BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marta Panizzut (Universität Osnabrück) DTSTART:20200424T120000Z DTEND:20200424T130000Z DTSTAMP:20260422T135314Z 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:20200424T131500Z DTEND:20200424T141500Z DTSTAMP:20260422T135314Z 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:20200424T143000Z DTEND:20200424T153000Z DTSTAMP:20260422T135314Z 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:20200529T120000Z DTEND:20200529T130000Z DTSTAMP:20260422T135314Z 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:20200529T131500Z DTEND:20200529T141500Z DTSTAMP:20260422T135314Z 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:20200529T143000Z DTEND:20200529T153000Z DTSTAMP:20260422T135314Z UID:TGiZ/6 DESCRIPTION:Title: The combinatorics and real lifting of tropical bitangents to plane quartics\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:20200626T120000Z DTEND:20200626T130000Z DTSTAMP:20260422T135314Z 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:20200626T131500Z DTEND:20200626T141500Z DTSTAMP:20260422T135314Z 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:20200626T143000Z DTEND:20200626T153000Z DTSTAMP:20260422T135314Z 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:20201204T130000Z DTEND:20201204T140000Z DTSTAMP:20260422T135314Z 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:20201204T141500Z DTEND:20201204T151500Z DTSTAMP:20260422T135314Z 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:20201204T153000Z DTEND:20201204T163000Z DTSTAMP:20260422T135314Z 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:20210122T130000Z DTEND:20210122T140000Z DTSTAMP:20260422T135314Z 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:20210122T141500Z DTEND:20210122T153000Z DTSTAMP:20260422T135314Z 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:20210122T153000Z DTEND:20210122T163000Z DTSTAMP:20260422T135314Z 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:20210219T130000Z DTEND:20210219T140000Z DTSTAMP:20260422T135314Z 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:20210219T141500Z DTEND:20210219T153000Z DTSTAMP:20260422T135314Z 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:20210219T153000Z DTEND:20210219T163000Z DTSTAMP:20260422T135314Z 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:20210312T130000Z DTEND:20210312T140000Z DTSTAMP:20260422T135314Z 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:20210312T141500Z DTEND:20210312T153000Z DTSTAMP:20260422T135314Z 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:20210312T153000Z DTEND:20210312T163000Z DTSTAMP:20260422T135314Z 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:20210430T131500Z DTEND:20210430T141500Z DTSTAMP:20260422T135314Z 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:20210430T143000Z DTEND:20210430T153000Z DTSTAMP:20260422T135314Z 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:20210430T120000Z DTEND:20210430T130000Z DTSTAMP:20260422T135314Z 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:20210528T120000Z DTEND:20210528T130000Z DTSTAMP:20260422T135314Z 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:20210528T143000Z DTEND:20210528T153000Z DTSTAMP:20260422T135314Z 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:20210528T131500Z DTEND:20210528T141500Z DTSTAMP:20260422T135314Z 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:20210625T120000Z DTEND:20210625T130000Z DTSTAMP:20260422T135314Z 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:20210625T131500Z DTEND:20210625T141500Z DTSTAMP:20260422T135314Z 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:20210625T143000Z DTEND:20210625T153000Z DTSTAMP:20260422T135314Z 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:20220121T130000Z DTEND:20220121T140000Z DTSTAMP:20260422T135314Z 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:20220121T141500Z DTEND:20220121T151500Z DTSTAMP:20260422T135314Z 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:20220121T153000Z DTEND:20220121T163000Z DTSTAMP:20260422T135314Z 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:20220218T130000Z DTEND:20220218T135000Z DTSTAMP:20260422T135314Z 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:20220218T141500Z DTEND:20220218T151500Z DTSTAMP:20260422T135314Z 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:20220218T153000Z DTEND:20220218T163000Z DTSTAMP:20260422T135314Z 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:20220513T130000Z DTEND:20220513T140000Z DTSTAMP:20260422T135314Z 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:20220520T143000Z DTEND:20220520T153000Z DTSTAMP:20260422T135314Z 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:20220610T130000Z DTEND:20220610T140000Z DTSTAMP:20260422T135314Z 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:20220610T141500Z DTEND:20220610T151500Z DTSTAMP:20260422T135314Z 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:20220708T120000Z DTEND:20220708T130000Z DTSTAMP:20260422T135314Z 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:20220708T133000Z DTEND:20220708T143000Z DTSTAMP:20260422T135314Z 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:20220708T144500Z DTEND:20220708T154500Z DTSTAMP:20260422T135314Z 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:20221125T130000Z DTEND:20221125T140000Z DTSTAMP:20260422T135314Z 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:20221125T143000Z DTEND:20221125T153000Z DTSTAMP:20260422T135314Z 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:20221125T154500Z DTEND:20221125T164000Z DTSTAMP:20260422T135314Z 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:20230203T130000Z DTEND:20230203T140000Z DTSTAMP:20260422T135314Z 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:20230203T143000Z DTEND:20230203T153000Z DTSTAMP:20260422T135314Z 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:20230203T154500Z DTEND:20230203T164500Z DTSTAMP:20260422T135314Z 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:20230505T120000Z DTEND:20230505T130000Z DTSTAMP:20260422T135314Z 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:20230505T133000Z DTEND:20230505T143000Z DTSTAMP:20260422T135314Z 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:20230505T144500Z DTEND:20230505T154500Z DTSTAMP:20260422T135314Z 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:20230707T130000Z DTEND:20230707T140000Z DTSTAMP:20260422T135314Z 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:20230707T144500Z DTEND:20230707T154500Z DTSTAMP:20260422T135314Z 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:20231214T133000Z DTEND:20231214T143000Z DTSTAMP:20260422T135314Z 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:20231214T150000Z DTEND:20231214T160000Z DTSTAMP:20260422T135314Z 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:20240202T150000Z DTEND:20240202T160000Z DTSTAMP:20260422T135314Z 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:20240202T133000Z DTEND:20240202T143000Z DTSTAMP:20260422T135314Z 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 BEGIN:VEVENT SUMMARY:Karin Schaller (Freie Universität Berlin) DTSTART:20240503T123000Z DTEND:20240503T133000Z DTSTAMP:20260422T135314Z UID:TGiZ/60 DESCRIPTION:Title: NO bodies are perfect\, semigroups are not\nby Karin Schaller (Freie Univ ersität Berlin) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n \nAbstract\nNewton-Okounkov bodies are asymptotic limits of certain valuat ion semigroups. Their construction depends on a given flag of subvarieties . We investigate toric surfaces together with non-toric flags and determin e when the associated valuation semigroups are finitely generated. This is a joint work with K. Altmann\, C. Haase\, A. Küronya\, and L. Walter.\n LOCATION:https://researchseminars.org/talk/TGiZ/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukas Kühne (Universität Bielefeld) DTSTART:20240503T140000Z DTEND:20240503T150000Z DTSTAMP:20260422T135314Z UID:TGiZ/61 DESCRIPTION:Title: Th e realization space of a matroid\nby Lukas Kühne (Universität Bielef eld) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\n A matroid is a fundamental and widely studied object in combinatorics. Fol lowing a brief introduction to matroids\, I will showcase parts of a new O SCAR module for matroids using several examples. My emphasis will be on th e computation of the realization space of a matroid\, which is the space o f all hyperplane arrangements that have the given matroid as their interse ction lattice.\n\nIn the second part\, I will discuss an application in th e realm of algebraic geometry\, namely a novel connection between matroid realization spaces and the elliptic modular surfaces.\n LOCATION:https://researchseminars.org/talk/TGiZ/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Pim Spelier (Leiden University) DTSTART:20240614T123000Z DTEND:20240614T133000Z DTSTAMP:20260422T135314Z UID:TGiZ/62 DESCRIPTION:Title: Th e log tautological ring of the moduli space of curves\nby Pim Spelier (Leiden University) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\ n\n\nAbstract\nThe tautological ring of Mgn-bar has been a crucial object in the study of the intersection theory of the moduli space of curves. Rec ently\, there has been more focus on the logarithmic enumerative geometry of Mgn-bar\, with interesting classes coming from e.g. log double ramifica tion cycles. We present a definition of the log tautological ring of Mgn-b ar\, together with a log decorated strata algebra\, and prove several stru cture results. The main new tools are the notions of cone stacks with boun dary and homological piecewise polynomials\, that capture the tropicalisat ion of strata of log smooth stacks and the combinatorial part of their int ersection theory.\nThis is joint work with Rahul Pandharipande\, Dhruv Ran ganathan and Johannes Schmitt.\n LOCATION:https://researchseminars.org/talk/TGiZ/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Gierczak (Institut Polytechnique de Paris) DTSTART:20240614T140000Z DTEND:20240614T150000Z DTSTAMP:20260422T135314Z UID:TGiZ/63 DESCRIPTION:Title: Co unting Weierstrass points on degenerating algebraic curves\nby Lucas G ierczak (Institut Polytechnique de Paris) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nWeierstrass points on algebraic curve s are special points of high importance in algebraic geometry and arithmet ic geometry. In this talk\, we study how those special points behave when the algebraic curve degenerates to a nodal curve. To this end\, we first e xplain why tropical geometry is a relevant formalism for studying degenera tion questions. We then define a tropical analogue on metric graphs (seen as tropical curves) for Weierstrass points\, and explore the properties of the so-called “tropical Weierstrass locus". We also associate intrinsic weights to the connected components of this locus\, and show that their t otal sum for a given metric graph and divisor is a function of few combina torial parameters (degree and rank of the divisor\, genus of the metric gr aph). Finally\, in the case the divisor on the metric graph comes from the tropicalization of a divisor on an algebraic curve\, we specify the compa tibility between the Weierstrass loci.\n LOCATION:https://researchseminars.org/talk/TGiZ/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Giusi Capobianco (Roma Tor Vergata) DTSTART:20250117T133000Z DTEND:20250117T143000Z DTSTAMP:20260422T135314Z UID:TGiZ/64 DESCRIPTION:Title: Th e tropical 1-fold Abel-Prym map\nby Giusi Capobianco (Roma Tor Vergata ) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe algebraic Abel-Prym map relates the geometry of a double cover of algebra ic curves with their corresponding Prym varieties. Birkenhake and Lange pr oved that the map has degree 2 if and only if the cover curve is hyperelli ptic.\nIn the talk I will present joint work with Yoav Len\, in which we i nvestigate the 1-fold Abel-Prym map in the tropical setting and prove simi lar results. I will describe a new combinatorial construction of hyperelli ptic double covers of metric graphs and prove that the tropical Abel-Prym map is a harmonic morphism of degree 2. Furthermore\, we will see that th e Jacobian of the image of this map is isomorphic\, as pptav\, to the Prym variety of the cover. When the double cover is not hyperelliptic however\ , contrary to the algebraic result\, the tropical Abel-Prym map is almost never injective. I will provide counterexamples and discuss its image.\n LOCATION:https://researchseminars.org/talk/TGiZ/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Shelby Cox (MPI Leipzig) DTSTART:20250117T140000Z DTEND:20250117T150000Z DTSTAMP:20260422T135314Z UID:TGiZ/65 DESCRIPTION:Title: Tr ee spaces in tropical geometry\nby Shelby Cox (MPI Leipzig) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe space of ph ylogenetic trees on n leaves arises naturally in tropical geometry through the tropical Grassmannian trop Gr(2\,n). The space of equidistant trees o n n leaves is the tropicalization of M_{0\,n}\, which is tropically convex . In this talk\, I will present recent work using tropical tree spaces for phylogenetic statistics and inference (joint with Curiel\, Sabol\, Talbut \, and Yoshida). I will also discuss a conjectural analogue of the space o f equidistant trees for type C (joint with Igor Makhlin)\n LOCATION:https://researchseminars.org/talk/TGiZ/65/ END:VEVENT BEGIN:VEVENT SUMMARY:George Balla (MPI Leipzig) DTSTART:20250207T133000Z DTEND:20250207T143000Z DTSTAMP:20260422T135314Z UID:TGiZ/66 DESCRIPTION:Title: Re gular subdivisions and bounds on initial ideals\nby George Balla (MPI Leipzig) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstra ct\nWe extend two known constructions that relate regular subdivisions to initial degenerations of projective toric varieties and Grassmannians. We associate a point configuration A with any homogeneous ideal I. We obtain upper and lower bounds on each initial ideal of I in terms of regular subd ivisions of A. We also investigate when these bounds are exact\, for examp le\, the lower bound is exact for every initial ideal of the Plücker idea l I(2\,n) with respect to points in the tropicalization. This talk is base d on joint work with Dan Corey\, Igor Makhlin\, and Victoria Schleis.\n LOCATION:https://researchseminars.org/talk/TGiZ/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Crumplin (Universität Heidelberg) DTSTART:20250207T150000Z DTEND:20250207T160000Z DTSTAMP:20260422T135314Z UID:TGiZ/67 DESCRIPTION:Title: Mo duli spaces of twisted maps to smooth pairs\nby Robert Crumplin (Unive rsität Heidelberg) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\ n\n\nAbstract\nThe question of counting maps from marked curves with fixed tangency conditions to a divisor in the target has been studied extensive ly over the past 15 years. One way of formulating these enumerative proble ms is via twisted maps to a root stack. I will describe the geometry of mo duli spaces of twisted maps using tropical techniques\, in particular givi ng new understanding to universal structural results of orbifold Gromov– Witten invariants. If time permits\, I will talk about upcoming work with Sam Johnston which relates these moduli spaces to their logarithmic counte rparts and provides a splitting of the virtual class in terms of the afore mentioned tropical data.\n LOCATION:https://researchseminars.org/talk/TGiZ/67/ END:VEVENT END:VCALENDAR