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David Roberts
Works at University of Adelaide
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David Roberts

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Title: Extensions of flat functors and theories of presheaf type
Author: Olivia Caramello

Abstract: We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a characterization theorem providing necessary and sufficient semantic conditions for a theory to be of presheaf type. This theorem subsumes all the previous partial results obtained on the subject and has several corollaries which can be used in practice for testing whether a given theory is of presheaf type as well as for generating new examples of theories belonging to this class. Along the way, we establish a number of other results of independent interest, including developments about colimits in the context of indexed categories, expansions of geometric theories and methods for constructing theories classified by a given presheaf topos.

http://arxiv.org/abs/1404.4610

#arXiv
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And it irks me when publishers want to remove urls and arXiv numbers in the references.
 
References should connect readers to full texts, and therefore favor OA editions.

A nice argument from Patrick Dunleavy: "What is the essential purpose of academic referencing? ...A completely out of date answer dominates current practice  — namely...[directing readers] to the same precise sources and pages that you yourself used in constructing an argument or a case....Referencing should instead be about directly connecting readers to the full text of your sources, ideally in a one-stop way....In other words, modern referencing is not about pointing to some source details for books that cost a small fortune and are buried away in some library where the reader is not present; still less about pointing to source details for an article in a pay-wall journal to which readers do not have access....With open access spreading now we can all do better, far better, if we follow one dominant principle. Referencing should connect readers as far as possible to open access sources, and scholars should in all cases and in every possible way treat the open access versions of texts as the primary source...."

#oa #openaccess #references   #citations  
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Great way for the publisher to cause people to avoid their version in favor of the superior, arXiv version.
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My notes from my talk at Category Theory 2013. This is the follow-on after my paper The weak choice principle WISC may fail in the category of sets (arXiv:1311.3074 - I released this much later than I should have).
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David Roberts

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I like this sense of humour:

"The problem of proving a general coherence theorem for pullbacks and pushforwards in the context of monoidal functors was mentioned in Fausk–Hu–May [FHM03] and said to be both unsolved and desirable; we do not claim to have solved it, though certainly, we have done something."
-Ryan Cohen Reich (http://www.tac.mta.ca/tac/volumes/29/4/29-04abs.html)

I also like very much the conceptual approach taken and described in the introduction, that it is important to extract the category-theoretic content from arguments and the necessary axioms for that part to hold.
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David Roberts

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Reimagining the Foundations of Algebraic Topology There were nice talks at the MSRI meeting a few days back, and well-done video recordings are available on the website: https://www.msri.org/workshops/689

Thomas Nikolaus recalled the new cohesive foundations of differential cohomology

  http://ncatlab.org/nlab/show/tangent+cohesive+(∞,1)-topos

here: 

  https://www.msri.org/workshops/689/schedules/18231

David Gepner recalled the general theory of integration in twisted generalized cohomology  

  http://ncatlab.org/nlab/show/twisted+Umkehr+map

here:
 
  https://www.msri.org/workshops/689/schedules/18244

 Goncalo Tabuada recalled the theory of noncommutative motives
 
  http://ncatlab.org/nlab/show/noncommutative+motive

here:
 
  https://www.msri.org/workshops/689/schedules/18243

David Ben-Zvi spoke on ideas about formulating the 6d field theory on the M5-brane

  http://ncatlab.org/nlab/show/6d+(2,0)-supersymmetric+QFT

here: 
 
  https://www.msri.org/workshops/689/schedules/18216

André Joyal recalled how to think of homotopy type theory as a definition of elementary infinity-toposes
 
 http://ncatlab.org/nlab/show/elementary+(infinity,1)-topos

here:

  https://www.msri.org/workshops/689/schedules/18227

and much more. 
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David Roberts

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A bunch of arXiv papers for today:

http://arxiv.org/abs/1404.3886
Title: Operadic categories and Duoidal Deligne's conjecture
Authors: Michael Batanin, Martin Markl

Abstract: The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. 
In Part 2 we use this new theory together with our previous results to prove that multiplicative 1-operads in duoidal categories admit, under some mild conditions on the underlying monoidal category, natural actions of contractible 2-operads. The result of D. Tamarkin on the structure of dg-categories, as well as the classical Deligne conjecture for the Hochschild cohomology, is a particular case of this statement.

http://arxiv.org/abs/1404.3955
Title: The centre of the extended Haagerup subfactor has 22 simple objects
Authors: +Scott Morrison +Kevin Walker 

Abstract: We explain a technique for discovering the number of simple objects in Z(C), the center of a fusion category C, as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring K(C) and the dimension function K(C) \to \mathbb{C}. 
The method is not guaranteed to succeed (it may give spurious answers besides the correct one, or it may simply take too much computer time), but it seems it often does. We illustrate by showing that there are 22 simple objects in the center of the extended Haagerup subfactor [arXiv:0909.4099].

and an older paper

http://arxiv.org/abs/1009.2245
Title: From WZW models to Modular Functors
Author: Eduard Looijenga

Abstract: In this survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory.
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Thanks for the last one! Should be added to the nLab at "Hitchin connection". (Looijenga is the author to whom also the identification in this context of the loop group reps to equivariant elliptic cohomology goes back to.)
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Haven't looked through this site, but it's partly organised by the Mathematisches Forschungsinstitut Oberwolfach, and looks nice. 
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David Roberts

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Do you like random graphs? Did you like #2048? You may like this

http://planarity.net/#

And you can skip ahead to levels (I looked at level 100... o.O)

EDIT: Took me eight minutes to do level 7.
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Ah, it's something to do with needing the Euler characteristic to be 2, for some choice of faces. (EDIT: actually, no. There is a wikipedia page for this game, with some relevant theory)
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Have him in circles
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I live in Adelaide, Australia.

I am a pure mathematician who works on category theory and a smattering of related fields such foundations and higher geometry.

I work as a post-doc at the University of Adelaide in the School of Mathematical Sciences.

My nLab page: http://ncatlab.org/nlab/show/David+Roberts
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