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BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (University of Groningen)
DTSTART:20250708T130000Z
DTEND:20250708T140000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/1/">Toolkit for the algebraic geometer II</a>\nby Oliver Lorscheid (Univ
 ersity of Groningen) as part of Geometry over Semirings\n\nLecture held in
  Escola de Doctorat\, UAB.\n\nAbstract\nIn this series of 3 lectures\, we 
 explain how to create your favorite geometry from a category of "model spa
 ces". As a first step\, we investigate the process of glueing the model sp
 aces to geometric objects\, such as open balls are glued to manifolds and 
 spectra of rings are glued to schemes. The main application in mind for th
 is conference are semiring schemes.\n\nThis process starts with first prin
 ciples: the information needed to glue "affine" spaces along open subspace
 s is the notion of open embeddings\, which is captured nicely in terms of 
 covering families. This allows us to mimic the glueing process in terms of
  sheaves for these covering families. This is similar in flavour to some e
 xisting approaches to F1-geometry\, but we simplify and generalize the exi
 sting approaches in this lecture.\n\nAs a secondary step\, we can derive a
  topological space of "underlying points" via Stone duality applied to the
  locale of open subobjects\, including its structure sheaf. This recovers 
 the usual spaces in the case of manifolds and schemes\, and dictates what 
 the spectrum of a semiring has to be.\n\nThe lectures are structured as fo
 llows:\n\n(1) Motivation\, recap on sheaves\, definition of an s-scheme.\n
 \n(2) More on s-schemes\, open subschemes\, Stone duality\, points of an s
 -scheme.\n\n(3) Semiring schemes: points as prime ideals\, prime k-ideals\
 , secondary topological spaces ("visualizations").\n
LOCATION:https://researchseminars.org/talk/geo-semirings/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (University of Groningen)
DTSTART:20250710T081000Z
DTEND:20250710T091000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/2/">Toolkit for the algebraic geometer III</a>\nby Oliver Lorscheid (Uni
 versity of Groningen) as part of Geometry over Semirings\n\nLecture held i
 n Escola de Doctorat\, UAB.\n\nAbstract\nIn this series of 3 lectures\, we
  explain how to create your favorite geometry from a category of "model sp
 aces". As a first step\, we investigate the process of glueing the model s
 paces to geometric objects\, such as open balls are glued to manifolds and
  spectra of rings are glued to schemes. The main application in mind for t
 his conference are semiring schemes.\n\nThis process starts from first pri
 nciples: the information needed to glue "affine" spaces along open subspac
 es is the notion of open embeddings\, which is captured nicely in terms of
  covering families. This allows us to mimic the glueing process in terms o
 f sheaves for these covering families. This is similar in flavour to some 
 existing approaches to F1-geometry\, but we simplify and generalize the ex
 isting approaches in this lecture.\n\nAs a secondary step\, we can derive 
 a topological space of "underlying points" via Stone duality applied to th
 e locale of open subobjects\, including its structure sheaf. This recovers
  the usual spaces in the case of manifolds and schemes\, and dictates what
  the spectrum of a semiring has to be.\n\nThe lectures are structured as f
 ollows:\n\n(1) Motivation\, recap on sheaves\, definition of an s-scheme.\
 n\n(2) More on s-schemes\, open subschemes\, Stone duality\, points of an 
 s-scheme.\n\n(3) Semiring schemes: points as prime ideals\, prime k-ideals
 \, secondary topological spaces ("visualizations").\n
LOCATION:https://researchseminars.org/talk/geo-semirings/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mayo Mayo Garcia (University of Warwick)
DTSTART:20250708T093500Z
DTEND:20250708T101500Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/3/">Tropical linear series and tropical ideals.</a>\nby Mayo Mayo Garcia
  (University of Warwick) as part of Geometry over Semirings\n\nLecture hel
 d in Escola de Doctorat\, UAB.\n\nAbstract\nOne of the approaches in tropi
 cal geometry takes a variety embedded in projective space and obtains a po
 lyhedral complex that preserves some relevant information about the variet
 y. In the case of (abstract) smooth curves\, another tropical approach exi
 sts where the dual graph of a semistable model of the curve is taken as th
 e tropicalization. I will talk about how to relate these two tropicalizati
 ons via the theory of valuated matroids\, some consequences and obstructio
 ns.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250707T124500Z
DTEND:20250707T130000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/4/">Registration</a>\nby NA as part of Geometry over Semirings\n\nLectur
 e held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250707T130000Z
DTEND:20250707T133000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/5/">Opening remarks</a>\nby NA as part of Geometry over Semirings\n\nLec
 ture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250707T150000Z
DTEND:20250707T163000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/6/">Group formation and discussions</a>\nby NA as part of Geometry over 
 Semirings\n\nLecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourayan Banerjee (Indian Institute of Technology Kanpur)
DTSTART:20250708T102000Z
DTEND:20250708T110000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/7/">Homotopy equivalence of algebraic K-theory over non-noetherian rings
 </a>\nby Sourayan Banerjee (Indian Institute of Technology Kanpur) as part
  of Geometry over Semirings\n\nLecture held in Escola de Doctorat\, UAB.\n
 \nAbstract\nThe word “K” in the Algebraic $K$-theory stands for the Ge
 rman word “Klasse”\, which means\nclass. The Grothendieck group $K_0(R
 )$ over any commutative ring with unity $R$ is defined to be the group com
 pletion of the commutative monoid $(\\text{isoP}(R)\, \\bigoplus)$\, where
  $\\text{isoP}(R)$ is the collection of all isomorphism classes of finitel
 y generated \n projective modules over R. Quillen\, in his seminal work\, 
 defined the higher $K$-groups as higher homotopy groups of a certain based
  topological space. Later\, Waldhausen further generalized it and equivale
 ntly defined that for any $n \\geq 0$\, $K_n(R) :=\\pi_{n+1} |wS.P(R)|$. S
 o naturally\, an isomorphism of two $K$-groups means an isomorphism betwee
 n\ntheir respective homotopy groups. It was Quillen who first proved that 
 $K$-theory is homotopy equivalent if $R$ is regular Noetherian\, i.e.\, fo
 r a regular Noetherian ring $R$\n$K_n(R) \\cong K_n(R[t_1\, t_2\, ...\, t_
 m])$\, $\\forall n\, m > 0$.\nBut for non-Noetherian rings\, it was still 
 unknown until very recently\, Kelly and Morrow proved in [KM21] that the a
 bove isomorphism holds for any valuation rings as well.\nIn this talk\, I 
 will primarily present a further generalization of Kelly Morrow’s result
 . First\, we will see that if $R$ is locally a valuation ring\, equivalent
 ly a Prufer domain\, then the homotopy equivalence holds [BS22]. Moreover\
 , the homotopy equivalence holds for any ring with weak global dimension $
 \\leq 1$ [BS22]. Now\, the canonical map from $P(R[t]) \\rightarrow P (R)$
 \, $t \\mapsto 0$ induces a split surjection $\\phi_*\\colon K_n(R[t])\\ri
 ghtarrow K_n(R)$. Thus we find that triviality of $\\ker(\\phi_*)$ results
  in an isomorphism.\n\nWe will conclude by showing the precise generators 
 of these kernels (even though these kernels\nare infinitely generated) [BS
 24]\, known as the obstruction groups to homotopy equivalence\,\nwith the 
 help of Grayson’s technique [Gra12].\n
LOCATION:https://researchseminars.org/talk/geo-semirings/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Ulirsch (Paderborn University)
DTSTART:20250709T070000Z
DTEND:20250709T080000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/8/">From tropical linear algebra to vector bundles</a>\nby Martin Ulirsc
 h (Paderborn University) as part of Geometry over Semirings\n\nLecture hel
 d in Escola de Doctorat\, UAB.\n\nAbstract\nIn this talk I will explain ho
 w our perspective on tropical linear algebra shapes our understanding of t
 ropical vector bundles. An elementary approach to this story is based on t
 ropical matrices. In this case we find an elementary and geometrically app
 ealing theory of tropical vector bundles\, which allows us to give a satis
 fying treatment of the process of tropicalization in abelian situations\, 
 e.g. in the case of the Tate curve or for semihomogenous vector bundles on
  abelian varieties. Expanding on these developments\, as a first step towa
 rds the more general non-abelian situation\, I will outline a framework to
  functorially tropicalize linear maps between finite-dimensional vector sp
 aces using the geometry of affine Bruhat--Tits buildings. This will provid
 e us with a pathway to study the tropical geometry of vector bundles on mo
 re general base spaces.\n\nMost of the new results in the talk will be bas
 ed on joint works with A. Gross and D. Zakharov\; A. Gross\, A. Kuhrs\, an
 d D. Zakharov\; I. Kaur\, A. Gross\, and A. Werner\; as well as with L. Ba
 ttistella\, K. Kuehn\, A. Kuhrs\, and A. Vargas.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana María Botero (Bielefeld University)
DTSTART:20250709T081000Z
DTEND:20250709T091000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/9/">On an arithmetic BKK theorem for toric vector bundles</a>\nby Ana Ma
 ría Botero (Bielefeld University) as part of Geometry over Semirings\n\nL
 ecture held in Escola de Doctorat\, UAB.\n\nAbstract\nClassical Newton pol
 yhedra theory gives formulas for discrete geometric and topological invari
 ants (such as the Euler characteristic) of complete intersections in the a
 lgebraic torus defined by generic Laurent polynomial equations. The result
 s use mixed volumes and number of lattice points. As a prominent example\,
  the Bernštein-Kušnirenko-Khovanskii theorem (BKK theorem) states that t
 he number of isolated common zeros (counted with multiplicities) of a fami
 ly of Laurent polynomials is bounded above by the mixed volume of its Newt
 on polytopes. In this talk\, we will see a generalization of\nthis result 
 for vector-valued Laurent polynomials using the theory of toric vector bun
 dles. Finally\, we discuss (archimedean and non-archimedean) toric metrics
  on toric vector bundles\, and compute compute some local arithmetic degre
 es\, as a first step towards an arithmetic BKK theorerm for toric vector b
 undles. This is joint work with José Burgos\, Kiumars Kaveh and Vivek Mal
 lik.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Kuhrs (Paderborn University)
DTSTART:20250709T093500Z
DTEND:20250709T101500Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/10/">Buildings\, valuated matroids\, and tropical linear spaces</a>\nby 
 Arne Kuhrs (Paderborn University) as part of Geometry over Semirings\n\nLe
 cture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Vargas (University of Warwick)
DTSTART:20250709T102000Z
DTEND:20250709T110000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/11/">The semiring of tropical rational functions over compact tropical h
 ypersurfaces</a>\nby Alejandro Vargas (University of Warwick) as part of G
 eometry over Semirings\n\nLecture held in Escola de Doctorat\, UAB.\n\nAbs
 tract\nIn the first half of the talk we review several important features 
 and properties of semirings of rational functions over metric graphs\, the
 ir connection to divisor theory on metric graphs\, boundedness of slopes\,
  pure dimensionality of the topological realization\, and ways to compute 
 tropical rank. In the second half we report on ongoing work with Diego Rob
 ayo to generalize to higher dimensions.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Xarles (Universitat Autònoma de Barcelona)
DTSTART:20250710T130000Z
DTEND:20250710T140000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/12/">II. Scheme Theory for commutative semirings with kernels</a>\nby Xa
 vier Xarles (Universitat Autònoma de Barcelona) as part of Geometry over 
 Semirings\n\nLecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Xarles (Universitat Autònoma de Barcelona)
DTSTART:20250708T081000Z
DTEND:20250708T091000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/13/">I. Scheme Theory for commutative semirings with ideals</a>\nby Xavi
 er Xarles (Universitat Autònoma de Barcelona) as part of Geometry over Se
 mirings\n\nLecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Martínez Méndez (University of Groningen)
DTSTART:20250710T093500Z
DTEND:20250710T101500Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/14/">Points on symmetric monoidal categories</a>\nby Alejandro Martínez
  Méndez (University of Groningen) as part of Geometry over Semirings\n\nL
 ecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Kühn (TU Berlin)
DTSTART:20250710T102000Z
DTEND:20250710T110000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/15/">Universal Realizable Matroids over Hyperfields</a>\nby Kevin Kühn 
 (TU Berlin) as part of Geometry over Semirings\n\nLecture held in Escola d
 e Doctorat\, UAB.\n\nAbstract\nAfter recalling some basic notions of matro
 ids over hyperfields\, we introduce the universal realizable matroid. The 
 ground set of this matroid is a whole vector space. We establish a theory 
 of linear spaces even in this highly infinite case. Of special interest ar
 e the cases of the tropical hyperfield\, the sign hyperfield\, and the sig
 ned tropical hyperfield. These correspond to the cases that the ground fie
 ld is equipped with a valuation\, an ordering\, or both. We explicitly com
 pute the associated linear spaces and show\, that these are exactly the re
 spective limits of the linear spaces associated to all finite restrictions
 . This is a linear version of Payne's result that the analytification is t
 he limit of all tropicalizations. In the case of the signed tropical hyper
 field\, we obtain a space of signed seminorms\, similar to the non-Archime
 dean analogues of symmetric spaces introduced by Goldman and Iwahori.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Giansiracusa (Durham University)
DTSTART:20250711T070000Z
DTEND:20250711T080000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/16/">Tropical algebra III: universal tropicalisation\, analytification\,
  and limit theorems</a>\nby Jeffrey Giansiracusa (Durham University) as pa
 rt of Geometry over Semirings\n\nLecture held in Escola de Doctorat\, UAB.
 \n\nAbstract\nIn 2008 Payne proved that the Berkovich analytification of a
 n affine variety is homeomorphic to the category-theoretic limit of all of
  its tropicalisations.  We'll explore this phenomenon from the perspective
  of tropical algebra\, bend relations\, and universal objects in category 
 theory.\n\nTropicalising a scheme $X$ requires a choice of an embedding in
 to a toric variety.  The limit of all such embeddings exists as a mild gen
 eralisation of a toric embedding\, and it can be explicitly described.  Th
 e tropicalisation determined by this embedding has a universal property: i
 t maps to all other tropicalisations.  The Berkovich analytification also 
 has this property\, and the two are in fact homeomorphic.\n\nIf $X = \\mat
 hrm{spec} \\: A$\, then the Berkovich analytification is the space of valu
 ations on $A$.  If one admits valuations taking values in idempotent semir
 ings that are not necessarily totally ordered\, then the category of valua
 tions on $A$ has an initial object\, and the target of this universal valu
 ation is precisely the algebra corresponding to the universal tropicalisat
 ion.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250711T093500Z
DTEND:20250711T110000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/17/">Group reports</a>\nby NA as part of Geometry over Semirings\n\nLect
 ure held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Mereta (KTH Stockholm)
DTSTART:20250708T143000Z
DTEND:20250708T151000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/18/">The congruence spectrum of tropical polynomials as the spectrum of 
 a ring</a>\nby Stefano Mereta (KTH Stockholm) as part of Geometry over Sem
 irings\n\nLecture held in Escola de Doctorat\, UAB.\n\nAbstract\nIn this t
 alk we will recall the notion of prime congruence on the tropical polynomi
 al semiring as introduced by Jóo and Mincheva and prove that the congruen
 ce spectrum is anti-homeomorphic to the spectrum of a commutative ring obt
 ained as the unit ball of a generalised Bézout valuation. \n\nWe will do 
 so by proving that the space of valuated preorders on the monomials of K[x
 1\,…\,xn] (for a valued field K) is homeomorphic to the k-spectrum of th
 e target of the aformentioned generalised valuation. \n\nThe anti-homeomor
 phism will allow us associate quotients by prime congruences in the tropic
 al world with localizations by prime ideals in the classical world. We wil
 l conclude by discussing briefly possible applications to the study of (tr
 opical) ideals of the tropical polynomial semiring.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250708T151000Z
DTEND:20250708T163000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/19/">Group discussions</a>\nby NA as part of Geometry over Semirings\n\n
 Lecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NA
DTSTART:20250710T143000Z
DTEND:20250710T163000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/21/">Group discussions</a>\nby NA as part of Geometry over Semirings\n\n
 Lecture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (University of Groningen)
DTSTART:20250707T140000Z
DTEND:20250707T150000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/22/">Toolkit for the algebraic geometer I</a>\nby Oliver Lorscheid (Univ
 ersity of Groningen) as part of Geometry over Semirings\n\nLecture held in
  Escola de Doctorat\, UAB.\n\nAbstract\nIn this series of 3 lectures\, we 
 explain how to create your favorite geometry from a category of "model spa
 ces". As a first step\, we investigate the process of glueing the model sp
 aces to geometric objects\, such as open balls are glued to manifolds and 
 spectra of rings are glued to schemes. The main application in mind for th
 is conference are semiring schemes.\n\nThis process starts with first prin
 ciples: the information needed to glue "affine" spaces along open subspace
 s is the notion of open embeddings\, which is captured nicely in terms of 
 covering families. This allows us to mimic the glueing process in terms of
  sheaves for these covering families. This is similar in flavour to some e
 xisting approaches to F1-geometry\, but we simplify and generalize the exi
 sting approaches in this lecture.\n\nAs a secondary step\, we can derive a
  topological space of "underlying points" via Stone duality applied to the
  locale of open subobjects\, including its structure sheaf. This recovers 
 the usual spaces in the case of manifolds and schemes\, and dictates what 
 the spectrum of a semiring has to be.\n\nThe lectures are structured as fo
 llows:\n\n(1) Motivation\, recap on sheaves\, definition of an s-scheme.\n
 \n(2) More on s-schemes\, open subschemes\, Stone duality\, points of an s
 -scheme.\n\n(3) Semiring schemes: points as prime ideals\, prime k-ideals\
 , secondary topological spaces ("visualizations").\n
LOCATION:https://researchseminars.org/talk/geo-semirings/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Giansiracusa (Durham University)
DTSTART:20250708T070000Z
DTEND:20250708T080000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/23/">Tropical algebra I: congruences\, ideals and bend relations</a>\nby
  Jeffrey Giansiracusa (Durham University) as part of Geometry over Semirin
 gs\n\nLecture held in Escola de Doctorat\, UAB.\n\nAbstract\nThe tropical 
 semiring $(\\mathbb{R} \\cup \\infty\, \\mathrm{min}\, +)$ is an interesti
 ng place to do algebra\, and it is intimately connected to tropical geomet
 ry.  In this talk\, I'll introduce tropical polynomials\, ideals\, congrue
 nces\, and how the connection with tropical geometry is made via congruenc
 es of bend relations.  Tropical geometry and matroid theory are telling us
  that we should focus attention of a narrow slice of the world of tropical
  algebra.  This leads to the theory of tropical ideals (as developed by Ma
 clagan and Rincon) and an abundance of interesting open questions.  I will
  try to summarise what we know and what we don't yet know about tropical i
 deals.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Giansiracusa (Durham University)
DTSTART:20250710T070000Z
DTEND:20250710T080000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/24/">Tropical algebra II: exterior algebras\, matrix algebras\, and Clif
 ford algebras</a>\nby Jeffrey Giansiracusa (Durham University) as part of 
 Geometry over Semirings\n\nLecture held in Escola de Doctorat\, UAB.\n\nAb
 stract\nIn this talk we will set aside geometry and focus on tropicalisati
 on via bend relations as a construction in commutative and non-commutative
  algebra.  By  starting at the level of tensor algebras\, constructions su
 ch as symmetric algebras\, exterior algebras\, matrix algebras\, and Cliff
 ord algebras can be tropicalised.\n\nIn the case of exterior algebras\, th
 e resulting tropical notion beautifully completes the picture of the Pluck
 er embedding\, and gives a new perspective on the tropical Plucker relatio
 ns.\n\nFor matrix algebras and Clifford algebras\, Morita theory becomes a
 n interesting aspect.  I will present some facts and some questions.\n
LOCATION:https://researchseminars.org/talk/geo-semirings/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Xarles (Universitat Autònoma de Barcelona)
DTSTART:20250711T081000Z
DTEND:20250711T091000Z
DTSTAMP:20260422T213049Z
UID:geo-semirings/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geo-semiring
 s/25/">III. Valuations for semirings and Schemes</a>\nby Xavier Xarles (Un
 iversitat Autònoma de Barcelona) as part of Geometry over Semirings\n\nLe
 cture held in Escola de Doctorat\, UAB.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/geo-semirings/25/
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