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University of Illinois – Urbana-Champaign

1. Yeakel, Sarah A. Goodwillie calculus and I.

Degree: PhD, Mathematics, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/90811

► We study the implications of using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of…
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Subjects/Keywords: Goodwillie calculus; homotopy theory; excisive functors

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APA (6^{th} Edition):

Yeakel, S. A. (2016). Goodwillie calculus and I. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/90811

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

Yeakel, Sarah A. “Goodwillie calculus and I.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/90811.

MLA Handbook (7^{th} Edition):

Yeakel, Sarah A. “Goodwillie calculus and I.” 2016. Web. 19 Sep 2020.

Vancouver:

Yeakel SA. Goodwillie calculus and I. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/90811.

Council of Science Editors:

Yeakel SA. Goodwillie calculus and I. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/90811

University of Illinois – Urbana-Champaign

2. Aramyan, Nerses. A construction of topological field theories.

Degree: PhD, Mathematics, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/92901

► We give an explicit construction of extended topological field theories over a manifold taking values in the deloopings of U(1) from the data of differential…
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Subjects/Keywords: topological field theories; cobordism hypothesis; Deligne complex; Dold-Kan construction

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APA (6^{th} Edition):

Aramyan, N. (2016). A construction of topological field theories. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/92901

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

Aramyan, Nerses. “A construction of topological field theories.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/92901.

MLA Handbook (7^{th} Edition):

Aramyan, Nerses. “A construction of topological field theories.” 2016. Web. 19 Sep 2020.

Vancouver:

Aramyan N. A construction of topological field theories. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/92901.

Council of Science Editors:

Aramyan N. A construction of topological field theories. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/92901

University of Illinois – Urbana-Champaign

3. Tebbe, Amelia Nora. Computing the Goodwillie-Taylor tower for discrete modules.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98276

► A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present…
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Subjects/Keywords: Functor calculus; Goodwillie calculus; Discrete modules; Atomic functors; Finite sets; Rank filtration; Algebraic topology; Homotopy theory

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APA (6^{th} Edition):

Tebbe, A. N. (2017). Computing the Goodwillie-Taylor tower for discrete modules. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98276

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

Tebbe, Amelia Nora. “Computing the Goodwillie-Taylor tower for discrete modules.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/98276.

MLA Handbook (7^{th} Edition):

Tebbe, Amelia Nora. “Computing the Goodwillie-Taylor tower for discrete modules.” 2017. Web. 19 Sep 2020.

Vancouver:

Tebbe AN. Computing the Goodwillie-Taylor tower for discrete modules. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/98276.

Council of Science Editors:

Tebbe AN. Computing the Goodwillie-Taylor tower for discrete modules. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98276

University of Illinois – Urbana-Champaign

4. Smith, Mychael. Equivariant E-infinity algebras.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/99207

► The equivariant ๐ผโG operad has the property that ๐ผโG(n) is the total space for the G-equivariant universal principal ฮฃn bundle. There is a forgetful functor…
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Subjects/Keywords: Equivariant; Homotopy theory; E-infinity algebra

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APA (6^{th} Edition):

Smith, M. (2017). Equivariant E-infinity algebras. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/99207

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

Smith, Mychael. “Equivariant E-infinity algebras.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/99207.

MLA Handbook (7^{th} Edition):

Smith, Mychael. “Equivariant E-infinity algebras.” 2017. Web. 19 Sep 2020.

Vancouver:

Smith M. Equivariant E-infinity algebras. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/99207.

Council of Science Editors:

Smith M. Equivariant E-infinity algebras. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/99207

5. Eldred, Rosona. Cosimplicial invariants and Calculus of homotopy functors.

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

URL: http://hdl.handle.net/2142/29665

► The origin of these investigations was the successful attempt by myself and coauthors to generalize rational equivalences of two constructions which suggest possible definitions of…
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Subjects/Keywords: Goodwillie Calculus; Homotopy Theory; Algebraic Topology; homotopy functor; homotopy limit

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APA (6^{th} Edition):

Eldred, R. (2012). Cosimplicial invariants and Calculus of homotopy functors. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29665

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

Eldred, Rosona. “Cosimplicial invariants and Calculus of homotopy functors.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/29665.

MLA Handbook (7^{th} Edition):

Eldred, Rosona. “Cosimplicial invariants and Calculus of homotopy functors.” 2012. Web. 19 Sep 2020.

Vancouver:

Eldred R. Cosimplicial invariants and Calculus of homotopy functors. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/29665.

Council of Science Editors:

Eldred R. Cosimplicial invariants and Calculus of homotopy functors. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29665

6. Lior, Dan. Computing the Goodwillie-Taylor tower of discrete modules.

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

URL: http://hdl.handle.net/2142/42374

► Let P_{m} and D_{m} be the m^{th} level and layer of the Goodwillie-Taylor tower for discrete modules. In the rank filtration of D_{1F} is described…
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Subjects/Keywords: Goodwillie; Functor Calculus; Taylor Tower; Robinson Bicomplex; Discrete Module; Discrete Functor

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

APA (6^{th} Edition):

Lior, D. (2013). Computing the Goodwillie-Taylor tower of discrete modules. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/42374

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

Lior, Dan. “Computing the Goodwillie-Taylor tower of discrete modules.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/42374.

MLA Handbook (7^{th} Edition):

Lior, Dan. “Computing the Goodwillie-Taylor tower of discrete modules.” 2013. Web. 19 Sep 2020.

Vancouver:

Lior D. Computing the Goodwillie-Taylor tower of discrete modules. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/42374.

Council of Science Editors:

Lior D. Computing the Goodwillie-Taylor tower of discrete modules. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/42374

7. Huan, Zhen. Quasi-elliptic cohomology.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97268

► We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring ℤ[q^{±}]. In Chapter 2 we build an orbifold…
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Subjects/Keywords: Quasi-elliptic cohomology; Tate K-theory; Power operation; Spectra; Global homotopy theory

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APA (6^{th} Edition):

Huan, Z. (2017). Quasi-elliptic cohomology. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97268

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

Huan, Zhen. “Quasi-elliptic cohomology.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/97268.

MLA Handbook (7^{th} Edition):

Huan, Zhen. “Quasi-elliptic cohomology.” 2017. Web. 19 Sep 2020.

Vancouver:

Huan Z. Quasi-elliptic cohomology. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/97268.

Council of Science Editors:

Huan Z. Quasi-elliptic cohomology. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97268

8. Rasekh, Nima. A theory of elementary higher toposes.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101508

► The end goal of this work is to define and study an elementary higher topos. We will achieve this by going through several steps. First…
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Subjects/Keywords: Homotopy Theory Higher Category Theory Topos Theory

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APA (6^{th} Edition):

Rasekh, N. (2018). A theory of elementary higher toposes. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101508

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

Rasekh, Nima. “A theory of elementary higher toposes.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/101508.

MLA Handbook (7^{th} Edition):

Rasekh, Nima. “A theory of elementary higher toposes.” 2018. Web. 19 Sep 2020.

Vancouver:

Rasekh N. A theory of elementary higher toposes. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/101508.

Council of Science Editors:

Rasekh N. A theory of elementary higher toposes. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101508

9. Nelson, Peter D. A small presentation for Morava E-theory power operations.

Degree: PhD, Mathematics, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/92811

► Let E denote a Morava E-theory at a prime p and height h. We characterize the power operations on ฯ0 of a K(h)-local Eโ-E-algebra in…
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Subjects/Keywords: Power Operations; Morava E-Theory

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APA (6^{th} Edition):

Nelson, P. D. (2016). A small presentation for Morava E-theory power operations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/92811

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

Nelson, Peter D. “A small presentation for Morava E-theory power operations.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/92811.

MLA Handbook (7^{th} Edition):

Nelson, Peter D. “A small presentation for Morava E-theory power operations.” 2016. Web. 19 Sep 2020.

Vancouver:

Nelson PD. A small presentation for Morava E-theory power operations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/92811.

Council of Science Editors:

Nelson PD. A small presentation for Morava E-theory power operations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/92811

10. Villeta-Garcia, Juan S. Stabilizing spectral functors of exact categories.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98290

► We define and study the K-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of…
(more)

Subjects/Keywords: Algebraic K-theory; Goodwillie calculus; Homotopy theory; Algebraic topology

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APA (6^{th} Edition):

Villeta-Garcia, J. S. (2017). Stabilizing spectral functors of exact categories. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98290

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

Villeta-Garcia, Juan S. “Stabilizing spectral functors of exact categories.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/98290.

MLA Handbook (7^{th} Edition):

Villeta-Garcia, Juan S. “Stabilizing spectral functors of exact categories.” 2017. Web. 19 Sep 2020.

Vancouver:

Villeta-Garcia JS. Stabilizing spectral functors of exact categories. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/98290.

Council of Science Editors:

Villeta-Garcia JS. Stabilizing spectral functors of exact categories. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98290

11. 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 September 19, 2020. http://hdl.handle.net/2142/26269.

MLA Handbook (7^{th} Edition):

Stapleton, Nathaniel J. “Transchromatic generalized character maps.” 2011. Web. 19 Sep 2020.

Vancouver:

Stapleton NJ. Transchromatic generalized character maps. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Sep 19]. 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

University of Illinois – Urbana-Champaign

12. Chen, Hsian-Yang. Torus equivariant elliptic cohomology and sigma orientations.

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

URL: http://hdl.handle.net/2142/16822

► Let 𝓒 \colon= \mathds{C}/ Λ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is…
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Subjects/Keywords: elliptic cohomology; sigma orientation

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APA (6^{th} Edition):

Chen, H. (2010). Torus equivariant elliptic cohomology and sigma orientations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16822

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

Chen, Hsian-Yang. “Torus equivariant elliptic cohomology and sigma orientations.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/16822.

MLA Handbook (7^{th} Edition):

Chen, Hsian-Yang. “Torus equivariant elliptic cohomology and sigma orientations.” 2010. Web. 19 Sep 2020.

Vancouver:

Chen H. Torus equivariant elliptic cohomology and sigma orientations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/16822.

Council of Science Editors:

Chen H. Torus equivariant elliptic cohomology and sigma orientations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16822

University of Illinois – Urbana-Champaign

13. Lipsky, David. Cocycle Constructions for Topological Field Theories.

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

URL: http://hdl.handle.net/2142/16929

► In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds Σ,…
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Subjects/Keywords: Algebraic topology; Topological field theory; Smooth Deligne cohomology; Cech cohomology

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

APA (6^{th} Edition):

Lipsky, D. (2010). Cocycle Constructions for Topological Field Theories. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16929

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

Lipsky, David. “Cocycle Constructions for Topological Field Theories.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/16929.

MLA Handbook (7^{th} Edition):

Lipsky, David. “Cocycle Constructions for Topological Field Theories.” 2010. Web. 19 Sep 2020.

Vancouver:

Lipsky D. Cocycle Constructions for Topological Field Theories. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/16929.

Council of Science Editors:

Lipsky D. Cocycle Constructions for Topological Field Theories. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16929

University of Illinois – Urbana-Champaign

14. Kim, Youngsoo. Motivic symmetric ring spectrum representing algebraic K-theory.

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

URL: http://hdl.handle.net/2142/16878

► Voevodsky showed that there is a motivic spectrum representing algebraic K-theory. We describe an equivalent spectrum that is also a symmetric ring spectrum. A coherence…
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Subjects/Keywords: motivic spectrum; algebraic K-theory; ring spectrum; standard vector bundles

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

APA (6^{th} Edition):

Kim, Y. (2010). Motivic symmetric ring spectrum representing algebraic K-theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16878

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

Kim, Youngsoo. “Motivic symmetric ring spectrum representing algebraic K-theory.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 19, 2020. http://hdl.handle.net/2142/16878.

MLA Handbook (7^{th} Edition):

Kim, Youngsoo. “Motivic symmetric ring spectrum representing algebraic K-theory.” 2010. Web. 19 Sep 2020.

Vancouver:

Kim Y. Motivic symmetric ring spectrum representing algebraic K-theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Sep 19]. Available from: http://hdl.handle.net/2142/16878.

Council of Science Editors:

Kim Y. Motivic symmetric ring spectrum representing algebraic K-theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16878