Greg Arone and Michael Ching, Goodwillie calculus
David Ayala and John Francis, A factorization homology primer
Tony Bahri, Martin Bendersky, and Fred Cohen,
Polyhedral products and features of their homotopy theory
"This is a highly awaited and much appreciated fine piece of work reviewing
a rapidly growing area in algebraic topology with connections to a plethora
Paul Balmer, A guide to tensor-triangular classification
Tobias Barthel and Agnes Beaudry,
Chromatic structures in stable homotopy theory
"Overall, this article serves as an excellent introduction for anyone wishing
to know more about the subject. Concepts are nicely motivated, and a wealth
of references is given in case the reader wants to pursue a topic in more
Mark Behrens, Topological modular and automorphic forms
"Especially nice is the discussion of the chromatic behaviour of topological modular
forms. Not only does the author discuss the K(1)- and K(2)-localizations of topological
modular forms, but he also gives a more general treatment of stacks associated to ring
spectra, following Hopkins. ...
The last section of the paper reflects the growing richness of the Tmf-literature by
giving a guided reading list to a large number of articles in the field. As it also contains
many references to recent work, this is important added value compared to older surveys."
Juli Bergner, A survey of models for (\infty,n)-categories
Gunnar Carlsson, Persistent homology and applied homotopy theory
"This clearly written and well-structured work contains a high-level discussion of the
current situation as well as active research directions in persistent homology and applied
homotopy theory as seen by one of the founders of the research area."
Natalia Castellana, Algebraic models in the homotopy theory of classifying spaces
Ralph Cohen, Floer homotopy theory, revisited
Benoit Fresse, Little discs operads, graph complexes, and Grothendieck-Teichmuller groups
Soren Galatius and Oscar Randal-Williams,
Moduli spaces of manifolds: a user's guide
David Gepner, An introduction to higher categorical algebra
"The chapter is a well written, useful introduction to higher categorical algebra, containing many helpful remarks about the similarity and differences of classical constructions and the new framework. No proofs are given, but results are carefully referenced.
This makes it easy to get a quick overview of definitions and results before diving into
the technical details of full proofs."
Moritz Groth, A short course on \infty-categories
Lars Hesselholt and Thomas Nikolaus, Topological cyclic homology
"As a splendid bonus, they use this to give
a purely p-adic proof of Bott periodicity."
Gijs Heuts, Lie algebra models for unstable homotopy theory
"This paper is a well-presented survey of known results of that kind, generalizing
and extending Quillen's theorem. A great deal of useful background is provided, giving
introductory treatments of operads, localization theory for spectra and spaces, the
Bousfield-Kuhn functor, topological Andre-Quillen cohomology, Koszul duality, and
partition complexes and the spectral Lie operad. This makes the paper approachable for
readers who may not have much background knowledge in the subject. Some ideas are
presented in ways that are insightful but not the most commonly found in the literature,
making the introductory material interesting even to a reader who already has some
background knowledge. Several open problems are given at the end."
Mike Hill, Equivariant stable homotopy theory
"This article traverses through the concepts which are currently useful in equivariant
stable homotopy theory over finite groups. This comprehensive survey may also serve
as a good introduction for those interested in learning about aspects of equivariant
Dan Isaksen and Paul Arne Ostvaer, Motivic stable homotopy groups
Tyler Lawson, E_n-spectra and Dyer-Lashof operations
Wolfgang Lueck, Assembly maps
Nat Stapleton, Lubin-Tate theory, character theory, and power operations
Kirsten Wickelgren and Ben Williams, Unstable motivic homotopy theory
"This is a well-written survey article about unstable motivic homotopy theory, a subject based on the idea that one can do homotopy theory in algebraic geometry, using the affine line A^1 as a substitute for the unit interval in topology."