New Hopf Structures on Binary Trees by Stefan Forcey, Aaron Lauve, Frank Sottile

“…The multiplihedra $\mathcal{M}_{\bullet} = (\mathcal{M}_n)_{n \geq 1}$ form a family of polytopes originating in the study of higher categories and homotopy theory. While the multiplihedra may be unfamiliar to the algebraic combinatorics community, it is nestled between two families of polytopes that certainly are not: the permutahedra $\mathfrak{S}_{\bullet}$ and associahedra $\mathcal{Y}_{\bullet}$. …”
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The nonabelian tensor squares of one family of bieberbach groups with point group C2 by Masri, Rohaidah, Aris, Nor'aini, Sarmin, Nor Haniza, Robert, Morse

“…The nonabelian tensor square is a special case of the nonabelian tensor product which has its origins in homotopy theory. The Bieberbach groups are extensions of a point group and a free abelian group of finite rank. …”
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Symmetry-Based Approach to Superconducting Nodes: Unification of Compatibility Conditions and Gapless Point Classifications by Seishiro Ono, Ken Shiozaki

“…While most previous studies are based on the homotopy theory, our theory is on the basis of the symmetry-based analysis of band topology, which enables systematic diagnoses of nodes in all nonmagnetic and magnetic space groups. …”
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The Gysin triangle via localization and A[superscript 1]-homotopy invariance by Van den Bergh, Michel, Trigo Neri Tabuada, Goncalo Jorge

“…Finally, as a third application, we construct explicit bridges relating motivic homotopy theory and mixed motives on the one side with noncommutative mixed motives on the other side. …”
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The Schur multiplier and capability of pairs of some finite groups by Nawi, Adnin Afifi

“…The homological functors of a group have its origin in homotopy theory and algebraic K-theory. The Schur multiplier of a group is one of the homological functors while the Schur multiplier of pairs of groups is an extension of the Schur multiplier of a group. …”
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Exact categories, Koszul duality, and derived analytic algebra by Kelly, J

“…</p> <p>We then develop the homotopy theory of algebras in <em>Ch</em>(<em>E</em>). …”