We construct two infinite sequences of immersions of the 3-sphere into 4-space, parameterized by the Dynkin diagrams of types A and D. The construction is based on immersions of 4-manifolds obtained as the plumbed immersions along the weighted Dynkin diagrams. We compute their Smale invariants and bordism classes of immersions by using Ekholm–Takase’s formula in terms of singular Seifert su…

Colleges and universities need to provide students with training and experience in (a) interdisciplinary research, (b) the fuzzy areas of responsible conduct of research, and (c) the mentor–mentee relationship. We developed workshops that combine the three content objectives— interdisciplinary research, responsible conduct of research, and mentor–mentee relationship, therefore promoting e…

We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices.

The first monarch citizen science program was launched in the 1950s and, since then, thousands of volunteers have made fundamental contributions to our accumulating knowledge of monarch biology. We quantified these efforts and the degree to which citizen science has contributed to monarch scholarship. We estimate that, in 2011, volunteers spent over 72,000 hours collecting data useful for monar…

We study the homeomorphism types of manifolds h-cobordant to a fixed one. Our investigation is partly motivated by the notion of special manifolds introduced by Milnor in his study of lens spaces. In particular, we revisit and clarify some of the claims concerning h-cobordisms of these manifolds.

We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over a commutative ring without non-trivial idempotents has no proper non-zero thick subcategories that are strongly generated. The main theorem is al…

We prove that for all n, simultaneously, we can choose prime filtrations of R/In such that the set of primes appearing in these filtrations is finite.

Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of the density properties of rational points on the Kummer variety Km(Ar) of the r-fold product of A with itself. One consequence of our results is the following. Fix an abelian variety A over k, and suppose that for so…

Adult somatic cells can be reprogrammed into pluripotent stem cells, which can indefinitely proliferate in a dish and differentiate into almost all the cell types that constitute the human body. These cells hold great promise for cell therapy and regenerative medicine, as well as drug screening and disease modeling. Theoretically, we can create a source of versatile, therapeutic cells that coul…

Let G be a locally compact group, and let B(G) denote its Fourier–Stieltjes algebra. We show that B(G) is Connes-amenable if and only if G is almost abelian.