Mahowald proved the height 1 telescope conjecture at prime 2 as an application of his seminal work on bo-resolutions. In this paper we study through lens tmf-resolutions. To end compute structure tmf-resolution for a specifc type complex Z. We find that, analogous to case, E1-page possesses decomposition into v2-periodic summand, and Eilenberg-MacLane summand which consists bounded v2-torsion. ...

Abstract We prove that the PPT $$^2$$ 2 conjecture holds for linear maps between matrix algebras which are covariant under action of diagonal unitary group. Many salient examples, like Choi-type maps, depolarizing dephasing amplitude damping and mixtures thereof, lie in thi...

We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg–Witten type. This result shows that there exists large class of topological 4-manifolds such all smooth structures have type, and yet some non-vanishing (mod 2) invariants. As corollaries, we obtain adjunction inequalities show mild condition, geometrically simply connected vanishing invari...

This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at point gets close to dangerous territory of the Riemann Hypothesis. We will mostly focus on open problems, we also provide proofs, just for adorning.