\, and provide some cover relations on the poset of degenerations. For s
mall examples\, we relate the observations on cover relations to the flat
irreducible locus studied in representation theory.\n
LOCATION:https://researchseminars.org/talk/TGiZ/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Monin (Universität Leipzig)
DTSTART;VALUE=DATE-TIME:20230203T143000Z
DTEND;VALUE=DATE-TIME:20230203T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/48
DESCRIPTION:Title: Po
lyhedral models for K-theory\nby Leonid Monin (Universität Leipzig) a
s part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nOne ca
n associate a commutative\, graded algebra which satisfies \nPoincare dual
ity to a homogeneous polynomial f on a vector space V. One \nparticularly
interesting example of this construction is when f is the volume \npolynom
ial on a suitable space of (virtual) polytopes. In this case the algebra \
nA_f recovers cohomology rings of toric or flag varieties. \n\nIn my talk
I will explain these results and present their recent generalizations. \nI
n particular\, I will explain how to associate an algebra with Gorenstein
duality \nto any function g on a lattice L. In the case when g is the Ehrh
art function on \na lattice of integer (virtual) polytopes\, this construc
tion recovers K-theory of \ntoric and full flag varieties.\n
LOCATION:https://researchseminars.org/talk/TGiZ/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20230203T154500Z
DTEND;VALUE=DATE-TIME:20230203T164500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/49
DESCRIPTION:Title: Un
iversality for tropical maps.\nby Navid Nabijou (Queen Mary University
of London) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbs
tract\nI will discuss recent work concerning maps from tropical curves to
orthants. A “combinatorial type” of such map is the data of an abstrac
t graph together with slope vectors along the edges. To each such combinat
orial type there is an associated moduli space\, which parametrises metric
enhancements of the graph compatible with the given slopes. This moduli s
pace is a rational polyhedral cone\, giving rise to an affine toric variet
y.\n\nOur main result shows that every rational polyhedral cone appears as
the moduli space associated to some combinatorial type of tropical map. T
his establishes universality (also known as Murphy’s law) for tropical m
aps. The proof is constructive and extremely concrete\, as I will demonstr
ate. Combined with insights from logarithmic geometry\, our result implies
that every toric singularity appears as a virtual singularity on a moduli
space of stable logarithmic maps.\n\nThis is joint work with Gabriel Corr
igan and Dan Simms.\n
LOCATION:https://researchseminars.org/talk/TGiZ/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (ENS)
DTSTART;VALUE=DATE-TIME:20230505T120000Z
DTEND;VALUE=DATE-TIME:20230505T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/50
DESCRIPTION:Title: Th
e SYZ conjecture for families of hypersurfaces\nby Léonard Pille-Schn
eider (ENS) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbs
tract\nLet $X \\to D^*$ be a polarized family of complex Calabi-Yau manifo
lds\, whose\ncomplex structure degenerates in the worst possible way. The
SYZ\nconjecture predicts that the fibers $X_t$\, as $t \\to 0$\, degenerat
e to a\ntropical object\; and in particular the program of Kontsevich and
Soibelman\nrelates it to the Berkovich analytification of $X$\, viewed as
a variety over\nthe non-archimedean field of complex Laurent series.\nI wi
ll explain the ideas of this program and some recent progress in the\ncase
of hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/TGiZ/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loujean Cobigo (Universität Tübingen)
DTSTART;VALUE=DATE-TIME:20230505T133000Z
DTEND;VALUE=DATE-TIME:20230505T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/51
DESCRIPTION:Title: Tr
opical spin Hurwitz numbers\nby Loujean Cobigo (Universität Tübingen
) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nCla
ssical Hurwitz numbers count the number of branched covers of a fixed targ
et curve that exhibit a certain ramification behaviour. It is an enumerati
ve problem deeply rooted in mathematical history. \n A modern twist: Spin
Hurwitz numbers were introduced by Eskin-Okounkov-Pandharipande for certai
n computations in the moduli space of differentials on a Riemann surface.\
n Similarly to Hurwitz numbers they are defined as a weighted count of bra
nched coverings of a smooth algebraic curve with fixed degree and branchin
g profile. In addition\,\n they include information about the lift of a th
eta characteristic of fixed parity on the base curve. \n\nIn this talk we
investigate them from a tropical point of view. We start by defining tropi
cal spin Hurwitz numbers as result of an algebraic degeneration procedure\
,\nbut soon notice that these have a natural place in the tropical world a
s tropical covers with tropical theta characteristics on source and target
curve. \nOur main results are two correspondence theorems stating the equ
ality of the tropical spin Hurwitz number with the classical one.\n
LOCATION:https://researchseminars.org/talk/TGiZ/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Ducros (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20230505T144500Z
DTEND;VALUE=DATE-TIME:20230505T154500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/52
DESCRIPTION:Title: Tr
opical functions on skeletons: a finiteness result\nby Antoine Ducros
(Sorbonne Université) as part of Tropical Geometry in Frankfurt/Zoom TGiF
/Z\n\n\nAbstract\nSkeletons are subsets of non-archimedean spaces (in the
sense of Berkovich) that inherit from the ambiant space a natural PL (piec
ewise-linear) structure\, and if $S$ is such a skeleton\, for every invert
ible holomorphic function $f$ defined in a neighborhood of $S$\, the restr
iction of $\\log |f|$ to $S$ is PL. \nIn this talk\, I will present a join
t work with E.Hrushovski F. Loeser and J. Ye in which we consider an irred
ucible algebraic variety $X$ over an algebraically closed\, non-trivially
valued and complete non-archimedean field $k$\, and a skeleton $S$ of the
analytification of $X$ defined using only algebraic functions\, and consis
ting of Zariski-generic points. If $f$ is a non-zero rational function on
$X$ then $\\log |f|$ induces a PL function on $S$\, and if we denote by $E
$ the group of all\nPL functions on $S$ that are of this form\, we prove t
he following finiteness result on the group $E$: it is stable under min an
d max\, and there exist finitely many non-zero rational functions $f_1\,\\
ldots\,f_m$ on $X$ such that $E$ is generated\, as a group\nequipped with
min and max operators\, by the $\\log |f_i|$ and the constants $|a|$ for $
a$ in $k^*$. Our proof makes a crucial use of Hrushovski-Loeser’s model-
theoretic approach of Berkovich spaces.\n
LOCATION:https://researchseminars.org/talk/TGiZ/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Gualdi (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20230707T130000Z
DTEND;VALUE=DATE-TIME:20230707T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/54
DESCRIPTION:Title: Fr
om amoebas to arithmetics\nby Roberto Gualdi (University of Regensburg
) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nMot
ivated by the computation of the integral of a piecewise linear func- tion
on the amoeba of the line (x1 + x2 + 1 = 0)\, we will show how tropical o
bjects play a role in arithmetics.\n\nThis will bring us to an excursion i
nto the Arakelov geometry of toric varieties\; in this framework\, we will
use our tropical computation to predict the arithmetic complexity of the
intersection of a projective planar line with its translate by a torsion p
oint. This is a joint work with Martín Sombra.\n
LOCATION:https://researchseminars.org/talk/TGiZ/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattias Jonsson (University of Michigan)
DTSTART;VALUE=DATE-TIME:20230707T144500Z
DTEND;VALUE=DATE-TIME:20230707T154500Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/55
DESCRIPTION:Title: A
tropical Monge-Ampere equation and the SYZ conjecture\nby Mattias Jons
son (University of Michigan) as part of Tropical Geometry in Frankfurt/Zoo
m TGiF/Z\n\n\nAbstract\nA celebrated result of Yau says that every compact
Kähler manifold with trivial canonical bundle admits a Ricci flat metric
in any given Kähler class. The proof amounts to solving a complex Monge-
Ampère equation. I will discuss joint work with Hultgren\, Mazzon\, and M
cCleerey\, where we solve a "tropical" Monge--Ampère equation\, on the bo
undary of simplex. Through recent work of Yang Li\, this has applications
to the SYZ conjecture\, on degenerations of Calabi-Yau manifolds.\n
LOCATION:https://researchseminars.org/talk/TGiZ/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Afandi (Universität Münster)
DTSTART;VALUE=DATE-TIME:20231214T133000Z
DTEND;VALUE=DATE-TIME:20231214T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/56
DESCRIPTION:Title: St
ationary Descendents and the Discriminant Modular Form\nby Adam Afandi
(Universität Münster) as part of Tropical Geometry in Frankfurt/Zoom TG
iF/Z\n\n\nAbstract\nBy using the Gromov-Witten/Hurwitz correspondence\, Ok
ounkov and Pandharipande showed that certain generating functions of stati
onary descendent Gromov-Witten invariants of a smooth elliptic curve are q
uasimodular forms. In this talk\, I will discuss the various ways one can
express the discriminant modular form in terms of these generating functio
ns. The motivation behind this calculation is to provide a new perspective
on tackling a longstanding conjecture of Lehmer from the middle of the 20
th century\; Lehmer posited that the Ramanujan tau function (i.e. the Four
ier coefficients of the discriminant modular form) never vanishes. The con
nection with Gromov-Witten invariants allows one to translate Lehmer's con
jecture into a combinatorial problem involving characters of the symmetric
group and shifted symmetric functions.\n
LOCATION:https://researchseminars.org/talk/TGiZ/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajith Urundolil-Kumaran (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20231214T150000Z
DTEND;VALUE=DATE-TIME:20231214T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/57
DESCRIPTION:Title: Re
fined tropical curve counting with descendants\nby Ajith Urundolil-Kum
aran (University of Cambridge) as part of Tropical Geometry in Frankfurt/Z
oom TGiF/Z\n\n\nAbstract\nWe introduce the enumerative geometry of curves
in the algebraic torus (C*)^2. We show that a certain class of invariants
associated with moduli spaces of curves in (C*)^2 can be calculated explic
itly using a refined tropical correspondence theorem. If time permits we w
ill explain how the proof relies on higher double ramification cycles and
work of Buryak-Rossi on integrable systems on the moduli space of curves.
This is joint work with Patrick Kennedy-Hunt and Qaasim Shafi.\n
LOCATION:https://researchseminars.org/talk/TGiZ/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Bernig (Goethe-Universität Frankfurt)
DTSTART;VALUE=DATE-TIME:20240202T150000Z
DTEND;VALUE=DATE-TIME:20240202T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/58
DESCRIPTION:Title: Ha
rd Lefschetz theorem and Hodge-Riemann relations for convex valuations
\nby Andreas Bernig (Goethe-Universität Frankfurt) as part of Tropical Ge
ometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe hard Lefschetz theorem
and the Hodge-Riemann relations have their origin in the cohomology theory
of compact Kähler manifolds. In recent years it has become clear that si
milar results hold in many different settings\, in particular in algebraic
geometry and combinatorics (work by Adiprasito\, Huh and others). In a re
cent joint work with Jan Kotrbatý and Thomas Wannerer\, we prove the hard
Lefschetz theorem and Hodge-Riemann relations for valuations on convex bo
dies. These results can be translated into an array of quadratic inequalit
ies for mixed volumes of smooth convex bodies\, giving a smooth analogue o
f the quadratic inequalities in McMullen's polytope algebra. Surprinsingly
\, these inequalities fail for general convex bodies. Our proof uses ellip
tic operators and perturbation theory of unbounded operators.\n
LOCATION:https://researchseminars.org/talk/TGiZ/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manoel Zanoelo Jarra (Universität Groningen)
DTSTART;VALUE=DATE-TIME:20240202T133000Z
DTEND;VALUE=DATE-TIME:20240202T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T122747Z
UID:TGiZ/59
DESCRIPTION:Title: Ca
tegory of matroids with coefficients\nby Manoel Zanoelo Jarra (Univers
ität Groningen) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n
\nAbstract\nMatroids are combinatorial abstractions of the concept of inde
pendence in linear algebra. There is a way back: when representing a matro
id over a field we get a linear subspace. Another algebraic object for whi
ch we can represent matroids is the semifield of tropical numbers\, which
gives us valuated matroids. In this talk we introduce Baker-Bowler's theor
y of matroids with coefficients\, which recovers both classical and valuat
ed matroids\, as well linear subspaces\, and we show how to give a categor
ical treatment to these objects that respects matroidal constructions\, as
minors and duality. This is a joint work with Oliver Lorscheid and Eduard
o Vital.\n
LOCATION:https://researchseminars.org/talk/TGiZ/59/
END:VEVENT
END:VCALENDAR