The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Tropical geometry and its applications
Open accessAbstract
From a formal perspective tropical geometry can be viewed as a branch of geometry manipulating with certain piecewise-linear objects that take over the rôle of classical algebraic varieties. This talk outlines some basic notions of this area and surveys some of its applications for the problems in classical (real and complex) geometry.
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Citations
Cites
Discriminants, Resultants, and Multidimensional Determinants
Gelfand, I. M., Kapranov, M. M., & Zelevinsky, A. V. (1994) · Birkhäuser Boston eBooks · doi:10.1007/978-0-8176-4771-1 · Cited by 2,306
Gromov-Witten classes, quantum cohomology, and enumerative geometry
Kontsevich, M., & Manin, Y. I. (1994) · Project Euclid (Cornell University) · Cited by 808
Solving Systems of Polynomial Equations
Sturmfels, B. (2002) · CBMS Regional Conference Series in Mathematics · doi:10.1090/cbms/097 · Cited by 792
Enumerative tropical algebraic geometry in ℝ²
Mikhalkin, G. (2005) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-05-00477-7 · Cited by 620
Self-citationGeometry of the Space of Phylogenetic Trees
Billera, L. J., Holmes, S. P., & Vogtmann, K. (2001) · Advances in Applied Mathematics · doi:10.1006/aama.2001.0759 · Cited by 611
Speyer, D. E., & Sturmfels, B. (2004) · Advances in Geometry · doi:10.1515/advg.2004.023 · Cited by 450
Affine Structures and Non-Archimedean Analytic Spaces
Kontsevich, M., & Soibelman, Y. (2007) · Progress in Mathematics · doi:10.1007/0-8176-4467-9_9 · Cited by 255
Tropical curves, their Jacobians and theta functions
Mikhalkin, G., & Zharkov, I. (2008) · Contemporary Mathematics · doi:10.1090/conm/465/09104 · Cited by 243
Self-citationLarge Complex Structure Limits of K3 Surfaces
Gross, M., & Wilson, P. M. H. (2000) · Journal of Differential Geometry · doi:10.4310/jdg/1090341262 · Cited by 242
Counting plane curves of any genus
Caporaso, L., & Harris, J. (1998) · Inventiones mathematicae · doi:10.1007/s002220050208 · Cited by 221
Cited by
Riemann–Roch and Abel–Jacobi theory on a finite graph
Baker, M., & Norine, S. (2007) · Advances in Mathematics · doi:10.1016/j.aim.2007.04.012 · Cited by 368
Metadata
- Authors
- Mikhalkin, G.
- Venue
- Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006
- Publisher
- EMS Press
- Published
- 2007-05-15
- Pages
- 827-852
- OpenAlex
- W2952603636
- Cited by
- 317
- References
- 10
- FWCI
- 93.11
- Type
- book chapter
- Language
- en
- Open access
- green
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