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Talk topicExpected dateSpeakerReferences and things to cover
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For everything: Weibel's K-book
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K_09/9David
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Simple homotopy theory
9/11/2019, 9/13/2019
BrandonMarshall: A course in simple-homotopy theory
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K_2 and Matsumoto's theorem
9/16/2019,09/18/2019
KimoiMilnor: Algebraic K-theory
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h-cobordism
9/20/2019,9/23/2019
Rodrigohttp://www.math.uchicago.edu/~may/VIGRE/VIGRE2011/REUPapers/MacKieMason.pdf, Milnor's notes on h-cobordism
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Definitions of K-theory: BGL9/25Andres
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Technical interlude: nerves of categories
9/27Inna
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Definitions of K-theory: Q9/30YunQuillen: Higher Algebraic K-Theory I
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Q = +10/2Guanyu
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Fundamental theorems10/4AnweshDevissage, Localization. Goal: prove the LES of a Dedekind domain
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Technical interlude: spectra10/7Inna
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Definitions of K-theory: Waldhausen10/23Elise
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Milnor K-theory10/25John
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The gamma-filtration (and Milnor K-theory)
Rodrigohttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.153.9301&rep=rep1&type=pdf
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AdditivityMaru
McCarthy: https://www.sciencedirect.com/science/article/pii/004093839390023O. Also, consider how an application of simplicial theorem A might simplify this.
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K-theory of finite fieldsDavidhttps://web.math.rochester.edu/people/faculty/doug/otherpapers/Mitchell-finitefieldsKtheory.pdf
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What is known about K(Z)Anwesh
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Pseudoisotopy and K_2http://folk.uio.no/bjoernj/papers/ig.pdf, Hatcher--Wagoner
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HH, THH and the Dennis trace
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TCKimoi
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K-theory of finite setsBrandon
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K(End) and witt vectorsAlmkvist, Grayson, Campbell
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Goodwillie calculus
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Dundas--Goodwillie--McCarthy EliseThe relationship between TC and K-theory in terms of Goodwillie calculus
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K-theory of spaces
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Quillen--Lichtenbaum conjecturesAnwesh
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rognes stable rank filtration, quillen's proof, Segal's proof
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Redshift conjectureDavid
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K-theory of schemes and motivic cohomology
Guanyu
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K-theory of 2/bi-categories?Brandonhttps://arxiv.org/abs/1503.07824 https://arxiv.org/abs/1005.2227
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Possible technical interludes
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Categories, functors and natural transformation
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Nerves of categories and Theorem A3
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