Browsing by Author "Gwiazda, Piotr"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
- ItemGeneralized entropy method for the renewal equation with measure data(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Gwiazda, Piotr; Wiedemann, EmilWe explore the explicit relationship between the descendant Gromov–Witten theory of target curves, operators on Fock spaces, and tropical curve counting. We prove a classical/tropical correspondence theorem for descendant invariants and give an algorithm that establishes a tropical Gromov–Witten/Hurwitz equivalence. Tropical curve counting is related to an algebra of operators on the Fock space by means of bosonification. In this manner, tropical geometry provides a convenient “graphical user interface” for Okounkov and Pandharipande’s celebrated GW/H correspondence. An important goal of this paper is to spell out the connections between these various perspectives for target dimension 1, as a first step in studying the analogous relationship between logarithmic descendant theory, tropical curve counting, and Fock space formalisms in higher dimensions.
- ItemRegularity and energy conservation for the compressible Euler equations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Feireisl, Eduard; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Wiedemann, EmilWe give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator estimates similar to those employed by P. Constantin et al. for the homogeneous incompressible Euler equations.