We show that the Kervaire invariant one elements θ_jϵπ_2^j+1-2S^0 exist only for j≤ 6. By
Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist …

This research monograph is divided into three parts. Broadly speaking, Part I belongs to the
realm of category theory, while Parts II and III pertain to algebraic combinatorics, although …

The purpose of this work is to prove the existence of an algebraic moduli classifying objects
in a given triangulated category. To any dg-category T (over some base ring k), we define a …

Derived algebraic geometry Page 1 EMS Surv. Math. Sci. 1 (2014), 153–240 DOI 10.4171/EMSS/4
EMS Surveys in Mathematical Sciences c European Mathematical Society Derived algebraic …

A stable model category is a setting for homotopy theory where the suspension functor is
invertible. The prototypical examples are the category of spectra in the sense of stable …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

We show that the homotopy theory of differential graded algebras coincides with the
homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences …

Consider a pair (X, L) of a Weinstein manifold X with an exact Lagrangian submanifold L,
with ideal contact boundary (Y, Λ), where Y is a contact manifold and Λ⊂ Y is a Legendrian …

We apply ideas from commutative algebra, and Morita theory to algebraic topology using
ring spectra. This allows us to prove new duality results in algebra and topology, and to view …

We prove that the rank of the cohomology of a closed symplectic manifold with coefficients in
a field of characteristic $ p $ is smaller than the number of periodic orbits of any non …