Recently, Marian–Oprea–Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending the work Johnson, they provided a conjectural correspondence between and Verlinde numbers. For surfaces with holomorphic 2-form, we propose generalizations their results moduli spaces stable sheaves any rank. Using Mochizuki's ...

We establish a relation between topological and quantum entanglement for a multi-qubit state by considering the unitary representations of the Artin braid group. We construct topological operators that can entangle multi-qubit state. In particular we construct operators that create quantum entanglement for multi-qubit states based on the Segre ideal of complex multi-projective space. We also in...

We’ve covered a lot of ground so far. I want to remind you that we’ve essentially defined a very few things, and spent all our energy on showing that they behave well with respect to each other. In particular: proper pushforward, flat pullback, c·, s·, s·(X, Y). Gysin pullback for divisors; intersecting with pseudo-divisors. Gysin pullback for 0sections of vector bundles. We know how to calcula...

We find minimal generators for the ideals of secant varieties of Segre varieties in the cases of σk(P 1 × P n × P ) for all k, n,m, σ2(P n × P m × P p × P ) for all n,m, p, r (GSS conjecture for four factors), and σ3(P n ×P m ×P ) for all n,m, p and prove they are normal with rational singularities in the first case and arithmetically Cohen-Macaulay in the second two.

Extinction efficiencies of coated absorbing aerosols measured by cavity ring down aerosol spectrometry A. A. Riziq, M. Trainic, C. Erlick, E. Segre, and Y. Rudich Department of Environmental Sciences, Weizmann Institute, Rehovot, 76100, Israel Dept. of Atmospheric Sciences, The Hebrew Univ. of Jerusalem, Jerusalem, 91904, Israel Physics Services, Weizmann Institute, Rehovot, 76100, Israel Recei...

In this paper, we ask the following question: what is the minimal value of the difference e HK (I) − e HK (I ′) for ideals I ′ ⊇ I with l A (I ′ /I) = 1? In order to answer to this question, we define the notion of minimal Hilbert-Kunz multiplicity for strongly F-regular rings. Moreover, we calculate this invariant for quotient singularities and for the coordinate ring of the Segre embedding: P...