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bio website personal.denison.edu/~whiteda
location Granville, OH
age
visits member for 4 years, 7 months
seen 6 hours ago

I am an assistant professor at Denison University. I completed my PhD at Wesleyan University in 2014 under the supervision of Mark Hovey, and I completed a masters degree in computer science under the supervision of Danny Krizanc. I'm mostly interested in questions involving (semi) model categories, Bousfield localization, and algebras over (colored) operads. I like to apply my work to stable, equivariant, and motivic homotopy theory. On the computer science side I like thinking about graph theory, probability, and social networks, with an eye towards algorithms. I've also begun to dabble in game theory and economics.


19h
comment Need M combinatorial for existence of injective model structure on $M^G$?
I think an even better example is Pro categories, which are not combinatorial but often are fibrantly generated, which is very related to having a Postnikov presentation (I think Postnikov presentations were invented to generalize the notion of fibrantly generated). This paper seems to give injective model structures over pro-categories.
Jul
24
answered An example for a construction on monads/operads?
Jul
23
awarded  Nice Question
Jul
23
comment Properly Discontinuous Action
Yes, it does seem Munkres is assuming fixed point free in his book. I suppose he's interested in the topology of the quotient, but it does seem restrictive. Thanks for pointing this out.
Jul
20
comment Are there connections between Homotopy type theory and Grothendieck's theory of motives?
@MarcHoyois: Thanks for sharing. I did not know about these type theoretic model categories but it sounds like the right way to side-step univalence from what I have read.
Jul
20
revised Are there connections between Homotopy type theory and Grothendieck's theory of motives?
edited title
Jul
17
comment Are there connections between Homotopy type theory and Grothendieck's theory of motives?
...assuming that homotopy type theory actually does end up modeling every infinity topos, which from what I understand has not been proven yet.
Jul
17
revised Reference for a generalization of Γ-spaces to monoidal model categories
Texified because it was on the front page anyway
Jul
17
revised When the restriction of a derived functor to a subcategory is the derived functor of the restriction
fixed typos since it was on the front page anyway
Jul
17
comment Stabilization of a generic pointed model category
@MarcNieper-Wisskirchen: Thanks for the PS. This clarifies things for me. I only really ever think about cofibrantly generated situations, and I definitely only had that case in mind with the answer here. So I think functorial factorizations are no problem. Emily Riehl has done great work related to that topic, especially in her thesis.
Jul
15
comment Stabilization of a generic pointed model category
@DylanWilson: I did not say anything was wrong with it, and even if I thought there was something wrong this would have been the wrong forum to bring it up. I just said I can't follow it, and can't make it work for model categories. Am I right that the step reducing it to $C$ small is a universe enlargement, or is there something else going on? You are saying you can read the proof straight through and follow every step? If so I have questions for you.
Jul
15
comment Stabilization of a generic pointed model category
@ZhenLin: I guess we both already thought about this point, and the conclusion was that you need to weaken the model category axioms to only ask for finite limits and colimits, right (i.e. take Quillen's version not Hovey's)? I'm thinking of mathoverflow.net/questions/106924 and mathoverflow.net/questions/108739
Jul
15
comment Is there a notion of a “model category which admits left Bousfield localization?”
Great example, thanks!
Jul
15
awarded  Nice Question
Jul
14
comment Stabilization of a generic pointed model category
@MarcNieper-Wisskirchen: Okay, I did my best to provide an answer. I am traveling so might be very slow to respond in the comments. Hopefully the answer clarifies things a bit.
Jul
14
answered Stabilization of a generic pointed model category
Jul
13
comment Stabilization of a generic pointed model category
@MarcNieper-Wisskirchen: Certainly not. See my recent MathOverflow question mathoverflow.net/questions/209734 Here are 3 counterexamples: the Strom model structure on Top, the absolute model structure on chain complexes, and pro model structures.
Jul
11
comment Is the $\infty$-category of presentable $\infty$-categories presentable?
Thanks for making the edit. This is all much clearer now to me at least. Previously it seemed like the two answers were at odds, but no longer.
Jul
10
comment Why do we need filtered categories to index ind-objects?
@DylanWilson Do you read it in French or has someone translated it to English?
Jul
5
revised Is the $\infty$-category of presentable $\infty$-categories presentable?
edited body