Garth Warner (changes) in nLab

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Selected writings

On Hecke operators:

• Garth Warner: Elementary Aspects of the Theory of Hecke Operators, University of Washington (1988) [[pdf](https://sites.math.washington.edu//~warner/Elementary_Aspects_of_the_Theory_of_Hecke_Operators.pdf), pdf]

On (toric) algebraic groups:

• Garth Warner: Abelian Theory, University of Washington [[arXiv:2012.15736](https://arxiv.org/abs/2012.15736), pdf]

On algebraic topology via the model categories (notably the classical model structure on topological spaces):

• Garth Warner: Topics in Topology and Homotopy Theory, EPrint Collection, University of Washington (2005) [hdl:1773/2641, pdf, arXiv:2007.02467]

On general relativity (gravity):

• Garth Warner: Mathematical Aspects of General Relativity, EPrint Collection, University Of Washington (2006) [[hdl:1773/2637](http://hdl.handle.net/1773/2637), pdf, pdf]

On (constructive) quantum field theory:

• Garth Warner: Bosonic Quantum Field Theory, EPrint Collection, University of Washington (2008) [[hdl:1773/3710](http://hdl.handle.net/1773/3710), pdf, pdf]

via Wightman axioms:

• Garth Warner: Quantum Field Theory Seminar (School of Wightman et al.), seminar notes, University of Washington [[pdf](https://sites.math.washington.edu//~warner/QFTSeminar_Warner.pdf), pdf]

via Haag-Kastler axioms (algebraic quantum field theory):

• Garth Warner: Quantum Field Theory Seminar (School of Haag-Kastler et al.), seminar notes, University of Washington [[pdf](https://sites.math.washington.edu//~warner/QFT2Seminar_Warner.pdf), pdf]

and for gauge theory:

• Garth Warner: Quantum Gauge Theory, seminar notes, University of Washington [[pdf](https://sites.math.washington.edu//~warner/QGTSeminar_Warner.pdf), pdf]

On Lagrangian classical mechanics:

• Garth Warner: Lagrangian Mechanics, EPrint Collection, University of Washington (2009) [[hdl:1773/4606](http://hdl.handle.net/1773/4606), pdf, pdf]

On $C^\ast$-algebras:

• Garth Warner, C *C^\ast-Algebras, EPrint Collection, University of Washington (2010) [[hdl:1773/16302](http://hdl.handle.net/1773/16302), pdf, pdf]

On quantum information theory via completely positive maps (quantum channels):

• Garth Warner: Positivity, EPrint Collection University of Washington (2010) [[hdl:1773/15549](http://hdl.handle.net/1773/15549), pdf, pdf]

On the Doplicher-Roberts reconstruction theorem:

• Garth Warner: Reconstruction Theory, EPrint Collection, University of Washington (2011) [[hdl:1773/16351](http://hdl.handle.net/1773/16351), pdf, pdf]

On fibered categories, the Grothendieck construction and sheaves:

• Garth Warner: Fibrations and Sheaves, EPrint Collection, University of Washington (2012) [[hdl:1773/20977](http://hdl.handle.net/1773/20977), pdf, pdf]

On (simplicial) homotopy theory via (simplicial) model categories:

• Garth Warner: Categorical Homotopy Theory, EPrint Collection, University of Washington (2012) [hdl:1773/19589, pdf, pdf]

On topos theory including the simplicial homotopy theory of simplicial sheaves via Cisinski model structures:

• Garth Warner, Homotopical Topos Theory, EPrint Collection, University of Washington (2012) [[hdl:1773/19722](http://hdl.handle.net/1773/19722), pdf, pdf]

On transcendental number theory (Schanuel's conjecture, …):

• Garth Warner: The exponential world, University of Washington (2021) [[arXiv:2105.05809](https://arxiv.org/abs/2105.05809), pdf]

On descriptive set theory:

• Garth Warner: Sets and Classes, University of Washington [[arXiv:2404.04766](https://arxiv.org/abs/2404.04766), pdf]