FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2247347232> ?p ?o ?g. }

• W2247347232 abstract "Tropical geometry is young field of mathematics that connects algebraic geometry and combinatorics. It considers “combinatorial shadows” of classical algebraic objects, which preserve information while being more susceptible to discrete methods. Tropical geometry has proven useful in such subjects as polynomial implicitization, scheduling problems, and phylogenetics. Of particular interesest in this work is the application of tropical geometry to study curves (and other varieties) over non-Archimedean fields, which can be tropicalized to tropical curves (and other tropical varieties). Chapter 1 presents background material on tropical geometry, and presents two perspectives on tropical curves: the embedded perspective, which treats them as balanced polyhedral complexes in Euclidean space, and the abstract perspective, which treats them as metric graphs. This chapter also presents the background on curves over non-Archimedean fields necessary for the rest of this work, including the moduli space of curves of a given genus and the Berkovich analytic space associated to a curve. Chapters 2 and 3 study tropical curves embedded in the plane. Chapter 2 deals with tropical plane curves that intersect non-transversely, and opens with a result on which configurations of points in such an intersection can be lifted to intersection points of classical curves. It then moves on to present a joint work with Matthew Baker, Yoav Len, Nathan Pflueger, and Qingchun Ren that builds up a theory of bitangents of smooth tropical plane quartic curves in parallel to the classical theory.Chapter 3 presents joint work with Sarah Brodsky, Michael Joswig, and Bernd Sturmfels, and is a study of which metric graphs arise as skeletons of smooth tropical plane curves. We begin by defining the moduli space of tropical plane curves, which is the tropical analog of Castryck and Voight’s space of nondegenerate curves in [CV09]. The first main theorem is that our space is full-dimensional inside of the tropicalization of the corresponding classical space, a result proved using honeycomb curves. The chapter proceeds to a computational study of the moduli space of tropical plane curves, and explicitly computes the spaces for genus up to 5. The chapter closes with both theoretical and computational results on tropical hyperelliptic curves that can be embedded in the plane.Chapter 4 presents joint work with Qingchun Ren and is an algorithmic treatment of a special family of curves over a non-Archimedean field called Mumford curves. These are of particular interest in tropical geometry, as they are the curves whose tropicalizations can have genus-many cycles. We build up a family of algorithms, implemented in sage [S+13], for computing many objects associated to such a curve over the field of p-adic numbers, including its Jacobian, its Berkovich skeleton, and points in its canonical embedding.Chapter 5 is joint work with Ngoc Tran, and is a departure from studying tropical curves. It considers what it means for matrix multiplication to commute tropically, both in the context of tropical linear algebra and by considering the tropicalization of the classical commuting variety, whose points are pairs of commuting matrices. We give necessary and sufficient conditions for small matrices to commute, and illustrate three different tropical spaces, each of which has some claim to being “the” space of tropical commuting matrices." @default.
• W2247347232 created "2016-06-24" @default.
• W2247347232 creator A5075168385 @default.
• W2247347232 date "2015-01-01" @default.
• W2247347232 modified "2023-09-27" @default.
• W2247347232 title "Tropical and non-Archimedean curves" @default.
• W2247347232 cites W119527372 @default.
• W2247347232 cites W1484433819 @default.
• W2247347232 cites W1485445902 @default.
• W2247347232 cites W1542427152 @default.
• W2247347232 cites W1546966947 @default.
• W2247347232 cites W1549562143 @default.
• W2247347232 cites W1555845291 @default.
• W2247347232 cites W1568502052 @default.
• W2247347232 cites W157418060 @default.
• W2247347232 cites W1577336772 @default.
• W2247347232 cites W1599288848 @default.
• W2247347232 cites W1605965057 @default.
• W2247347232 cites W1609080720 @default.
• W2247347232 cites W1678516906 @default.
• W2247347232 cites W174628562 @default.
• W2247347232 cites W1796467332 @default.
• W2247347232 cites W1893041278 @default.
• W2247347232 cites W1907285070 @default.
• W2247347232 cites W1963534149 @default.
• W2247347232 cites W1964445456 @default.
• W2247347232 cites W1966832055 @default.
• W2247347232 cites W1973957485 @default.
• W2247347232 cites W1974037599 @default.
• W2247347232 cites W1977415556 @default.
• W2247347232 cites W1978394569 @default.
• W2247347232 cites W1996589670 @default.
• W2247347232 cites W1999289183 @default.
• W2247347232 cites W201452274 @default.
• W2247347232 cites W2019402168 @default.
• W2247347232 cites W2021591064 @default.
• W2247347232 cites W2036822603 @default.
• W2247347232 cites W2050170085 @default.
• W2247347232 cites W2051364804 @default.
• W2247347232 cites W2055287661 @default.
• W2247347232 cites W2059110368 @default.
• W2247347232 cites W2070385985 @default.
• W2247347232 cites W2075832453 @default.
• W2247347232 cites W2078131426 @default.
• W2247347232 cites W2083387674 @default.
• W2247347232 cites W2088667958 @default.
• W2247347232 cites W2116789145 @default.
• W2247347232 cites W2119087156 @default.
• W2247347232 cites W2135606603 @default.
• W2247347232 cites W2136372517 @default.
• W2247347232 cites W2144715077 @default.
• W2247347232 cites W2171942149 @default.
• W2247347232 cites W2209316191 @default.
• W2247347232 cites W2233474732 @default.
• W2247347232 cites W2255136811 @default.
• W2247347232 cites W2615794307 @default.
• W2247347232 cites W2940228116 @default.
• W2247347232 cites W2949578759 @default.
• W2247347232 cites W2952697825 @default.
• W2247347232 cites W2962881705 @default.
• W2247347232 cites W2963003902 @default.
• W2247347232 cites W2963117880 @default.
• W2247347232 cites W2963438905 @default.
• W2247347232 cites W2964010416 @default.
• W2247347232 cites W2964052832 @default.
• W2247347232 cites W2973290529 @default.
• W2247347232 cites W3037914599 @default.
• W2247347232 cites W3098301923 @default.
• W2247347232 cites W3106181011 @default.
• W2247347232 cites W341186930 @default.
• W2247347232 cites W634790569 @default.
• W2247347232 hasPublicationYear "2015" @default.
• W2247347232 type Work @default.
• W2247347232 sameAs 2247347232 @default.
• W2247347232 citedByCount "1" @default.
• W2247347232 countsByYear W22473472322020 @default.
• W2247347232 crossrefType "journal-article" @default.
• W2247347232 hasAuthorship W2247347232A5075168385 @default.
• W2247347232 hasConcept C129782007 @default.
• W2247347232 hasConcept C130432447 @default.
• W2247347232 hasConcept C134306372 @default.
• W2247347232 hasConcept C186219872 @default.
• W2247347232 hasConcept C194596105 @default.
• W2247347232 hasConcept C202444582 @default.
• W2247347232 hasConcept C202652594 @default.
• W2247347232 hasConcept C205649164 @default.
• W2247347232 hasConcept C207043602 @default.
• W2247347232 hasConcept C2524010 @default.
• W2247347232 hasConcept C33923547 @default.
• W2247347232 hasConcept C43809302 @default.
• W2247347232 hasConcept C51544822 @default.
• W2247347232 hasConcept C58640448 @default.
• W2247347232 hasConcept C64543145 @default.
• W2247347232 hasConcept C68363185 @default.
• W2247347232 hasConcept C73373263 @default.
• W2247347232 hasConcept C77462122 @default.
• W2247347232 hasConcept C78045399 @default.
• W2247347232 hasConceptScore W2247347232C129782007 @default.
• W2247347232 hasConceptScore W2247347232C130432447 @default.
• W2247347232 hasConceptScore W2247347232C134306372 @default.

• next