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University of Illinois – Urbana-Champaign

1. Tian, Hongfei. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.

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

URL: http://hdl.handle.net/2142/99314

► In this thesis we prove the existence of Jordan Decomposition in D_{G/k}, the ring of invariant differential operators on a semisimple algebraic group over a…
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Subjects/Keywords: Representation theory; Positive characteristic; Invariant differential operators; Semisimple center

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

APA (6^{th} Edition):

Tian, H. (2017). On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/99314

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

Tian, Hongfei. “On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed October 23, 2020. http://hdl.handle.net/2142/99314.

MLA Handbook (7^{th} Edition):

Tian, Hongfei. “On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.” 2017. Web. 23 Oct 2020.

Vancouver:

Tian H. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Oct 23]. Available from: http://hdl.handle.net/2142/99314.

Council of Science Editors:

Tian H. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/99314

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

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 October 23, 2020. http://hdl.handle.net/2142/42274.

MLA Handbook (7^{th} Edition):

Beder, Jesse. “The Grade Conjecture and asymptotic intersection multiplicity.” 2013. Web. 23 Oct 2020.

Vancouver:

Beder J. The Grade Conjecture and asymptotic intersection multiplicity. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Oct 23]. 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

3. 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…
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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 October 23, 2020. http://hdl.handle.net/2142/31129.

MLA Handbook (7^{th} Edition):

To, Jin Hyung. “Holomorphic chains on the projective line.” 2012. Web. 23 Oct 2020.

Vancouver:

To JH. Holomorphic chains on the projective line. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Oct 23]. 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

4. 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…
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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 October 23, 2020. http://hdl.handle.net/2142/34220.

MLA Handbook (7^{th} Edition):

Choi, Jinwon. “Enumerative invariants for local Calabi-Yau threefolds.” 2012. Web. 23 Oct 2020.

Vancouver:

Choi J. Enumerative invariants for local Calabi-Yau threefolds. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Oct 23]. 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