subject:(Geometry )

California State Polytechnic University – Pomona

1. Trendt, Jacqueline Christine. Building the Language of Geometry Through the Use of Examples and Non-Examples.

Degree: MS, Mathematics, 2014, California State Polytechnic University – Pomona

URL: http://hdl.handle.net/10211.3/123923

► In this study we examine definitions of seven geometric concepts constructed by groups of pre-service elementary school teachers through the use of examples and nonexamples.… (more)

Subjects/Keywords: geometry

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APA (6^th Edition):

Trendt, J. C. (2014). Building the Language of Geometry Through the Use of Examples and Non-Examples. (Masters Thesis). California State Polytechnic University – Pomona. Retrieved from http://hdl.handle.net/10211.3/123923

Chicago Manual of Style (16^th Edition):

Trendt, Jacqueline Christine. “Building the Language of Geometry Through the Use of Examples and Non-Examples.” 2014. Masters Thesis, California State Polytechnic University – Pomona. Accessed March 03, 2021. http://hdl.handle.net/10211.3/123923.

MLA Handbook (7^th Edition):

Trendt, Jacqueline Christine. “Building the Language of Geometry Through the Use of Examples and Non-Examples.” 2014. Web. 03 Mar 2021.

Vancouver:

Trendt JC. Building the Language of Geometry Through the Use of Examples and Non-Examples. [Internet] [Masters thesis]. California State Polytechnic University – Pomona; 2014. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/10211.3/123923.

Council of Science Editors:

Trendt JC. Building the Language of Geometry Through the Use of Examples and Non-Examples. [Masters Thesis]. California State Polytechnic University – Pomona; 2014. Available from: http://hdl.handle.net/10211.3/123923

University of California – Berkeley

2. McMillan, Aaron Fraenkel. On Embedding Singular Poisson Spaces.

Degree: Mathematics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/6xz306q4

► This dissertation investigates the problem of locally embedding singular Poisson spaces. Specifically, it seeks to understand when a singular symplectic quotient V/G of a symplectic… (more)

Subjects/Keywords: Mathematics; Poisson geometry; Symplectic geometry

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APA (6^th Edition):

McMillan, A. F. (2011). On Embedding Singular Poisson Spaces. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/6xz306q4

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):

McMillan, Aaron Fraenkel. “On Embedding Singular Poisson Spaces.” 2011. Thesis, University of California – Berkeley. Accessed March 03, 2021. http://www.escholarship.org/uc/item/6xz306q4.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

McMillan, Aaron Fraenkel. “On Embedding Singular Poisson Spaces.” 2011. Web. 03 Mar 2021.

Vancouver:

McMillan AF. On Embedding Singular Poisson Spaces. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2021 Mar 03]. Available from: http://www.escholarship.org/uc/item/6xz306q4.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McMillan AF. On Embedding Singular Poisson Spaces. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/6xz306q4

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Rochester

3. Cho, Hyunjoo. Existence of almost contact structures on manifolds with G2-structures and generalizations.

Degree: PhD, 2012, University of Rochester

URL: http://hdl.handle.net/1802/21273

► This dissertation consists of two main results. First, we investigate the relationship between almost contact structures and G2-structures on seven-dimensional Riemannian manifolds: we show that… (more)

Subjects/Keywords: Differential geometry; Symplectic geometry

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APA (6^th Edition):

Cho, H. (2012). Existence of almost contact structures on manifolds with G2-structures and generalizations. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/21273

Chicago Manual of Style (16^th Edition):

Cho, Hyunjoo. “Existence of almost contact structures on manifolds with G2-structures and generalizations.” 2012. Doctoral Dissertation, University of Rochester. Accessed March 03, 2021. http://hdl.handle.net/1802/21273.

MLA Handbook (7^th Edition):

Cho, Hyunjoo. “Existence of almost contact structures on manifolds with G2-structures and generalizations.” 2012. Web. 03 Mar 2021.

Vancouver:

Cho H. Existence of almost contact structures on manifolds with G2-structures and generalizations. [Internet] [Doctoral dissertation]. University of Rochester; 2012. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/1802/21273.

Council of Science Editors:

Cho H. Existence of almost contact structures on manifolds with G2-structures and generalizations. [Doctoral Dissertation]. University of Rochester; 2012. Available from: http://hdl.handle.net/1802/21273

Columbia University

4. Osinenko, Anton. The two-legged K-theoretic equivariant vertex.

Degree: 2019, Columbia University

URL: https://doi.org/10.7916/d8-ze3v-0g40

► In this work we study K-theoretic Donaldson-Thomas theory. We derive an explicit formula for the capped vertex with two legs in a certain gauge. Using… (more)

Subjects/Keywords: Mathematics; Geometry; Geometry, Enumerative

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APA (6^th Edition):

Osinenko, A. (2019). The two-legged K-theoretic equivariant vertex. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-ze3v-0g40

Chicago Manual of Style (16^th Edition):

Osinenko, Anton. “The two-legged K-theoretic equivariant vertex.” 2019. Doctoral Dissertation, Columbia University. Accessed March 03, 2021. https://doi.org/10.7916/d8-ze3v-0g40.

MLA Handbook (7^th Edition):

Osinenko, Anton. “The two-legged K-theoretic equivariant vertex.” 2019. Web. 03 Mar 2021.

Vancouver:

Osinenko A. The two-legged K-theoretic equivariant vertex. [Internet] [Doctoral dissertation]. Columbia University; 2019. [cited 2021 Mar 03]. Available from: https://doi.org/10.7916/d8-ze3v-0g40.

Council of Science Editors:

Osinenko A. The two-legged K-theoretic equivariant vertex. [Doctoral Dissertation]. Columbia University; 2019. Available from: https://doi.org/10.7916/d8-ze3v-0g40

University of Adelaide

5. Marshall, Daniel. Conics, unitals and net replacement.

Degree: 2010, University of Adelaide

URL: http://hdl.handle.net/2440/61625

► The main concerns of this thesis are inherited unitals and conics in finite translation planes. Translation planes may be constructed from particular incidences in other… (more)

▼ The main concerns of this thesis are inherited unitals and conics in finite translation planes. Translation planes may be constructed from particular incidences in other translation planes. One method for doing this is "net-derivation" or the corresponding operation "net replacement". We consider conics and unitals of the finite projective plane PG(2,q²) and observe the effect of net-derivation on their pointsets. Our aim is to determine when the pointsets of conics and unitals of PG(2,q²) are conics and unitals respectively in the translation planes formed after net-derivation. In particular, we focus on t-nest replacement and the corresponding nest-derivation sets. Chapter one introduces all the necessary background on finite affine and projective planes. We consider all relevant substructures and concepts. Of major importance are the definitions of unitals, quadrics, Baer subplanes, Baer sublines and derivation. Chapter two introduces the Bruck-Bose correspondence. We use the Bruck-Bose correspondence extensively in chapters three and four. The Bruck-Bose correspondence is a correspondence between PG(2,q²) and certain incidences in PG(4,q). The key elements are spreads of PG(3,q) as a subspace of PG(4,q). We also detail the known correspondences for Baer sublines, Baer subplanes and unitals as well as the equivalent operation for derivation. Chapter three is where we begin our main work. Here we define net replacement in spreads and show the equivalence to net-derivation sets in PG(2,q²). We look at t-nests in depth, which are an example of net replacement. We prove several known results as well as a host of new geometric and combinatorial properties about t-nests. We show a detailed example of a known t-nest and also define a particular type of replacement set that is common to most t-nests. We finish with examples of different kinds of net-derivation. Chapter four looks at unitals of PG(2,q²) and the effect of general net-derivation. Given a unital of PG(2,q²), suppose we perform net-derivation in PG(2,q²) to form a new translation plane. Can we complete the affine points of the unital to a unital in the new translation plane? We first detail the known results for unitals and derivation. We then prove results for unitals and general net-derivation for all known cases where the net-derivation set lies on l8. The particular case for t-nests was published separately by the author in [9]. We prove a new result for when the net-derivation set is not on l8 which is also a new result when just considering derivation. Next, we generalise several other results about derivation and unitals to include general net-derivation. We show the existence of non-inherited unitals in translation planes formed by t-nest replacement of a type that are not present in translation planes formed by derivation. We finish by considering O'Nan configurations contained in unitals in PG(2,q²) and planes formed by net-derivation. Chapter five considers conics and the effect of multiple derivation. Given a conic of PG(2,q²), suppose we… Advisors/Committee Members: Barwick, Susan Gay (advisor), Quinn, Catherine (advisor), Brown, Matthew (advisor), Wolff, Alison (advisor), Casse, Rey (advisor), School of Mathematical Sciences : Pure Mathematics (school).

Subjects/Keywords: finite geometry; projective geometry

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APA (6^th Edition):

Marshall, D. (2010). Conics, unitals and net replacement. (Thesis). University of Adelaide. Retrieved from http://hdl.handle.net/2440/61625

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):

Marshall, Daniel. “Conics, unitals and net replacement.” 2010. Thesis, University of Adelaide. Accessed March 03, 2021. http://hdl.handle.net/2440/61625.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Marshall, Daniel. “Conics, unitals and net replacement.” 2010. Web. 03 Mar 2021.

Vancouver:

Marshall D. Conics, unitals and net replacement. [Internet] [Thesis]. University of Adelaide; 2010. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/2440/61625.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Marshall D. Conics, unitals and net replacement. [Thesis]. University of Adelaide; 2010. Available from: http://hdl.handle.net/2440/61625

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Chicago

6. 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 March 03, 2021. 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. 03 Mar 2021.

Vancouver:

Sommars JC. Algorithms and Implementations in Computational Algebraic Geometry. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2021 Mar 03]. 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

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oxford

7. Saratchandran, Hemanth. Four dimensional hyperbolic link complements via Kirby calculus.

Degree: PhD, 2015, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647681

► The primary aim of this thesis is to construct explicit examples of four dimensional hyperbolic link complements. Using the theory of Kirby diagrams and Kirby… (more)

Subjects/Keywords: 514; Geometry; hyperbolic geometry

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APA (6^th Edition):

Saratchandran, H. (2015). Four dimensional hyperbolic link complements via Kirby calculus. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647681

Chicago Manual of Style (16^th Edition):

Saratchandran, Hemanth. “Four dimensional hyperbolic link complements via Kirby calculus.” 2015. Doctoral Dissertation, University of Oxford. Accessed March 03, 2021. http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647681.

MLA Handbook (7^th Edition):

Saratchandran, Hemanth. “Four dimensional hyperbolic link complements via Kirby calculus.” 2015. Web. 03 Mar 2021.

Vancouver:

Saratchandran H. Four dimensional hyperbolic link complements via Kirby calculus. [Internet] [Doctoral dissertation]. University of Oxford; 2015. [cited 2021 Mar 03]. Available from: http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647681.

Council of Science Editors:

Saratchandran H. Four dimensional hyperbolic link complements via Kirby calculus. [Doctoral Dissertation]. University of Oxford; 2015. Available from: http://ora.ox.ac.uk/objects/uuid:ba72ee75-c22f-4800-a38c-76e5cf411ad9 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647681

University of Toronto

8. Uren, James. Toric Varieties Associated with Moduli Spaces.

Degree: 2011, University of Toronto

URL: http://hdl.handle.net/1807/31960

►

Any genus g surface, Σ_g,n, with n boundary components may be given a trinion decomposition: a realization of the surface as a union of 2g-2+n… (more)

Subjects/Keywords: Symplectic Geometry; Toric Geometry; 0405

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APA (6^th Edition):

Uren, J. (2011). Toric Varieties Associated with Moduli Spaces. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/31960

Chicago Manual of Style (16^th Edition):

Uren, James. “Toric Varieties Associated with Moduli Spaces.” 2011. Doctoral Dissertation, University of Toronto. Accessed March 03, 2021. http://hdl.handle.net/1807/31960.

MLA Handbook (7^th Edition):

Uren, James. “Toric Varieties Associated with Moduli Spaces.” 2011. Web. 03 Mar 2021.

Vancouver:

Uren J. Toric Varieties Associated with Moduli Spaces. [Internet] [Doctoral dissertation]. University of Toronto; 2011. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/1807/31960.

Council of Science Editors:

Uren J. Toric Varieties Associated with Moduli Spaces. [Doctoral Dissertation]. University of Toronto; 2011. Available from: http://hdl.handle.net/1807/31960

Louisiana State University

9. Jegart, Damayanthi Srimathi. Unit assessments for high school geometry.

Degree: MNS, Physical Sciences and Mathematics, 2012, Louisiana State University

URL: etd-07052012-115636 ; https://digitalcommons.lsu.edu/gradschool_theses/3055

► Abstract Eight unit tests closely aligned with the Louisiana Comprehensive Curriculum for high school geometry were developed. Five of these were administered, each to the… (more)

Subjects/Keywords: History of Geometry; Geometry Tests

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APA (6^th Edition):

Jegart, D. S. (2012). Unit assessments for high school geometry. (Masters Thesis). Louisiana State University. Retrieved from etd-07052012-115636 ; https://digitalcommons.lsu.edu/gradschool_theses/3055

Chicago Manual of Style (16^th Edition):

Jegart, Damayanthi Srimathi. “Unit assessments for high school geometry.” 2012. Masters Thesis, Louisiana State University. Accessed March 03, 2021. etd-07052012-115636 ; https://digitalcommons.lsu.edu/gradschool_theses/3055.

MLA Handbook (7^th Edition):

Jegart, Damayanthi Srimathi. “Unit assessments for high school geometry.” 2012. Web. 03 Mar 2021.

Vancouver:

Jegart DS. Unit assessments for high school geometry. [Internet] [Masters thesis]. Louisiana State University; 2012. [cited 2021 Mar 03]. Available from: etd-07052012-115636 ; https://digitalcommons.lsu.edu/gradschool_theses/3055.

Council of Science Editors:

Jegart DS. Unit assessments for high school geometry. [Masters Thesis]. Louisiana State University; 2012. Available from: etd-07052012-115636 ; https://digitalcommons.lsu.edu/gradschool_theses/3055

University of Oklahoma

10. BYUN, TAECHANG. HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n.

Degree: PhD, 2011, University of Oklahoma

URL: http://hdl.handle.net/11244/318678

► The Riemannian submersion π : SO₀(1,n) ->Hⁿ is a principal bundle and its fiber at π (e) is the imbedding of SO(n) into SO₀(1,n) ,… (more)

Subjects/Keywords: Conformal geometry; Geometry, Differential

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APA (6^th Edition):

BYUN, T. (2011). HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/318678

Chicago Manual of Style (16^th Edition):

BYUN, TAECHANG. “HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n.” 2011. Doctoral Dissertation, University of Oklahoma. Accessed March 03, 2021. http://hdl.handle.net/11244/318678.

MLA Handbook (7^th Edition):

BYUN, TAECHANG. “HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n.” 2011. Web. 03 Mar 2021.

Vancouver:

BYUN T. HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n. [Internet] [Doctoral dissertation]. University of Oklahoma; 2011. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/11244/318678.

Council of Science Editors:

BYUN T. HOLONOMY DISPLACEMENT OF CURVES IN BUNDLE SO(N)->SO_0(1,N)->H^n. [Doctoral Dissertation]. University of Oklahoma; 2011. Available from: http://hdl.handle.net/11244/318678

University of Cambridge

11. Xu, Yanning. Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties.

Degree: PhD, 2020, University of Cambridge

URL: https://doi.org/10.17863/CAM.58891 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.818201

► This thesis aims to generalise the theory of complements to log canonical Fano varieties and relate theory of complements to the index conjecture of log… (more)

Subjects/Keywords: Algebraic Geometry; Birational Geometry; Mathematics

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APA (6^th Edition):

Xu, Y. (2020). Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.58891 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.818201

Chicago Manual of Style (16^th Edition):

Xu, Yanning. “Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties.” 2020. Doctoral Dissertation, University of Cambridge. Accessed March 03, 2021. https://doi.org/10.17863/CAM.58891 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.818201.

MLA Handbook (7^th Edition):

Xu, Yanning. “Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties.” 2020. Web. 03 Mar 2021.

Vancouver:

Xu Y. Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties. [Internet] [Doctoral dissertation]. University of Cambridge; 2020. [cited 2021 Mar 03]. Available from: https://doi.org/10.17863/CAM.58891 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.818201.

Council of Science Editors:

Xu Y. Complements on log canonical Fano varieties and index conjecture of Log Calabi-Yau varieties. [Doctoral Dissertation]. University of Cambridge; 2020. Available from: https://doi.org/10.17863/CAM.58891 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.818201

University of Cambridge

12. Xu, Yanning. Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties.

Degree: PhD, 2020, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/311801

► This thesis aims to generalise the theory of complements to log canonical Fano varieties and relate theory of complements to the index conjecture of log… (more)

Subjects/Keywords: Algebraic Geometry; Birational Geometry; Mathematics

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APA (6^th Edition):

Xu, Y. (2020). Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/311801

Chicago Manual of Style (16^th Edition):

Xu, Yanning. “Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties.” 2020. Doctoral Dissertation, University of Cambridge. Accessed March 03, 2021. https://www.repository.cam.ac.uk/handle/1810/311801.

MLA Handbook (7^th Edition):

Xu, Yanning. “Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties.” 2020. Web. 03 Mar 2021.

Vancouver:

Xu Y. Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties. [Internet] [Doctoral dissertation]. University of Cambridge; 2020. [cited 2021 Mar 03]. Available from: https://www.repository.cam.ac.uk/handle/1810/311801.

Council of Science Editors:

Xu Y. Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties. [Doctoral Dissertation]. University of Cambridge; 2020. Available from: https://www.repository.cam.ac.uk/handle/1810/311801

Rutgers University

13. Shabbir, Mudassir. Some results in computational and combinatorial geometry.

Degree: PhD, Computer Science, 2014, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/45458/

►

In this thesis we present some new results in the field of discrete and computational geometry. The techniques and tools developed to achieve these results… (more)

▼

In this thesis we present some new results in the field of discrete and computational geometry. The techniques and tools developed to achieve these results add to our understanding of important geometric objects like line arrangements, and geometric measures of depth. Given a set S of n points, a {em weak ε-net} X is a set of points (not necessarily in S) such that any convex set, called a range, that contains more than an ε fraction of S must meet X for a fixed eps>0 . Aronov {em et al.} gave the first bounds on eps when the cardinality of X is a fixed small number in the plane. Later Mustafa and Ray proved that |X|=2 can be chosen so that we hit all convex ranges that contain 4n/7 points of S. We describe an O(nlog⁴ n) time algorithm to find points z₁ ot = z₂, at least one of which must meet any convex set of ``size'' greater than 4n/7; z₁ and z₂ comprise a hitting set of size two for such convex ranges. This is the first algorithm for computing the hitting sets of fixed size. Data-depth measures are real valued functions that are defined on the points of Re^d with respect to a given set S in Re^d. They are helpful in nonparametric statistical analysis by partitioning the space in a center-outwardly fashion. We introduced a new framework to study many well-known data-depth measures in a uniform way. We define and provide first bounds for {em line-depth} and show how it bridges the relation among Tukey-depth, simplicial-depth, and ray-shooting depth measures in Re³. We also develop the first algorithm to efficiently compute a point of {em high} ray-shooting depth in the plane. Faults and viruses often spread in the networked environments by propagating from a site to neighboring site. We model this process of {em network contamination} by using graphs. Consider a graph G=(V,E), whose vertex set is contaminated. Our goal is to decontaminate the set V(G) using the mobile agents that move along the edge set of G. The {em temporal immunity }au(G) ge 0 is defined as the time that a decontaminated vertex of G can remain continuously exposed to a contaminated neighbor without getting infected itself. We study the lower and upper bounds on the temporal immunity required to decontaminate some classes of graphs - mostly geometric - that correspond to some well-known network topologies, and we present an upper bounds on ι₁(G), in some cases with matching lower bounds.

Advisors/Committee Members: Steiger, William (chair), Kahn, Jeffry (internal member), Szegedy, Mario (internal member), Aronov, Boris (outside member).

Subjects/Keywords: Discrete geometry; Computational geometry

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APA (6^th Edition):

Shabbir, M. (2014). Some results in computational and combinatorial geometry. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/45458/

Chicago Manual of Style (16^th Edition):

Shabbir, Mudassir. “Some results in computational and combinatorial geometry.” 2014. Doctoral Dissertation, Rutgers University. Accessed March 03, 2021. https://rucore.libraries.rutgers.edu/rutgers-lib/45458/.

MLA Handbook (7^th Edition):

Shabbir, Mudassir. “Some results in computational and combinatorial geometry.” 2014. Web. 03 Mar 2021.

Vancouver:

Shabbir M. Some results in computational and combinatorial geometry. [Internet] [Doctoral dissertation]. Rutgers University; 2014. [cited 2021 Mar 03]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45458/.

Council of Science Editors:

Shabbir M. Some results in computational and combinatorial geometry. [Doctoral Dissertation]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45458/

San Jose State University

14. Ngo, Khanh Quoc. Integrability vs Non-Integrability of Distributions : Frobenius vs Chow.

Degree: MA, Mathematics, 2011, San Jose State University

URL: https://doi.org/10.31979/etd.xmff-z3dw ; https://scholarworks.sjsu.edu/etd_theses/4105

► In this thesis, we explore the following question: what is the accessible set of a distribution H on a manifold M? In particular, when… (more)

Subjects/Keywords: Riemann Geometry

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APA (6^th Edition):

Ngo, K. Q. (2011). Integrability vs Non-Integrability of Distributions : Frobenius vs Chow. (Masters Thesis). San Jose State University. Retrieved from https://doi.org/10.31979/etd.xmff-z3dw ; https://scholarworks.sjsu.edu/etd_theses/4105

Chicago Manual of Style (16^th Edition):

Ngo, Khanh Quoc. “Integrability vs Non-Integrability of Distributions : Frobenius vs Chow.” 2011. Masters Thesis, San Jose State University. Accessed March 03, 2021. https://doi.org/10.31979/etd.xmff-z3dw ; https://scholarworks.sjsu.edu/etd_theses/4105.

MLA Handbook (7^th Edition):

Ngo, Khanh Quoc. “Integrability vs Non-Integrability of Distributions : Frobenius vs Chow.” 2011. Web. 03 Mar 2021.

Vancouver:

Ngo KQ. Integrability vs Non-Integrability of Distributions : Frobenius vs Chow. [Internet] [Masters thesis]. San Jose State University; 2011. [cited 2021 Mar 03]. Available from: https://doi.org/10.31979/etd.xmff-z3dw ; https://scholarworks.sjsu.edu/etd_theses/4105.

Council of Science Editors:

Ngo KQ. Integrability vs Non-Integrability of Distributions : Frobenius vs Chow. [Masters Thesis]. San Jose State University; 2011. Available from: https://doi.org/10.31979/etd.xmff-z3dw ; https://scholarworks.sjsu.edu/etd_theses/4105

University of Utah

15. Mann, Brian. Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees.

Degree: PhD, Mathematics, 2014, University of Utah

URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3097/rec/2219

► We define a new graph on which Out(FN) acts and show that it is hyperbolic. Also we give a new proof, based on an argument… (more)

Subjects/Keywords: Geometry; Topology

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APA (6^th Edition):

Mann, B. (2014). Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3097/rec/2219

Chicago Manual of Style (16^th Edition):

Mann, Brian. “Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees.” 2014. Doctoral Dissertation, University of Utah. Accessed March 03, 2021. http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3097/rec/2219.

MLA Handbook (7^th Edition):

Mann, Brian. “Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees.” 2014. Web. 03 Mar 2021.

Vancouver:

Mann B. Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees. [Internet] [Doctoral dissertation]. University of Utah; 2014. [cited 2021 Mar 03]. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3097/rec/2219.

Council of Science Editors:

Mann B. Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees. [Doctoral Dissertation]. University of Utah; 2014. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/3097/rec/2219

Cornell University

16. Hoffman, Benjamin S. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.

Degree: PhD, Mathematics, 2020, Cornell University

URL: http://hdl.handle.net/1813/70413

► I present three papers written on the theme of the interaction between polyhedra and Hamil- tonian mechanics. In the first, I extend Delzant’s classification of… (more)

Subjects/Keywords: Symplectic Geometry

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APA (6^th Edition):

Hoffman, B. S. (2020). POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/70413

Chicago Manual of Style (16^th Edition):

Hoffman, Benjamin S. “POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.” 2020. Doctoral Dissertation, Cornell University. Accessed March 03, 2021. http://hdl.handle.net/1813/70413.

MLA Handbook (7^th Edition):

Hoffman, Benjamin S. “POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION.” 2020. Web. 03 Mar 2021.

Vancouver:

Hoffman BS. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. [Internet] [Doctoral dissertation]. Cornell University; 2020. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/1813/70413.

Council of Science Editors:

Hoffman BS. POLYTOPES AND HAMILTONIAN GEOMETRY: STACKS, TORIC DEGENERATIONS, AND PARTIAL TROPICALIZATION. [Doctoral Dissertation]. Cornell University; 2020. Available from: http://hdl.handle.net/1813/70413

University of Oxford

17. Wilkins, Nicholas. Quantum Steenrod squares, related operations, and their properties.

Degree: PhD, 2018, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

► In this thesis, we generalise the Steenrod square on the cohomology of a topological space to a quantum Steenrod square on the quantum cohomology of… (more)

Subjects/Keywords: Symplectic geometry

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APA (6^th Edition):

Wilkins, N. (2018). Quantum Steenrod squares, related operations, and their properties. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

Chicago Manual of Style (16^th Edition):

Wilkins, Nicholas. “Quantum Steenrod squares, related operations, and their properties.” 2018. Doctoral Dissertation, University of Oxford. Accessed March 03, 2021. http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593.

MLA Handbook (7^th Edition):

Wilkins, Nicholas. “Quantum Steenrod squares, related operations, and their properties.” 2018. Web. 03 Mar 2021.

Vancouver:

Wilkins N. Quantum Steenrod squares, related operations, and their properties. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2021 Mar 03]. Available from: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593.

Council of Science Editors:

Wilkins N. Quantum Steenrod squares, related operations, and their properties. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:aa8b1c6f-3457-42f7-9ae0-85ec9861a128 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791593

McMaster University

18. Chiu, Vincent. A numerical study of cohomogeneity one manifolds.

Degree: MSc, 2016, McMaster University

URL: http://hdl.handle.net/11375/20601

►

This dissertation explores numerical solutions for the cohomogeneity one Einstein and Ricci soliton equations when the principal orbits are SU(3)/T² and Sp(3)/Sp(1)³. We present new… (more)

Subjects/Keywords: Differential Geometry

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APA (6^th Edition):

Chiu, V. (2016). A numerical study of cohomogeneity one manifolds. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/20601

Chicago Manual of Style (16^th Edition):

Chiu, Vincent. “A numerical study of cohomogeneity one manifolds.” 2016. Masters Thesis, McMaster University. Accessed March 03, 2021. http://hdl.handle.net/11375/20601.

MLA Handbook (7^th Edition):

Chiu, Vincent. “A numerical study of cohomogeneity one manifolds.” 2016. Web. 03 Mar 2021.

Vancouver:

Chiu V. A numerical study of cohomogeneity one manifolds. [Internet] [Masters thesis]. McMaster University; 2016. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/11375/20601.

Council of Science Editors:

Chiu V. A numerical study of cohomogeneity one manifolds. [Masters Thesis]. McMaster University; 2016. Available from: http://hdl.handle.net/11375/20601

19. Winter, Dale A. Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds.

Degree: PhD, Mathematics, 2015, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:419439/

► This thesis will discuss generalizations of Selberg’s 3/16 theorem to hyperbolic surfaces of infinite area. These Selberg type theorems are deeply related to orbit counting… (more)

Subjects/Keywords: hyperbolic geometry

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APA (6^th Edition):

Winter, D. A. (2015). Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:419439/

Chicago Manual of Style (16^th Edition):

Winter, Dale A. “Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds.” 2015. Doctoral Dissertation, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:419439/.

MLA Handbook (7^th Edition):

Winter, Dale A. “Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds.” 2015. Web. 03 Mar 2021.

Vancouver:

Winter DA. Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds. [Internet] [Doctoral dissertation]. Brown University; 2015. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:419439/.

Council of Science Editors:

Winter DA. Mixing Properties of Flows on Geometrically Finite Hyperbolic Manifolds. [Doctoral Dissertation]. Brown University; 2015. Available from: https://repository.library.brown.edu/studio/item/bdr:419439/

20. Lai, Kuan-Wen. Cremona transformations and rational parametrizations inspired by Hodge theory.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792697/

► This thesis exhibits two of the author's works: the first is about interpreting the derived equivalences of K3 surfaces through Cremona transformations, where we construct… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Lai, K. (2018). Cremona transformations and rational parametrizations inspired by Hodge theory. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792697/

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):

Lai, Kuan-Wen. “Cremona transformations and rational parametrizations inspired by Hodge theory.” 2018. Thesis, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:792697/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lai, Kuan-Wen. “Cremona transformations and rational parametrizations inspired by Hodge theory.” 2018. Web. 03 Mar 2021.

Vancouver:

Lai K. Cremona transformations and rational parametrizations inspired by Hodge theory. [Internet] [Thesis]. Brown University; 2018. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:792697/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lai K. Cremona transformations and rational parametrizations inspired by Hodge theory. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792697/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

21. Marcus, Steffen S. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.

Degree: PhD, Mathematics, 2011, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11253/

► The main subject of this dissertation is the study of certain moduli spaces intimately related to the enumerative geometry of complex algebraic varieties and orbifolds.… (more)

▼ The main subject of this dissertation is the study of certain moduli spaces intimately related to the enumerative geometry of complex algebraic varieties and orbifolds. In three separate but related directions, we contribute to the development and use of recent variants of Gromov-Witten (GW) theory and relative GW theory. The work of this dissertation took place in collaborative projects with Dan Abramovich, Renzo Cavalieri, Qile Chen, William Gillam, Henning Ulfarsson and Jonathan Wise.Very twisted stable maps.We construct the moduli stack of very twisted stable maps to a smooth projective Deligne-Mumford stack, extending the notion of twisted stable maps (due to Abramovich and Vistoli) to allow for generic stabilizers on the source curves. We also consider the GW theory given by this construction.The evaluation space of logarithmic stable maps.The evaluation stack for minimal logarithmic stable maps is constructed, parameterizing families of standard log points in the target log scheme. This construction provides the ingredients necessary to define appropriate evaluation maps for minimal log stable maps and establish the logarithmic GW theory of a log-smooth Deligne-Faltings log scheme.Polynomial families of tautological classes on the moduli space of curves.We study double Hurwitz classes on the rational tails locus of the moduli space of curves. These are defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized projective line with prescribed ramification over zero and infinity. A comparison with classes arising from sections of the universal Jacobian shows that double Hurwitz classes are polynomial in the parts of the partitions indexing the special ramification data. Virtual localization on moduli spaces of relative stable maps gives sufficient relations to compute the coefficients of these polynomials in various cases. Advisors/Committee Members: Abramovich, Dan (Director), Cavalieri, Renzo (Reader), Lichtenbaum, Stephen (Reader).

Subjects/Keywords: algebraic geometry

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APA (6^th Edition):

Marcus, S. S. (2011). Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11253/

Chicago Manual of Style (16^th Edition):

Marcus, Steffen S. “Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.” 2011. Doctoral Dissertation, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:11253/.

MLA Handbook (7^th Edition):

Marcus, Steffen S. “Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes.” 2011. Web. 03 Mar 2021.

Vancouver:

Marcus SS. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. [Internet] [Doctoral dissertation]. Brown University; 2011. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:11253/.

Council of Science Editors:

Marcus SS. Spaces of Stable Maps, Evaluation Spaces, and Polynomial Families of Tautological Classes. [Doctoral Dissertation]. Brown University; 2011. Available from: https://repository.library.brown.edu/studio/item/bdr:11253/

22. Ascher, Kenneth Brian. Higher Dimensional Birational Geometry: Moduli and Arithmetic.

Degree: Department of Mathematics, 2017, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:733261/

► While the study of algebraic curves and their moduli has been a celebrated subject in algebraic and arithmetic geometry, generalizations of many results that hold… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Ascher, K. B. (2017). Higher Dimensional Birational Geometry: Moduli and Arithmetic. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:733261/

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):

Ascher, Kenneth Brian. “Higher Dimensional Birational Geometry: Moduli and Arithmetic.” 2017. Thesis, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:733261/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ascher, Kenneth Brian. “Higher Dimensional Birational Geometry: Moduli and Arithmetic.” 2017. Web. 03 Mar 2021.

Vancouver:

Ascher KB. Higher Dimensional Birational Geometry: Moduli and Arithmetic. [Internet] [Thesis]. Brown University; 2017. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:733261/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ascher KB. Higher Dimensional Birational Geometry: Moduli and Arithmetic. [Thesis]. Brown University; 2017. Available from: https://repository.library.brown.edu/studio/item/bdr:733261/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

23. Bejleri, Dori. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792818/

► Moduli spaces play a central role in algebraic geometry. In this thesis we study the geometry of two particular moduli spaces. In Part I we… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Bejleri, D. (2018). A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792818/

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):

Bejleri, Dori. “A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.” 2018. Thesis, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:792818/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bejleri, Dori. “A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces.” 2018. Web. 03 Mar 2021.

Vancouver:

Bejleri D. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. [Internet] [Thesis]. Brown University; 2018. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:792818/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bejleri D. A tale of two moduli spaces: Hilbert schemes of singular curves and moduli of elliptic surfaces. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792818/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

24. Jain, Vishal. Motion Segmentation Using Differential Geometry of Curves and Edges.

Degree: PhD, Division of Engineering. Electrical Sciences and Computer Engineering, 2009, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:91/

► This thesis proposes to solve the problem is of segmenting independently moving objects which is specifically useful in applications for compression, initialization for tracking, input… (more)

▼ This thesis proposes to solve the problem is of segmenting independently moving objects which is specifically useful in applications for compression, initialization for tracking, input for recognition of the target and others. The existing approaches which can be broadly classified into feature-based and dense image flow-based approaches. A central tenant of this thesis is to propose that curves act as complimentary representation in regard to features and pixels as most of the features (mainly corners) lie on the curves and a pair of curves do bound the regions of pixels. The approach proposed comprises of two stages. The first stage is to obtain segmentation from a single/two views and two different approaches are discussed for case of stationary camera and moving camera. In case of moving camera, the correspondence of the curves is extracted from two views. The alignment for the correct pair of corresponding curve is used to fit a 2D parametric model such as affine and the curves with similar parametric models are grouped to obtain segmentation. In case of stationary camera, the position and orientation of sub-pixel edges of the background are modeled and any deviation from this model is detected as foreground. This modeling of edges compared to traditional intensity based approaches is more robust to sudden changes in illumination and requires fewer frames to build the model. The second stage of this approach enriches the impoverished segmentations obtained from first stage by using multiple frame consistency. First, edges of the segmentations from different frames (5 or 7) are aligned on a central frame using a Thin Plate Spline model. After the edge maps have been aligned, the edges which fit a smooth local curve supported by edges from different frames are kept and the rest are discarded leading to removal of noise and filling in the gaps even in case of significant occlusions. Finally, this work also gives a theoretical analysis to estimate 3D translation direction which shows infeasibility to obtain reasonable estimate. However, some aspect of 3D translation which is ratio of translation parallel to the image can be recovered. Advisors/Committee Members: Kimia, Benjamin (director), Taubin, Gabriel (reader), Cooper, David (reader).

Subjects/Keywords: Differential Geometry

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APA (6^th Edition):

Jain, V. (2009). Motion Segmentation Using Differential Geometry of Curves and Edges. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:91/

Chicago Manual of Style (16^th Edition):

Jain, Vishal. “Motion Segmentation Using Differential Geometry of Curves and Edges.” 2009. Doctoral Dissertation, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:91/.

MLA Handbook (7^th Edition):

Jain, Vishal. “Motion Segmentation Using Differential Geometry of Curves and Edges.” 2009. Web. 03 Mar 2021.

Vancouver:

Jain V. Motion Segmentation Using Differential Geometry of Curves and Edges. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:91/.

Council of Science Editors:

Jain V. Motion Segmentation Using Differential Geometry of Curves and Edges. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:91/

25. Wiygul, David J. Doubling Constructions with Asymmetric Sides.

Degree: PhD, Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386256/

► Extending work of Kapouleas and Yang, we construct sequences of closed minimal surfaces embedded in the round unit 3-sphere and converging to a Cliﬀord torus… (more)

Subjects/Keywords: differential geometry

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APA (6^th Edition):

Wiygul, D. J. (2014). Doubling Constructions with Asymmetric Sides. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386256/

Chicago Manual of Style (16^th Edition):

Wiygul, David J. “Doubling Constructions with Asymmetric Sides.” 2014. Doctoral Dissertation, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:386256/.

MLA Handbook (7^th Edition):

Wiygul, David J. “Doubling Constructions with Asymmetric Sides.” 2014. Web. 03 Mar 2021.

Vancouver:

Wiygul DJ. Doubling Constructions with Asymmetric Sides. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:386256/.

Council of Science Editors:

Wiygul DJ. Doubling Constructions with Asymmetric Sides. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386256/

26. Harper, Alicia Deen. Factorization of Deligne-Mumford Stacks.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792829/

► We prove a weak factorization result on birational maps of Deligne-Mumford stacks, and deduce the following: Let U \subset X be an open embedding of… (more)

Subjects/Keywords: Geometry; Algebraic

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APA (6^th Edition):

Harper, A. D. (2018). Factorization of Deligne-Mumford Stacks. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792829/

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):

Harper, Alicia Deen. “Factorization of Deligne-Mumford Stacks.” 2018. Thesis, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:792829/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Harper, Alicia Deen. “Factorization of Deligne-Mumford Stacks.” 2018. Web. 03 Mar 2021.

Vancouver:

Harper AD. Factorization of Deligne-Mumford Stacks. [Internet] [Thesis]. Brown University; 2018. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:792829/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Harper AD. Factorization of Deligne-Mumford Stacks. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792829/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Molcho, Samouil. Logarithmic Stable Maps with Torus Actions.

Degree: PhD, Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386232/

► We study the moduli stacks of logarithmic stable maps when the target variety X is equipped with an action of a one-dimensional torus C*. Specifically,… (more)

Subjects/Keywords: Algebraic Geometry

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APA (6^th Edition):

Molcho, S. (2014). Logarithmic Stable Maps with Torus Actions. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386232/

Chicago Manual of Style (16^th Edition):

Molcho, Samouil. “Logarithmic Stable Maps with Torus Actions.” 2014. Doctoral Dissertation, Brown University. Accessed March 03, 2021. https://repository.library.brown.edu/studio/item/bdr:386232/.

MLA Handbook (7^th Edition):

Molcho, Samouil. “Logarithmic Stable Maps with Torus Actions.” 2014. Web. 03 Mar 2021.

Vancouver:

Molcho S. Logarithmic Stable Maps with Torus Actions. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2021 Mar 03]. Available from: https://repository.library.brown.edu/studio/item/bdr:386232/.

Council of Science Editors:

Molcho S. Logarithmic Stable Maps with Torus Actions. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386232/

Wake Forest University

28. Sintay, Benjamin. Using Poisson's Equation to Characterize Brain Tumor Shape.

Degree: 2009, Wake Forest University

URL: http://hdl.handle.net/10339/14840

► The role that tumor shape plays in disease treatment, progression, and outcome is not well understood. This work investigates the quantification of shape information required… (more)

Subjects/Keywords: Geometry

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APA (6^th Edition):

Sintay, B. (2009). Using Poisson's Equation to Characterize Brain Tumor Shape. (Thesis). Wake Forest University. Retrieved from http://hdl.handle.net/10339/14840

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):

Sintay, Benjamin. “Using Poisson's Equation to Characterize Brain Tumor Shape.” 2009. Thesis, Wake Forest University. Accessed March 03, 2021. http://hdl.handle.net/10339/14840.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sintay, Benjamin. “Using Poisson's Equation to Characterize Brain Tumor Shape.” 2009. Web. 03 Mar 2021.

Vancouver:

Sintay B. Using Poisson's Equation to Characterize Brain Tumor Shape. [Internet] [Thesis]. Wake Forest University; 2009. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/10339/14840.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sintay B. Using Poisson's Equation to Characterize Brain Tumor Shape. [Thesis]. Wake Forest University; 2009. Available from: http://hdl.handle.net/10339/14840

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Oregon State University

29. Driessel, Kenneth Richard. Significance and invariance in mathematical structures.

Degree: PhD, Mathematics, 1967, Oregon State University

URL: http://hdl.handle.net/1957/17200

See pdf Advisors/Committee Members: Carter, D. S. (advisor).

Subjects/Keywords: Geometry

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APA (6^th Edition):

Driessel, K. R. (1967). Significance and invariance in mathematical structures. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/17200

Chicago Manual of Style (16^th Edition):

Driessel, Kenneth Richard. “Significance and invariance in mathematical structures.” 1967. Doctoral Dissertation, Oregon State University. Accessed March 03, 2021. http://hdl.handle.net/1957/17200.

MLA Handbook (7^th Edition):

Driessel, Kenneth Richard. “Significance and invariance in mathematical structures.” 1967. Web. 03 Mar 2021.

Vancouver:

Driessel KR. Significance and invariance in mathematical structures. [Internet] [Doctoral dissertation]. Oregon State University; 1967. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/1957/17200.

Council of Science Editors:

Driessel KR. Significance and invariance in mathematical structures. [Doctoral Dissertation]. Oregon State University; 1967. Available from: http://hdl.handle.net/1957/17200

Boston University

30. Ogura, Masako. Symplectic and orthogonal geometry.

Degree: MA, Mathematics, 1964, Boston University

URL: http://hdl.handle.net/2144/32814

► This thesis treats metric structures and transformations of finite dimensional spaces over commutative fields. The definition of metric structures of spaces is given in the… (more)

▼ This thesis treats metric structures and transformations of finite dimensional spaces over commutative fields. The definition of metric structures of spaces is given in the first section of the chapter I. How such metric structures can be described in terms of bases and how the expressions depend upon the choices of bases are then studied. The geometries where XY = 0 implies YX = 0 for any elements X,Y of the space are sought in section 2. The orthogonal and symplectic geometries are introduced as the only two types of geometries which satisfy this condition. In connection with metric structures of spaces, bilinear and quadratic forms are discussed in section 3. Metric structures of orthogonal geometries are shown to be determined by symmetric bilinear forms and those of symplectic geometries are determined by skew symmetric bilinear forms. A study of orthogonal geometries is shown·to be equivalent to a study of quadratic forms. Irreducible subspaces of orthogonal and symplectic geometries are discussed in section 4, by considering the properties of kernels, radicals and singularities of spaces and defining isotropic spaces and vectors. As a result one can see that an orthogonal geometry is an orthogonal sum of lines and that a nonsingular symplectic space is an orthogonal sum of hyperbolic planes. For example, a Euclidean space is an orthogonal sum of lines generated by the characteristic vectors of the matrix describing its metric structure. Reducing bilinear forms to its canonical forms, one can see that there exists only one non-singular symplectic space, if a dimension and a field are given. The subject of chapter II is mappings of spaces on which metric structures are defined. The definition of homomorphisms and isometries are first given in section_l and 2, together with their matrix representations relative to bases of spaces. Rotations and reflexions are then introduced as two types of isometries. In section 3, the definition of involutions is given. It then follows that every involution has a form -1u perpendicular lw, where U and W are mutually orthogonal subspaces. Some important properties of isometries on orthogonal geometries are stated in section 4. As examples, isometries on two- and three-dimensional Euclidean spaces and Lorentz transformations on two dimensional space are discussed in section 5 and 6. Finally orthogonal geometries of n-dimensional spaces over finite fields are discussed, together with an example of geometric structures and isometries of a two-dimensional orthogonal space over a field J3.

Subjects/Keywords: Geometry

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

APA (6^th Edition):

Ogura, M. (1964). Symplectic and orthogonal geometry. (Masters Thesis). Boston University. Retrieved from http://hdl.handle.net/2144/32814

Chicago Manual of Style (16^th Edition):

Ogura, Masako. “Symplectic and orthogonal geometry.” 1964. Masters Thesis, Boston University. Accessed March 03, 2021. http://hdl.handle.net/2144/32814.

MLA Handbook (7^th Edition):

Ogura, Masako. “Symplectic and orthogonal geometry.” 1964. Web. 03 Mar 2021.

Vancouver:

Ogura M. Symplectic and orthogonal geometry. [Internet] [Masters thesis]. Boston University; 1964. [cited 2021 Mar 03]. Available from: http://hdl.handle.net/2144/32814.

Council of Science Editors:

Ogura M. Symplectic and orthogonal geometry. [Masters Thesis]. Boston University; 1964. Available from: http://hdl.handle.net/2144/32814

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Open Access Theses and Dissertations