About

Dean R. Baskin is a professor in the Department of Mathematics at Texas A&M University. His office is located in Blocker 614B. The provided information indicates his role as a faculty member within the department, but does not include specific details about his research focus, background, or key contributions.

Research topics

• Mathematics
• Pure mathematics
• Mathematical analysis
• Physics
• Quantum mechanics
• Geometry
• Mathematical physics
• Quantum electrodynamics
• Chemistry

Selected publications

• The Klein-Gordon equation on asymptotically Minkowski spacetimes: the Feynman propagator

  ArXiv.org · 2025-07-02

  preprintOpen access1st authorCorresponding

  We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities estimates in Vasy's 3sc-calculus. We combine these estimates to prove global spacetime mapping properties for the Feynman propagator, and to show that it satisfies a microlocal Hadamard condition. We show that the Feynman propagator can be realized as the inverse of a mapping between appropriate $L^2$-based Sobolev spaces with additional regularity near the asymptotic sources of the Hamiltonian flow, realized as a family of radial points on a compactified spacetime.

  PublisherOA PDFDOI

• Price’s law for the massless Dirac–Coulombsystem

  Pacific Journal of Mathematics · 2025-04-18

  articleOpen access1st authorCorresponding

  We consider the pointwise decay of solutions to wave-type equations in two model singular settings.Our main result is a form of Price's law for solutions of the massless Dirac-Coulomb system in (3+1)-dimensions.Using identical techniques, we prove a similar theorem for the wave equation on Minkowski space with an inverse square potential.One novel feature of these singular models is that solutions exhibit two different leading decay rates at timelike infinity in two regimes, distinguished by whether the spatial momentum along a curve which approaches timelike infinity is zero or nonzero.An important feature of our analysis is that it yields a precise description of solutions at the interface of these two regions which comprise the whole of timelike infinity.

  PublisherOA PDFDOI

• Singularities of Dirac-Coulomb propagators

  ArXiv.org · 2025-07-21

  preprintOpen access1st authorCorresponding

  In this paper we study singularities of propagators and $N$-point functions for Dirac fields in a Coulomb potential, possibly with a $t$-dependent smooth part for $|t|

  PublisherOA PDFDOI

• Propagation of Singularities for the Wave Equation

  MATRIX book series · 2024-01-01

  book-chapter1st author
  PublisherDOI

• The Klein-Gordon equation on asymptotically Minkowski spacetimes: causal propagators

  arXiv (Cornell University) · 2024-09-02

  preprintOpen access1st authorCorresponding

  We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for forward/backward solutions to the inhomogeneous, perturbed Klein-Gordon equation, including in the presence of bound states of the limiting spatial Hamiltonians. To this end, we prove propagation of singularities estimates in all regions of infinity (spatial, null, and causal) and use the estimates to prove that the Klein-Gordon operator is an invertible mapping between adapted weighted Sobolev spaces. This builds off work of Vasy in which inverses of hyperbolic PDEs are obtained via construction of a Fredholm mapping problem using radial points propagation estimates. To deal with the presence of a perturbation which persists in time, we employ a class of pseudodifferential operators first explored in Vasy's many-body work.

  PublisherOA PDFDOI

• Diffraction for the Dirac–Coulomb Propagator

  Annales Henri Poincaré · 2023 · 2 citations

  1st authorCorresponding
  • Physics
  • Mathematical physics
  • Quantum electrodynamics
  PublisherOA PDFDOI

• Riemann moduli spaces are quantum ergodic

  Journal of Differential Geometry · 2023-03-01 · 1 citations

  article1st authorCorresponding

  In this note we show that the Riemann moduli spaces $M_{\gamma,n}$ equipped with the Weil–Petersson metric are quantum ergodic for $3 \gamma + n \geq 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.

  PublisherDOI

• Asymptotics of the radiation field for the massless Dirac–Coulomb system

  Journal of Functional Analysis · 2023-07-31 · 2 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• The radiation field on product cones

  Advances in Mathematics · 2022 · 7 citations

  1st authorCorresponding
  • Mathematics
  • Mathematical analysis
  • Pure mathematics
  PublisherDOI

• Price's law on Minkowski space in the presence of an inverse square potential

  arXiv (Cornell University) · 2022-07-13

  preprintOpen access1st authorCorresponding

  We consider the pointwise decay of solutions to wave-type equations in two model singular settings. Our main result is a form of Price's law for solutions of the massless Dirac-Coulomb system in (3+1)-dimensions. Using identical techniques, we prove a similar theorem for the wave equation on Minkowski space with an inverse square potential. One novel feature of these singular models is that solutions exhibit two different leading decay rates at timelike infinity in two regimes, distinguished by whether the spatial momentum along a curve which approaches timelike infinity is zero or non-zero. An important feature of our analysis is that it yields a precise description of solutions at the interface of these two regions which comprise the whole of timelike infinity.

  PublisherOA PDFDOI

Recent grants

• CAREER: Wave evolution on singular spacetimes

  NSF · $419k · 2017–2024

• Scattering theory on singular spaces

  NSF · $157k · 2015–2019

• PostDoctoral Research Fellowship

  NSF · $135k · 2011–2015

Frequent coauthors

• Jared Wunsch

  Northwestern University

  20 shared

• András Vasy

  Stanford University

  8 shared

• Jeremy L. Marzuola

  7 shared

• Euan A. Spence

  University of Bath

  7 shared

• Jesse Gell‐Redman

  6 shared

• Antônio Sá Barreto

  Purdue University West Lafayette

  6 shared

• Kiril Datchev

  2 shared

• Xiaolong Han

  2 shared

Awards & honors

• NSF CAREER grant DMS-1654056