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University of Illinois – Chicago

1.
Sommars, Jeffrey C.
Algorithms and Implementations in Computational Algebraic * Geometry*.

Degree: 2018, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/22687

► In this thesis, we explore several areas of computational algebraic *geometry*, and develop new algorithms and software in each. We are generally interested in solving…
(more)

Subjects/Keywords: Tropical geometry; computational algebraic geometry

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APA (6^{th} Edition):

Sommars, J. C. (2018). Algorithms and Implementations in Computational Algebraic Geometry. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/22687

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Sommars, Jeffrey C. “Algorithms and Implementations in Computational Algebraic Geometry.” 2018. Thesis, University of Illinois – Chicago. Accessed October 26, 2020. http://hdl.handle.net/10027/22687.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Sommars, Jeffrey C. “Algorithms and Implementations in Computational Algebraic Geometry.” 2018. Web. 26 Oct 2020.

Vancouver:

Sommars JC. Algorithms and Implementations in Computational Algebraic Geometry. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/10027/22687.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sommars JC. Algorithms and Implementations in Computational Algebraic Geometry. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/22687

Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

2.
Lin, Bo.
Combinatorics and Computations in *Tropical* Mathematics.

Degree: Mathematics, 2017, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/7cv95652

► In recent decades, *tropical* mathematics gradually evolved as a field of study in mathematics and it has more and more interactions with other fields and…
(more)

Subjects/Keywords: Mathematics; combinatorics; computation; tropical geometry

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APA (6^{th} Edition):

Lin, B. (2017). Combinatorics and Computations in Tropical Mathematics. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7cv95652

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Lin, Bo. “Combinatorics and Computations in Tropical Mathematics.” 2017. Thesis, University of California – Berkeley. Accessed October 26, 2020. http://www.escholarship.org/uc/item/7cv95652.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Lin, Bo. “Combinatorics and Computations in Tropical Mathematics.” 2017. Web. 26 Oct 2020.

Vancouver:

Lin B. Combinatorics and Computations in Tropical Mathematics. [Internet] [Thesis]. University of California – Berkeley; 2017. [cited 2020 Oct 26]. Available from: http://www.escholarship.org/uc/item/7cv95652.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lin B. Combinatorics and Computations in Tropical Mathematics. [Thesis]. University of California – Berkeley; 2017. Available from: http://www.escholarship.org/uc/item/7cv95652

Not specified: Masters Thesis or Doctoral Dissertation

University of Alberta

3.
Cuevas Pineda, Guillermo Javier.
*Tropical**Geometry* and Kapranov's Theorem.

Degree: MS, Department of Mathematical and Statistical Sciences, 2013, University of Alberta

URL: https://era.library.ualberta.ca/files/cr494vk28j

► The *tropical* variety of a function (f=∑ c_{ux}^{u}∈ K[x_{1},∙s,x_{n}]) is the set of points (r∈ℝ^{n}) where the minimum of (\val(c_{u})+< r,u>) is attained at least…
(more)

Subjects/Keywords: Initial forms; Tropical Geometry

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APA (6^{th} Edition):

Cuevas Pineda, G. J. (2013). Tropical Geometry and Kapranov's Theorem. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/cr494vk28j

Chicago Manual of Style (16^{th} Edition):

Cuevas Pineda, Guillermo Javier. “Tropical Geometry and Kapranov's Theorem.” 2013. Masters Thesis, University of Alberta. Accessed October 26, 2020. https://era.library.ualberta.ca/files/cr494vk28j.

MLA Handbook (7^{th} Edition):

Cuevas Pineda, Guillermo Javier. “Tropical Geometry and Kapranov's Theorem.” 2013. Web. 26 Oct 2020.

Vancouver:

Cuevas Pineda GJ. Tropical Geometry and Kapranov's Theorem. [Internet] [Masters thesis]. University of Alberta; 2013. [cited 2020 Oct 26]. Available from: https://era.library.ualberta.ca/files/cr494vk28j.

Council of Science Editors:

Cuevas Pineda GJ. Tropical Geometry and Kapranov's Theorem. [Masters Thesis]. University of Alberta; 2013. Available from: https://era.library.ualberta.ca/files/cr494vk28j

Columbia University

4.
Deopurkar, Ashwin.
*Tropical**geometry* of curves with large theta characteristics.

Degree: 2017, Columbia University

URL: https://doi.org/10.7916/D8J67V6R

► In this dissertation we study tropicalization curves which have a theta characteristic with large rank. This fits in the more general framework of studying the…
(more)

Subjects/Keywords: Mathematics; Tropical geometry; Curves

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APA (6^{th} Edition):

Deopurkar, A. (2017). Tropical geometry of curves with large theta characteristics. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/D8J67V6R

Chicago Manual of Style (16^{th} Edition):

Deopurkar, Ashwin. “Tropical geometry of curves with large theta characteristics.” 2017. Doctoral Dissertation, Columbia University. Accessed October 26, 2020. https://doi.org/10.7916/D8J67V6R.

MLA Handbook (7^{th} Edition):

Deopurkar, Ashwin. “Tropical geometry of curves with large theta characteristics.” 2017. Web. 26 Oct 2020.

Vancouver:

Deopurkar A. Tropical geometry of curves with large theta characteristics. [Internet] [Doctoral dissertation]. Columbia University; 2017. [cited 2020 Oct 26]. Available from: https://doi.org/10.7916/D8J67V6R.

Council of Science Editors:

Deopurkar A. Tropical geometry of curves with large theta characteristics. [Doctoral Dissertation]. Columbia University; 2017. Available from: https://doi.org/10.7916/D8J67V6R

University of Colorado

5.
Willis, John Martin.
Topological Foundations of *Tropical* * Geometry*.

Degree: PhD, 2019, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/70

► We construct two subcanonical Grothendieck Topologies on the category of commutative, integral monoids and show that the moduli space of *tropical* curves is a…
(more)

Subjects/Keywords: algebraic geometry; monoids; topology; tropical geometry; Mathematics

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APA (6^{th} Edition):

Willis, J. M. (2019). Topological Foundations of Tropical Geometry. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/70

Chicago Manual of Style (16^{th} Edition):

Willis, John Martin. “Topological Foundations of Tropical Geometry.” 2019. Doctoral Dissertation, University of Colorado. Accessed October 26, 2020. https://scholar.colorado.edu/math_gradetds/70.

MLA Handbook (7^{th} Edition):

Willis, John Martin. “Topological Foundations of Tropical Geometry.” 2019. Web. 26 Oct 2020.

Vancouver:

Willis JM. Topological Foundations of Tropical Geometry. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2020 Oct 26]. Available from: https://scholar.colorado.edu/math_gradetds/70.

Council of Science Editors:

Willis JM. Topological Foundations of Tropical Geometry. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/math_gradetds/70

University of California – Berkeley

6.
Tran, Ngoc Mai.
Topics in *Tropical* Linear Algebra and Applied Probability.

Degree: Statistics, 2013, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/0gc3m4p1

► *Tropical* linear algebra is the study of classical linear algebra problems with arithmeticdone over the *tropical* semiring, namely with addition replaced by max, and multiplicationreplaced…
(more)

Subjects/Keywords: Statistics; Mathematics; hopfield network; size-biased permutation; tropical eigenvector; tropical geometry; tropical linear algebra

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APA (6^{th} Edition):

Tran, N. M. (2013). Topics in Tropical Linear Algebra and Applied Probability. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/0gc3m4p1

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Tran, Ngoc Mai. “Topics in Tropical Linear Algebra and Applied Probability.” 2013. Thesis, University of California – Berkeley. Accessed October 26, 2020. http://www.escholarship.org/uc/item/0gc3m4p1.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Tran, Ngoc Mai. “Topics in Tropical Linear Algebra and Applied Probability.” 2013. Web. 26 Oct 2020.

Vancouver:

Tran NM. Topics in Tropical Linear Algebra and Applied Probability. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2020 Oct 26]. Available from: http://www.escholarship.org/uc/item/0gc3m4p1.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tran NM. Topics in Tropical Linear Algebra and Applied Probability. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/0gc3m4p1

Not specified: Masters Thesis or Doctoral Dissertation

7.
Zwick, Patrick Dylan.
Variations on a theme of symmetric *tropical* matrices.

Degree: PhD, Mathematics, 2014, University of Utah

URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3287/rec/2883

► *Tropical* *geometry* connects the fields of algebraic and polyhedral *geometry*. This connection has been used to discover much simpler proofs of fundamental theorems in algebraic…
(more)

Subjects/Keywords: Algebraic geometry; Tropical geometry

…BASICS OF *TROPICAL* *GEOMETRY* AND
*TROPICAL* LINEAR ALGEBRA
*Tropical* *geometry* is a relatively new… …fundamental definitions and concepts from *tropical* *geometry*
and *tropical* linear algebra that will… …*geometry* is the book by Maclagan
and Sturmfels [13].
1.1
Ranks of *Tropical* Matrices… …basic objects of *tropical* algebra and *tropical* *geometry*.
am is a symbol, and represents a… …in
Figure 1.1.
Just as in standard algebraic *geometry*, there is a *tropical* notion of…

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APA (6^{th} Edition):

Zwick, P. D. (2014). Variations on a theme of symmetric tropical matrices. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3287/rec/2883

Chicago Manual of Style (16^{th} Edition):

Zwick, Patrick Dylan. “Variations on a theme of symmetric tropical matrices.” 2014. Doctoral Dissertation, University of Utah. Accessed October 26, 2020. http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3287/rec/2883.

MLA Handbook (7^{th} Edition):

Zwick, Patrick Dylan. “Variations on a theme of symmetric tropical matrices.” 2014. Web. 26 Oct 2020.

Vancouver:

Zwick PD. Variations on a theme of symmetric tropical matrices. [Internet] [Doctoral dissertation]. University of Utah; 2014. [cited 2020 Oct 26]. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3287/rec/2883.

Council of Science Editors:

Zwick PD. Variations on a theme of symmetric tropical matrices. [Doctoral Dissertation]. University of Utah; 2014. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3287/rec/2883

University of Oregon

8. Kutler, Max. Faithful tropicalization of hypertoric varieties.

Degree: PhD, Department of Mathematics, 2017, University of Oregon

URL: http://hdl.handle.net/1794/22756

► The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety.…
(more)

Subjects/Keywords: Hypertoric varieties; Matroids; Non-Archimedean Geometry; Tropical geometry

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APA (6^{th} Edition):

Kutler, M. (2017). Faithful tropicalization of hypertoric varieties. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/22756

Chicago Manual of Style (16^{th} Edition):

Kutler, Max. “Faithful tropicalization of hypertoric varieties.” 2017. Doctoral Dissertation, University of Oregon. Accessed October 26, 2020. http://hdl.handle.net/1794/22756.

MLA Handbook (7^{th} Edition):

Kutler, Max. “Faithful tropicalization of hypertoric varieties.” 2017. Web. 26 Oct 2020.

Vancouver:

Kutler M. Faithful tropicalization of hypertoric varieties. [Internet] [Doctoral dissertation]. University of Oregon; 2017. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/1794/22756.

Council of Science Editors:

Kutler M. Faithful tropicalization of hypertoric varieties. [Doctoral Dissertation]. University of Oregon; 2017. Available from: http://hdl.handle.net/1794/22756

9.
Katz, Brian Paul.
* Tropical* Hurwitz spaces.

Degree: PhD, Mathematics, 2011, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2011-12-4777

► Hurwitz numbers are a weighted count of degree d ramified covers of curves with specified ramification profiles at marked points on the codomain curve. Isomorphism…
(more)

Subjects/Keywords: Tropical geometry; Algebraic geometry

…*tropical* *geometry*. This introduction
establishes the basic definitions in each domain and frames… …*Tropical* *Geometry*
Algebraic *geometry* is the study of the *geometry* of a set through properties
of… …fields.
1.2.1
The *Tropical* Numbers, T
*Tropical* algebraic *geometry* is algebraic *geometry* over… …the *tropical* numbers.
To do *tropical* *geometry*, we must first define the *tropical* numbers and… …*geometry*, it should be a field. It turns out that the *tropical* numbers are not
a field because of…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Katz, B. P. (2011). Tropical Hurwitz spaces. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-12-4777

Chicago Manual of Style (16^{th} Edition):

Katz, Brian Paul. “Tropical Hurwitz spaces.” 2011. Doctoral Dissertation, University of Texas – Austin. Accessed October 26, 2020. http://hdl.handle.net/2152/ETD-UT-2011-12-4777.

MLA Handbook (7^{th} Edition):

Katz, Brian Paul. “Tropical Hurwitz spaces.” 2011. Web. 26 Oct 2020.

Vancouver:

Katz BP. Tropical Hurwitz spaces. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2011. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/2152/ETD-UT-2011-12-4777.

Council of Science Editors:

Katz BP. Tropical Hurwitz spaces. [Doctoral Dissertation]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-12-4777

The Ohio State University

10. Nash, Evan D., Nash. Extended Tropicalization of Spherical Varieties.

Degree: PhD, Mathematics, 2018, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

► The first steps in defining a notion of spherical tropicalization were recently takenby Tassos Vogiannou in his thesis and by Kiumars Kaveh and Christopher Manonin…
(more)

Subjects/Keywords: Mathematics; tropical geometry; algebraic geometry; spherical varieties; spherical homogeneous spaces

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APA (6^{th} Edition):

Nash, Evan D., N. (2018). Extended Tropicalization of Spherical Varieties. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

Chicago Manual of Style (16^{th} Edition):

Nash, Evan D., Nash. “Extended Tropicalization of Spherical Varieties.” 2018. Doctoral Dissertation, The Ohio State University. Accessed October 26, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178.

MLA Handbook (7^{th} Edition):

Nash, Evan D., Nash. “Extended Tropicalization of Spherical Varieties.” 2018. Web. 26 Oct 2020.

Vancouver:

Nash, Evan D. N. Extended Tropicalization of Spherical Varieties. [Internet] [Doctoral dissertation]. The Ohio State University; 2018. [cited 2020 Oct 26]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178.

Council of Science Editors:

Nash, Evan D. N. Extended Tropicalization of Spherical Varieties. [Doctoral Dissertation]. The Ohio State University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

11.
Chan, Melody Tung.
* Tropical* curves and metric graphs.

Degree: Mathematics, 2012, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/0nm4157r

► In just ten years, *tropical* *geometry* has established itself as an important new field bridging algebraic *geometry* and combinatorics whose techniques have been used to…
(more)

Subjects/Keywords: Mathematics; tropical curves; tropical geometry

…*tropical* *geometry* has established itself as an important new field
bridging algebraic *geometry*… …fields. *Tropical* *geometry* also has important connections
to areas as diverse as geometric group… …*tropical* *geometry*. On the one hand, it is
a “combinatorial shadow” of algebraic *geometry* [… …perspective from which *tropical* *geometry* is a tool for taking
finite snapshots of Berkovich… …perspective we take here is the perspective of *tropical* *geometry* [MS10]. From
this…

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APA (6^{th} Edition):

Chan, M. T. (2012). Tropical curves and metric graphs. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/0nm4157r

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Chan, Melody Tung. “Tropical curves and metric graphs.” 2012. Thesis, University of California – Berkeley. Accessed October 26, 2020. http://www.escholarship.org/uc/item/0nm4157r.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Chan, Melody Tung. “Tropical curves and metric graphs.” 2012. Web. 26 Oct 2020.

Vancouver:

Chan MT. Tropical curves and metric graphs. [Internet] [Thesis]. University of California – Berkeley; 2012. [cited 2020 Oct 26]. Available from: http://www.escholarship.org/uc/item/0nm4157r.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chan MT. Tropical curves and metric graphs. [Thesis]. University of California – Berkeley; 2012. Available from: http://www.escholarship.org/uc/item/0nm4157r

Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

12. Sen, Aritra. Module Grobner Bases Over Fields With Valuation.

Degree: MSc Engg, Faculty of Engineering, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2644

► *Tropical* *geometry* is an area of mathematics that interfaces algebraic *geometry* and combinatorics. The main object of study in *tropical* *geometry* is the *tropical* variety,…
(more)

Subjects/Keywords: Grobner Basis; Tropical Algebraic Geometry; Grobner Basis Theory; Hilbert Polynomials; Syzygies; Free Resolutions; Computational Geometry; Grobner Basis Computation; Algebraic Geometry; Tropical Geometry; Grobner Bases; Mathematics

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APA (6^{th} Edition):

Sen, A. (2017). Module Grobner Bases Over Fields With Valuation. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2644

Chicago Manual of Style (16^{th} Edition):

Sen, Aritra. “Module Grobner Bases Over Fields With Valuation.” 2017. Masters Thesis, Indian Institute of Science. Accessed October 26, 2020. http://etd.iisc.ac.in/handle/2005/2644.

MLA Handbook (7^{th} Edition):

Sen, Aritra. “Module Grobner Bases Over Fields With Valuation.” 2017. Web. 26 Oct 2020.

Vancouver:

Sen A. Module Grobner Bases Over Fields With Valuation. [Internet] [Masters thesis]. Indian Institute of Science; 2017. [cited 2020 Oct 26]. Available from: http://etd.iisc.ac.in/handle/2005/2644.

Council of Science Editors:

Sen A. Module Grobner Bases Over Fields With Valuation. [Masters Thesis]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2644

University of Illinois – Chicago

13. Bliss, Nathan R. Computing Series Expansions of Algebraic Space Curves.

Degree: 2018, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/22682

► We work towards a series-based computational approach for polynomial systems having positive-dimensional solution sets. The *tropical* variety gives information on the exponents of the leading…
(more)

Subjects/Keywords: computational algebraic geometry; puiseux series; gauss-newton algorithm; tropical geometry; polynomial systems; homotopy continuation

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APA (6^{th} Edition):

Bliss, N. R. (2018). Computing Series Expansions of Algebraic Space Curves. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/22682

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Thesis, University of Illinois – Chicago. Accessed October 26, 2020. http://hdl.handle.net/10027/22682.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Web. 26 Oct 2020.

Vancouver:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/10027/22682.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/22682

Not specified: Masters Thesis or Doctoral Dissertation

University of Kentucky

14.
Sawyer, Kalila Joelle.
Scrollar Invariants of *Tropical* Chains of Loops.

Degree: 2020, University of Kentucky

URL: https://uknowledge.uky.edu/math_etds/68

► We define scrollar invariants of *tropical* curves with a fixed divisor of rank 1. We examine the behavior of scrollar invariants under specialization, and compute…
(more)

Subjects/Keywords: tropical geometry; divisor theory; scrollar invariants; Maroni invariant; young tableaux; Algebraic Geometry

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APA (6^{th} Edition):

Sawyer, K. J. (2020). Scrollar Invariants of Tropical Chains of Loops. (Doctoral Dissertation). University of Kentucky. Retrieved from https://uknowledge.uky.edu/math_etds/68

Chicago Manual of Style (16^{th} Edition):

Sawyer, Kalila Joelle. “Scrollar Invariants of Tropical Chains of Loops.” 2020. Doctoral Dissertation, University of Kentucky. Accessed October 26, 2020. https://uknowledge.uky.edu/math_etds/68.

MLA Handbook (7^{th} Edition):

Sawyer, Kalila Joelle. “Scrollar Invariants of Tropical Chains of Loops.” 2020. Web. 26 Oct 2020.

Vancouver:

Sawyer KJ. Scrollar Invariants of Tropical Chains of Loops. [Internet] [Doctoral dissertation]. University of Kentucky; 2020. [cited 2020 Oct 26]. Available from: https://uknowledge.uky.edu/math_etds/68.

Council of Science Editors:

Sawyer KJ. Scrollar Invariants of Tropical Chains of Loops. [Doctoral Dissertation]. University of Kentucky; 2020. Available from: https://uknowledge.uky.edu/math_etds/68

15.
Jun, Jai Ung.
Algebraic *geometry* over semi-structures and hyper-structures of characteristic one.

Degree: 2015, Johns Hopkins University

URL: http://jhir.library.jhu.edu/handle/1774.2/37850

► In this thesis, we study algebraic *geometry* in characteristic one from the perspective of semirings and hyperrings. The thesis largely consists of three parts: (1)…
(more)

Subjects/Keywords: geometries in characteristic one; tropical geometry; semiring schemes; hyperring schemes

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APA (6^{th} Edition):

Jun, J. U. (2015). Algebraic geometry over semi-structures and hyper-structures of characteristic one. (Thesis). Johns Hopkins University. Retrieved from http://jhir.library.jhu.edu/handle/1774.2/37850

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Jun, Jai Ung. “Algebraic geometry over semi-structures and hyper-structures of characteristic one.” 2015. Thesis, Johns Hopkins University. Accessed October 26, 2020. http://jhir.library.jhu.edu/handle/1774.2/37850.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Jun, Jai Ung. “Algebraic geometry over semi-structures and hyper-structures of characteristic one.” 2015. Web. 26 Oct 2020.

Vancouver:

Jun JU. Algebraic geometry over semi-structures and hyper-structures of characteristic one. [Internet] [Thesis]. Johns Hopkins University; 2015. [cited 2020 Oct 26]. Available from: http://jhir.library.jhu.edu/handle/1774.2/37850.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jun JU. Algebraic geometry over semi-structures and hyper-structures of characteristic one. [Thesis]. Johns Hopkins University; 2015. Available from: http://jhir.library.jhu.edu/handle/1774.2/37850

Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Chicago

16.
Brasile, Andrew.
Essential Spunnormal Surfaces via *Tropical* * Geometry*.

Degree: 2013, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/10117

► Methods for finding essential surfaces in 3-manifolds have been given in several seminal papers in 3-manifold topology and *geometry*. This thesis continues in this vein…
(more)

Subjects/Keywords: spunnormal; ideal triangulation; essential surface; tropical geometry; boundary slope; deformation variety

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APA (6^{th} Edition):

Brasile, A. (2013). Essential Spunnormal Surfaces via Tropical Geometry. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/10117

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Brasile, Andrew. “Essential Spunnormal Surfaces via Tropical Geometry.” 2013. Thesis, University of Illinois – Chicago. Accessed October 26, 2020. http://hdl.handle.net/10027/10117.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Brasile, Andrew. “Essential Spunnormal Surfaces via Tropical Geometry.” 2013. Web. 26 Oct 2020.

Vancouver:

Brasile A. Essential Spunnormal Surfaces via Tropical Geometry. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/10027/10117.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brasile A. Essential Spunnormal Surfaces via Tropical Geometry. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/10117

Not specified: Masters Thesis or Doctoral Dissertation

University of Kentucky

17. Kang, Qiwen. UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES.

Degree: 2019, University of Kentucky

URL: https://uknowledge.uky.edu/statistics_etds/39

► A phylogenetic tree is a tree to represent an evolutionary history between species or other entities. Phylogenomics is a new field intersecting phylogenetics and genomics…
(more)

Subjects/Keywords: Evolutionary models; Gene trees; Phylogenomics; MCMC; Tropical geometry; Biostatistics; Statistical Methodology

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APA (6^{th} Edition):

Kang, Q. (2019). UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES. (Doctoral Dissertation). University of Kentucky. Retrieved from https://uknowledge.uky.edu/statistics_etds/39

Chicago Manual of Style (16^{th} Edition):

Kang, Qiwen. “UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES.” 2019. Doctoral Dissertation, University of Kentucky. Accessed October 26, 2020. https://uknowledge.uky.edu/statistics_etds/39.

MLA Handbook (7^{th} Edition):

Kang, Qiwen. “UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES.” 2019. Web. 26 Oct 2020.

Vancouver:

Kang Q. UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES. [Internet] [Doctoral dissertation]. University of Kentucky; 2019. [cited 2020 Oct 26]. Available from: https://uknowledge.uky.edu/statistics_etds/39.

Council of Science Editors:

Kang Q. UNSUPERVISED LEARNING IN PHYLOGENOMIC ANALYSIS OVER THE SPACE OF PHYLOGENETIC TREES. [Doctoral Dissertation]. University of Kentucky; 2019. Available from: https://uknowledge.uky.edu/statistics_etds/39

18.
Haque, Mohammad Moinul.
Realizability of *tropical* lines in the fan *tropical* plane.

Degree: PhD, Mathematics, 2013, University of Texas – Austin

URL: http://hdl.handle.net/2152/21209

► In this thesis we construct an analogue in *tropical* *geometry* for a class of Schubert varieties from classical *geometry*. In particular, we look at the…
(more)

Subjects/Keywords: Tropical geometry; Algebraic geometry; Geometry; Tropical; Deformation theory; Obstruction; Realizability

…x
58
60
61
62
64
66
69
70
71
Chapter 1
Introduction
*Tropical* *geometry* deals with the… …schemes [3]. Using *tropical* *geometry*, Mikhalkin was able to compute the same number by… …x5B;2].
4
Chapter 2
Background on *Tropical* *Geometry*
*Tropical* *geometry* is a branch… …makes *tropical* *geometry* useful for algebraic geometers, as it provides a means of gaining… …Computations of The Obstruction
57
6.1 *Tropical* Lines of Type 2A in the Fan *Tropical* Plane…

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APA (6^{th} Edition):

Haque, M. M. (2013). Realizability of tropical lines in the fan tropical plane. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/21209

Chicago Manual of Style (16^{th} Edition):

Haque, Mohammad Moinul. “Realizability of tropical lines in the fan tropical plane.” 2013. Doctoral Dissertation, University of Texas – Austin. Accessed October 26, 2020. http://hdl.handle.net/2152/21209.

MLA Handbook (7^{th} Edition):

Haque, Mohammad Moinul. “Realizability of tropical lines in the fan tropical plane.” 2013. Web. 26 Oct 2020.

Vancouver:

Haque MM. Realizability of tropical lines in the fan tropical plane. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2013. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/2152/21209.

Council of Science Editors:

Haque MM. Realizability of tropical lines in the fan tropical plane. [Doctoral Dissertation]. University of Texas – Austin; 2013. Available from: http://hdl.handle.net/2152/21209

Texas A&M University

19.
Ergur, Alperen Ali.
Sparsity, Randomness and Convexity in Applied Algebraic * Geometry*.

Degree: PhD, Mathematics, 2016, Texas A&M University

URL: http://hdl.handle.net/1969.1/157846

► In this dissertation we study three problems in applied algebraic *geometry*. The first problem is to construct an algorithmically efficient approximation to the real part…
(more)

Subjects/Keywords: convex geometric analysis; algebraic geometry; tropical geometry; condition number; random polynomials; sums of squares; semidefinite programing

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APA (6^{th} Edition):

Ergur, A. A. (2016). Sparsity, Randomness and Convexity in Applied Algebraic Geometry. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/157846

Chicago Manual of Style (16^{th} Edition):

Ergur, Alperen Ali. “Sparsity, Randomness and Convexity in Applied Algebraic Geometry.” 2016. Doctoral Dissertation, Texas A&M University. Accessed October 26, 2020. http://hdl.handle.net/1969.1/157846.

MLA Handbook (7^{th} Edition):

Ergur, Alperen Ali. “Sparsity, Randomness and Convexity in Applied Algebraic Geometry.” 2016. Web. 26 Oct 2020.

Vancouver:

Ergur AA. Sparsity, Randomness and Convexity in Applied Algebraic Geometry. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/1969.1/157846.

Council of Science Editors:

Ergur AA. Sparsity, Randomness and Convexity in Applied Algebraic Geometry. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/157846

Freie Universität Berlin

20. Castillejo Blasco, Pedro Ángel. Die Topologie der konjugierten Berkovich-Räume.

Degree: 2020, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-27448

► We want to understand how the topology of Berkovich spaces varies when we conjugate the non-archimedean base field. After a short introduction with a discussion…
(more)

Subjects/Keywords: arithmetic geometric; non-archimedean geometry; tropical geometry; topology; Berkovich spaces; ddc:512; ddc:513; ddc:516

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APA (6^{th} Edition):

Castillejo Blasco, P. . (2020). Die Topologie der konjugierten Berkovich-Räume. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-27448

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Castillejo Blasco, Pedro Ángel. “Die Topologie der konjugierten Berkovich-Räume.” 2020. Thesis, Freie Universität Berlin. Accessed October 26, 2020. http://dx.doi.org/10.17169/refubium-27448.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Castillejo Blasco, Pedro Ángel. “Die Topologie der konjugierten Berkovich-Räume.” 2020. Web. 26 Oct 2020.

Vancouver:

Castillejo Blasco P. Die Topologie der konjugierten Berkovich-Räume. [Internet] [Thesis]. Freie Universität Berlin; 2020. [cited 2020 Oct 26]. Available from: http://dx.doi.org/10.17169/refubium-27448.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Castillejo Blasco P. Die Topologie der konjugierten Berkovich-Räume. [Thesis]. Freie Universität Berlin; 2020. Available from: http://dx.doi.org/10.17169/refubium-27448

Not specified: Masters Thesis or Doctoral Dissertation

21.
El Hilany, Boulos.
Géométrie tropicale et systèmes polynomiaux : *Tropical* *geometry* and polynomial systems.

Degree: Docteur es, Mathématiques, 2016, Université Grenoble Alpes (ComUE)

URL: http://www.theses.fr/2016GREAM037

► Les systèmes polynomiaux réels sont omniprésents dans de nombreux domaines des mathématiques pures et appliquées. A. Khovanskii a fourni une borne fewnomiale supérieure sur le…
(more)

Subjects/Keywords: Géométrie Algébrique Réelle; Théorie des Fewnomials; Géométrie Tropicale; Systèmes Polynomiaux; Real Algebraic Geometry; Theory of Fewnomials; Tropical Geometry; Polynomial Systems; 516

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APA (6^{th} Edition):

El Hilany, B. (2016). Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2016GREAM037

Chicago Manual of Style (16^{th} Edition):

El Hilany, Boulos. “Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems.” 2016. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed October 26, 2020. http://www.theses.fr/2016GREAM037.

MLA Handbook (7^{th} Edition):

El Hilany, Boulos. “Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems.” 2016. Web. 26 Oct 2020.

Vancouver:

El Hilany B. Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2016. [cited 2020 Oct 26]. Available from: http://www.theses.fr/2016GREAM037.

Council of Science Editors:

El Hilany B. Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2016. Available from: http://www.theses.fr/2016GREAM037

University of California – Berkeley

22.
Cueto, Maria Angelica.
* Tropical* implicitization.

Degree: Mathematics, 2010, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/7d6845sr

► In recent years, *tropical* *geometry* has developed as a theory on its own. Its two main aims are to answer open questions in algebraic *geometry*…
(more)

Subjects/Keywords: Mathematics; algebraic statistics; geometric tropicalization; Hadamard products; Newton polytope; secant varieties; tropical geometry

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APA (6^{th} Edition):

Cueto, M. A. (2010). Tropical implicitization. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7d6845sr

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Cueto, Maria Angelica. “Tropical implicitization.” 2010. Thesis, University of California – Berkeley. Accessed October 26, 2020. http://www.escholarship.org/uc/item/7d6845sr.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Cueto, Maria Angelica. “Tropical implicitization.” 2010. Web. 26 Oct 2020.

Vancouver:

Cueto MA. Tropical implicitization. [Internet] [Thesis]. University of California – Berkeley; 2010. [cited 2020 Oct 26]. Available from: http://www.escholarship.org/uc/item/7d6845sr.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cueto MA. Tropical implicitization. [Thesis]. University of California – Berkeley; 2010. Available from: http://www.escholarship.org/uc/item/7d6845sr

Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

23.
Alfarra, Motasem.
Applications of *Tropical* *Geometry* in Deep Neural Networks.

Degree: 2020, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/662473

► This thesis tackles the problem of understanding deep neural network with piece- wise linear activation functions. We leverage *tropical* *geometry*, a relatively new field in…
(more)

Subjects/Keywords: Deep Learning; Deep Neural Networks; Tropical Geometry; Network Pruning; Lottery Ticket Hypothesis; Adversarial Attacks

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APA (6^{th} Edition):

Alfarra, M. (2020). Applications of Tropical Geometry in Deep Neural Networks. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/662473

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Alfarra, Motasem. “Applications of Tropical Geometry in Deep Neural Networks.” 2020. Thesis, King Abdullah University of Science and Technology. Accessed October 26, 2020. http://hdl.handle.net/10754/662473.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Alfarra, Motasem. “Applications of Tropical Geometry in Deep Neural Networks.” 2020. Web. 26 Oct 2020.

Vancouver:

Alfarra M. Applications of Tropical Geometry in Deep Neural Networks. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2020. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/10754/662473.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alfarra M. Applications of Tropical Geometry in Deep Neural Networks. [Thesis]. King Abdullah University of Science and Technology; 2020. Available from: http://hdl.handle.net/10754/662473

Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

24.
Vinzant, Cynthia Leslie.
Real Algebraic *Geometry* in Convex Optimization.

Degree: Mathematics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/5dt9t63z

► In the past twenty years, a strong interplay has developed between convex optimization and algebraic *geometry*. Algebraic *geometry* provides necessary tools to analyze the behavior…
(more)

Subjects/Keywords: Mathematics; Applied Mathematics; central paths; convex hulls of curves; quartic plane curves; real tropical geometry; semidefinite programming; sums of squares

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APA (6^{th} Edition):

Vinzant, C. L. (2011). Real Algebraic Geometry in Convex Optimization. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/5dt9t63z

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Vinzant, Cynthia Leslie. “Real Algebraic Geometry in Convex Optimization.” 2011. Thesis, University of California – Berkeley. Accessed October 26, 2020. http://www.escholarship.org/uc/item/5dt9t63z.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Vinzant, Cynthia Leslie. “Real Algebraic Geometry in Convex Optimization.” 2011. Web. 26 Oct 2020.

Vancouver:

Vinzant CL. Real Algebraic Geometry in Convex Optimization. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2020 Oct 26]. Available from: http://www.escholarship.org/uc/item/5dt9t63z.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Vinzant CL. Real Algebraic Geometry in Convex Optimization. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/5dt9t63z

Not specified: Masters Thesis or Doctoral Dissertation

Brigham Young University

25.
Ellis, Amanda.
Classifcation of Conics in the *Tropical* Projective Plane.

Degree: MS, 2005, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1696&context=etd

► This paper defines *tropical* projective space, TP^n, and the *tropical* general linear group TPGL(n). After discussing some simple examples of *tropical* polynomials and their hypersurfaces,…
(more)

Subjects/Keywords: tropical; algebraic geometry; convex hull; conics; Mathematics

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APA (6^{th} Edition):

Ellis, A. (2005). Classifcation of Conics in the Tropical Projective Plane. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1696&context=etd

Chicago Manual of Style (16^{th} Edition):

Ellis, Amanda. “Classifcation of Conics in the Tropical Projective Plane.” 2005. Masters Thesis, Brigham Young University. Accessed October 26, 2020. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1696&context=etd.

MLA Handbook (7^{th} Edition):

Ellis, Amanda. “Classifcation of Conics in the Tropical Projective Plane.” 2005. Web. 26 Oct 2020.

Vancouver:

Ellis A. Classifcation of Conics in the Tropical Projective Plane. [Internet] [Masters thesis]. Brigham Young University; 2005. [cited 2020 Oct 26]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1696&context=etd.

Council of Science Editors:

Ellis A. Classifcation of Conics in the Tropical Projective Plane. [Masters Thesis]. Brigham Young University; 2005. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1696&context=etd

26. Lin, Yu-Shen. Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing.

Degree: 2013, Harvard University

URL: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11158239

We defined a new type of open Gromov-Witten invariants on hyperKäher manifolds with holomorphic

Mathematics

Subjects/Keywords: Mathematics; Gromov-Witten; tropical geometry; Wall-Crossing

…*tropical* *geometry* and holomorphic *geometry*. We will present an non-trivial example of wall… …to learn algebraic *geometry*
from Professor Jung-Kai Chen and it is Professor I-Hsun Tsai… …conjecture. They incorporated the
instanton problems of complex structure with the *tropical*… …*geometry*.
Inspiring by closed topological string theory, Gromov-Witten theory is
a useful tool in… …probing algebraic *geometry*/ symplectic *geometry* and produces interesting enumerative invariants…

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APA (6^{th} Edition):

Lin, Y. (2013). Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing. (Thesis). Harvard University. Retrieved from http://nrs.harvard.edu/urn-3:HUL.InstRepos:11158239

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Lin, Yu-Shen. “Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing.” 2013. Thesis, Harvard University. Accessed October 26, 2020. http://nrs.harvard.edu/urn-3:HUL.InstRepos:11158239.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Lin, Yu-Shen. “Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing.” 2013. Web. 26 Oct 2020.

Vancouver:

Lin Y. Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing. [Internet] [Thesis]. Harvard University; 2013. [cited 2020 Oct 26]. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11158239.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lin Y. Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing. [Thesis]. Harvard University; 2013. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11158239

Not specified: Masters Thesis or Doctoral Dissertation

Freie Universität Berlin

27. Olarte, Jorge Alberto. Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven.

Degree: 2020, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-26531

► This thesis studies three particular types polytopal subdivisions with concrete applica- tions to other mathematical objects, particularly in algebraic *geometry*. The first type of polytopal…
(more)

Subjects/Keywords: Polytopal subdivisions; Grassmannians; tropical linear spaces; Harnack curves; 500 Natural sciences and mathematics::510 Mathematics::516 Geometry

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APA (6^{th} Edition):

Olarte, J. A. (2020). Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-26531

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Olarte, Jorge Alberto. “Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven.” 2020. Thesis, Freie Universität Berlin. Accessed October 26, 2020. http://dx.doi.org/10.17169/refubium-26531.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Olarte, Jorge Alberto. “Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven.” 2020. Web. 26 Oct 2020.

Vancouver:

Olarte JA. Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven. [Internet] [Thesis]. Freie Universität Berlin; 2020. [cited 2020 Oct 26]. Available from: http://dx.doi.org/10.17169/refubium-26531.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Olarte JA. Polytopen-Unterteilungen in Grassmannschen, tropische Geometrie und algebraische Kurven. [Thesis]. Freie Universität Berlin; 2020. Available from: http://dx.doi.org/10.17169/refubium-26531

Not specified: Masters Thesis or Doctoral Dissertation

Georgia Tech

28. Backman, Spencer Christopher Foster. Combinatorial divisor theory for graphs.

Degree: PhD, Mathematics, 2014, Georgia Tech

URL: http://hdl.handle.net/1853/51908

► Chip-firing is a deceptively simple game played on the vertices of a graph, which was independently discovered in probability theory, poset theory, graph theory, and…
(more)

Subjects/Keywords: Chip-firing; Graph; Tropical curve; Riemann-Roch; Orientation; Divisor theory; Combinatorial analysis; Graph theory; Geometry, Algebraic; Number theory

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APA (6^{th} Edition):

Backman, S. C. F. (2014). Combinatorial divisor theory for graphs. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/51908

Chicago Manual of Style (16^{th} Edition):

Backman, Spencer Christopher Foster. “Combinatorial divisor theory for graphs.” 2014. Doctoral Dissertation, Georgia Tech. Accessed October 26, 2020. http://hdl.handle.net/1853/51908.

MLA Handbook (7^{th} Edition):

Backman, Spencer Christopher Foster. “Combinatorial divisor theory for graphs.” 2014. Web. 26 Oct 2020.

Vancouver:

Backman SCF. Combinatorial divisor theory for graphs. [Internet] [Doctoral dissertation]. Georgia Tech; 2014. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/1853/51908.

Council of Science Editors:

Backman SCF. Combinatorial divisor theory for graphs. [Doctoral Dissertation]. Georgia Tech; 2014. Available from: http://hdl.handle.net/1853/51908

29. Peabody, Jamie. The GIT fan for a Mori dream space and the μ-secondary polytope.

Degree: PhD, Department of Mathematics, 2019, Kansas State University

URL: http://hdl.handle.net/2097/40016

► Geometric invariant theory (GIT) was developed by Mumford as a method for constructing quotients by group actions in the context of algebraic *geometry*. This construction…
(more)

Subjects/Keywords: Geometric invariant theory; Mori dream spaces; Tropical geometry; Toric geometry

…*tropical* *geometry*, following
the conventions in [MS15]. A process called… …*tropical* *geometry*, questions
about algebraic varieties can be translated into questions about… …with chambers labeled by the corresponding triangulation
21
3.1
Examples of *tropical*… …x5B;MFK94] and studies quotients by group actions in the context of algebraic *geometry*… …because they have a nice combinatorial description. The *geometry* of a toric
variety is…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Peabody, J. (2019). The GIT fan for a Mori dream space and the μ-secondary polytope. (Doctoral Dissertation). Kansas State University. Retrieved from http://hdl.handle.net/2097/40016

Chicago Manual of Style (16^{th} Edition):

Peabody, Jamie. “The GIT fan for a Mori dream space and the μ-secondary polytope.” 2019. Doctoral Dissertation, Kansas State University. Accessed October 26, 2020. http://hdl.handle.net/2097/40016.

MLA Handbook (7^{th} Edition):

Peabody, Jamie. “The GIT fan for a Mori dream space and the μ-secondary polytope.” 2019. Web. 26 Oct 2020.

Vancouver:

Peabody J. The GIT fan for a Mori dream space and the μ-secondary polytope. [Internet] [Doctoral dissertation]. Kansas State University; 2019. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/2097/40016.

Council of Science Editors:

Peabody J. The GIT fan for a Mori dream space and the μ-secondary polytope. [Doctoral Dissertation]. Kansas State University; 2019. Available from: http://hdl.handle.net/2097/40016

30.
Diemer, Colin.
The Birational *Geometry* of *Tropical* Compactifications.

Degree: 2010, University of Pennsylvania

URL: https://repository.upenn.edu/edissertations/96

► We study compactifications of subvarieties of algebraic tori using methods from the still developing *subject* of *tropical* *geometry*. Associated to each ``*tropical*" compactification is a…
(more)

Subjects/Keywords: Tropical; Birational; Compactifications; Algebraic Geometry; Toric Varieties; Log Geometry; Algebraic Geometry

…*Geometry*
In this chapter we review the theory of *tropical* compactifications, introduced in
[… …foundations of the subject of *tropical* *geometry* as a whole, and instead focus only on constructions… …*geometry*, or also the in progress
draft of a textbook on *tropical* *geometry* by Maclagan and… …assume knowl4
edge of basic algebraic *geometry*, and may introduce definitions and basic… …divisor if and only if each irreducible component
of D is smooth.
5
Chapter 1
*Tropical*…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Diemer, C. (2010). The Birational Geometry of Tropical Compactifications. (Thesis). University of Pennsylvania. Retrieved from https://repository.upenn.edu/edissertations/96

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Diemer, Colin. “The Birational Geometry of Tropical Compactifications.” 2010. Thesis, University of Pennsylvania. Accessed October 26, 2020. https://repository.upenn.edu/edissertations/96.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Diemer, Colin. “The Birational Geometry of Tropical Compactifications.” 2010. Web. 26 Oct 2020.

Vancouver:

Diemer C. The Birational Geometry of Tropical Compactifications. [Internet] [Thesis]. University of Pennsylvania; 2010. [cited 2020 Oct 26]. Available from: https://repository.upenn.edu/edissertations/96.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Diemer C. The Birational Geometry of Tropical Compactifications. [Thesis]. University of Pennsylvania; 2010. Available from: https://repository.upenn.edu/edissertations/96

Not specified: Masters Thesis or Doctoral Dissertation