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University of Illinois – Urbana-Champaign

1. Seceleanu, Alexandra. The syzygy theorem and the weak Lefschetz Property.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26091

► This thesis consists of two research topics in commutative algebra. In the first chapter, a comprehensive analysis is given of the Weak Lefschetz property in…
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Subjects/Keywords: syzygy; syzygy theorem; weak Lefschetz Property; fat points; homological conjectures

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APA (6^{th} Edition):

Seceleanu, A. (2011). The syzygy theorem and the weak Lefschetz Property. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26091

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

Seceleanu, Alexandra. “The syzygy theorem and the weak Lefschetz Property.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/26091.

MLA Handbook (7^{th} Edition):

Seceleanu, Alexandra. “The syzygy theorem and the weak Lefschetz Property.” 2011. Web. 10 Jul 2020.

Vancouver:

Seceleanu A. The syzygy theorem and the weak Lefschetz Property. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/26091.

Council of Science Editors:

Seceleanu A. The syzygy theorem and the weak Lefschetz Property. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26091

University of Illinois – Urbana-Champaign

2. Li, Chunyi. Deformations of the Hilbert scheme of points on a del Pezzo surface.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/49684

► The Hilbert scheme of n points in a smooth del Pezzo surface S parameterizes zero-dimensional subschemes with length n on S. We construct a flat…
(more)

Subjects/Keywords: Hilbert scheme; deformation theory; del Pezzo surface

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APA (6^{th} Edition):

Li, C. (2014). Deformations of the Hilbert scheme of points on a del Pezzo surface. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49684

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

Li, Chunyi. “Deformations of the Hilbert scheme of points on a del Pezzo surface.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/49684.

MLA Handbook (7^{th} Edition):

Li, Chunyi. “Deformations of the Hilbert scheme of points on a del Pezzo surface.” 2014. Web. 10 Jul 2020.

Vancouver:

Li C. Deformations of the Hilbert scheme of points on a del Pezzo surface. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/49684.

Council of Science Editors:

Li C. Deformations of the Hilbert scheme of points on a del Pezzo surface. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49684

3. Morton, Daniel. GKM manifolds with low Betti numbers.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/29636

► A GKM manifold is a symplectic manifold with a torus action such that the fixed points are isolated and the isotropy weights at the fixed…
(more)

Subjects/Keywords: GKM Manifolds; GKM Graphs; Symplectic Geometry; Symplectic Manifolds; Torus Actions

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APA (6^{th} Edition):

Morton, D. (2012). GKM manifolds with low Betti numbers. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29636

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

Morton, Daniel. “GKM manifolds with low Betti numbers.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/29636.

MLA Handbook (7^{th} Edition):

Morton, Daniel. “GKM manifolds with low Betti numbers.” 2012. Web. 10 Jul 2020.

Vancouver:

Morton D. GKM manifolds with low Betti numbers. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/29636.

Council of Science Editors:

Morton D. GKM manifolds with low Betti numbers. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29636

4. Stapleton, Nathaniel J. Transchromatic generalized character maps.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26269

► In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel discovered a generalized character theory that proved useful in studying cohomology rings…
(more)

Subjects/Keywords: Algebraic Topology; Stable Homotopy Theory; Generalized Cohomology Theory; p-Divisible Group; Barsotti-Tate Group; Morava E-theory

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APA (6^{th} Edition):

Stapleton, N. J. (2011). Transchromatic generalized character maps. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26269

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

Stapleton, Nathaniel J. “Transchromatic generalized character maps.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/26269.

MLA Handbook (7^{th} Edition):

Stapleton, Nathaniel J. “Transchromatic generalized character maps.” 2011. Web. 10 Jul 2020.

Vancouver:

Stapleton NJ. Transchromatic generalized character maps. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/26269.

Council of Science Editors:

Stapleton NJ. Transchromatic generalized character maps. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26269

5. Shen, Jiashun. Multiplicative codes of Reed-Muller type.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50529

► This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications. Our codes apply to the elds of cryptography and coding theory,…
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Subjects/Keywords: coding theory; Reed-Muller codes; secret sharing; multiparty computation; combinatorics; multiplicity

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APA (6^{th} Edition):

Shen, J. (2014). Multiplicative codes of Reed-Muller type. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50529

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

Shen, Jiashun. “Multiplicative codes of Reed-Muller type.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/50529.

MLA Handbook (7^{th} Edition):

Shen, Jiashun. “Multiplicative codes of Reed-Muller type.” 2014. Web. 10 Jul 2020.

Vancouver:

Shen J. Multiplicative codes of Reed-Muller type. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/50529.

Council of Science Editors:

Shen J. Multiplicative codes of Reed-Muller type. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50529

6. Kirov, Radoslav M. Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16738

► The main goal of this work is to improve algebraic geometric/number theoretic constructions of error-correcting codes and secret sharing schemes. For both objects we define…
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Subjects/Keywords: algebraic geometric codes; error-correcting codes; linear secret sharing schemes; hermitian curve; suzuki curve

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APA (6^{th} Edition):

Kirov, R. M. (2010). Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16738

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

Kirov, Radoslav M. “Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16738.

MLA Handbook (7^{th} Edition):

Kirov, Radoslav M. “Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves.” 2010. Web. 10 Jul 2020.

Vancouver:

Kirov RM. Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16738.

Council of Science Editors:

Kirov RM. Improved Bounds for Codes and Secret Sharing Schemes from Algebraic Curves. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16738

7. Beder, Jesse. The Grade Conjecture and asymptotic intersection multiplicity.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/42274

► In this thesis, we study Peskine and Szpiro's Grade Conjecture and its connection with asymptotic intersection multiplicity χ_∞. Given an A-module M of finite projective…
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Subjects/Keywords: commutative algebra; grade conjecture; characteristic p; frobenius; intersection multiplicity

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APA (6^{th} Edition):

Beder, J. (2013). The Grade Conjecture and asymptotic intersection multiplicity. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/42274

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

Beder, Jesse. “The Grade Conjecture and asymptotic intersection multiplicity.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/42274.

MLA Handbook (7^{th} Edition):

Beder, Jesse. “The Grade Conjecture and asymptotic intersection multiplicity.” 2013. Web. 10 Jul 2020.

Vancouver:

Beder J. The Grade Conjecture and asymptotic intersection multiplicity. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/42274.

Council of Science Editors:

Beder J. The Grade Conjecture and asymptotic intersection multiplicity. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/42274

8. Im, Mee Seong. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/49392

► We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of…
(more)

Subjects/Keywords: Algebraic geometry; representation theory; quiver varieties; filtered quiver variety; quiver flag variety; semi-invariant polynomials; invariant subring; Derksen-Weyman; Domokos-Zubkov; Schofield-van den Bergh; ADE-Dynkin quivers; affine Dynkin quivers; quivers with at most two pathways between any two vertices; filtration of vector spaces; classical invariant theory; the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution; almost-commuting varieties; affine quotient

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APA (6^{th} Edition):

Im, M. S. (2014). On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49392

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

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/49392.

MLA Handbook (7^{th} Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Web. 10 Jul 2020.

Vancouver:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/49392.

Council of Science Editors:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49392

9. Fu, Yong. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16874

► In this thesis, we first use the {ℂ^*}^{2}-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some…
(more)

Subjects/Keywords: Gromov-Witten invariants; quantum product

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

APA (6^{th} Edition):

Fu, Y. (2010). Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16874

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

Fu, Yong. “Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16874.

MLA Handbook (7^{th} Edition):

Fu, Yong. “Quantum cohomology of a Hilbert scheme of a Hirzebruch surface.” 2010. Web. 10 Jul 2020.

Vancouver:

Fu Y. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16874.

Council of Science Editors:

Fu Y. Quantum cohomology of a Hilbert scheme of a Hirzebruch surface. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16874

10. Sheshmani, Artan. Towards studying of the higher rank theory of stable pairs.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26229

► This thesis is composed of two parts. In the first part we introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on…
(more)

Subjects/Keywords: Calabi-Yau threefold; Stable pairs; Deformation-obstruction theory; Derived categories; Equivariant cohomology; Virtual localization; Wallcrossing

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APA (6^{th} Edition):

Sheshmani, A. (2011). Towards studying of the higher rank theory of stable pairs. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26229

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

Sheshmani, Artan. “Towards studying of the higher rank theory of stable pairs.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/26229.

MLA Handbook (7^{th} Edition):

Sheshmani, Artan. “Towards studying of the higher rank theory of stable pairs.” 2011. Web. 10 Jul 2020.

Vancouver:

Sheshmani A. Towards studying of the higher rank theory of stable pairs. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/26229.

Council of Science Editors:

Sheshmani A. Towards studying of the higher rank theory of stable pairs. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26229

11. To, Jin Hyung. Holomorphic chains on the projective line.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/31129

► Holomorphic chains on a smooth algebraic curve are tuples of vector bundles on the curve together with the homomorphisms between them. A type of a…
(more)

Subjects/Keywords: Holomorphic chains; α-stability; Chamber; Geometric Invariant Theory (GIT); Nonreductive GIT; Symplectic quotient; Co-Higgs bundles.

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

APA (6^{th} Edition):

To, J. H. (2012). Holomorphic chains on the projective line. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/31129

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

To, Jin Hyung. “Holomorphic chains on the projective line.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/31129.

MLA Handbook (7^{th} Edition):

To, Jin Hyung. “Holomorphic chains on the projective line.” 2012. Web. 10 Jul 2020.

Vancouver:

To JH. Holomorphic chains on the projective line. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/31129.

Council of Science Editors:

To JH. Holomorphic chains on the projective line. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/31129

12. Choi, Jinwon. Enumerative invariants for local Calabi-Yau threefolds.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34220

► This thesis consists of three parts. In the first part, we compute the topological Euler characteristics of the moduli spaces of stable sheaves of dimension…
(more)

Subjects/Keywords: Bogomol'nyi-Prasad-Sommerfeld (BPS) invariant; moduli space; equivariant sheaf; toric variety; wall crossing

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

APA (6^{th} Edition):

Choi, J. (2012). Enumerative invariants for local Calabi-Yau threefolds. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34220

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

Choi, Jinwon. “Enumerative invariants for local Calabi-Yau threefolds.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/34220.

MLA Handbook (7^{th} Edition):

Choi, Jinwon. “Enumerative invariants for local Calabi-Yau threefolds.” 2012. Web. 10 Jul 2020.

Vancouver:

Choi J. Enumerative invariants for local Calabi-Yau threefolds. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/34220.

Council of Science Editors:

Choi J. Enumerative invariants for local Calabi-Yau threefolds. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34220

13. Mak, Kit Ho. On congruence function fields with many rational places.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34193

► In this thesis, we study congruence function fields, in particular those with many rational places. This thesis consists of three parts, the first two parts…
(more)

Subjects/Keywords: function fields; maximal curves; Ihara constants; asymptotic bounds; subcover problem

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

APA (6^{th} Edition):

Mak, K. H. (2012). On congruence function fields with many rational places. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34193

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

Mak, Kit Ho. “On congruence function fields with many rational places.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/34193.

MLA Handbook (7^{th} Edition):

Mak, Kit Ho. “On congruence function fields with many rational places.” 2012. Web. 10 Jul 2020.

Vancouver:

Mak KH. On congruence function fields with many rational places. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/34193.

Council of Science Editors:

Mak KH. On congruence function fields with many rational places. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34193