In Fall 2026, the seminar meets in Blocker 302 on Thursdays at 4pm.

2026Fall

  • October 29, 2026

    Benjamin Yang, TAMU

    Title: The symmetric structure of the inviscid shallow water equations with gravity and surface tension

    Abstract: I will present a new, more physically intuitive proof of the local well-posedness of the inviscid shallow water equations with gravity and surface tension. Our proof is based on identifying the good variables and uncovering the hidden symmetric structure of the equations. Joint work with Xin Liu (Texas A&M).

  • October 22, 2026

    Dean Baskin, TAMU

    Title: Construction of the Feynman propagator in the “simplest” setting

    Abstract: In this talk I’ll describe a microlocal construction (due to Vasy) of the Feynman propagator for the Klein–Gordon equation on an asymptotically Minkowski spacetime. I’ll finish describing the estimates and how you put them together and give a rough idea of how, given the pseudodifferential calculus, you can get the estimates relatively cheaply.

  • October 15, 2026

    Dean Baskin, TAMU

    Title: Construction of the Feynman propagator in the “simplest” setting

    Abstract: In this talk I’ll describe a microlocal construction (due to Vasy) of the Feynman propagator for the Klein–Gordon equation on an asymptotically Minkowski spacetime.

  • October 1, 2026

    Andrew Comech, TAMU

    Title: Complete characterization of linear stability for nonlinear Dirac equation in 1D

    Abstract: One says that a solitary wave solution is “spectrally stable” if the operator of linearization at this wave has no eigenvalues with positive real part. In the case of the nonlinear Dirac equation, this question becomes very convoluted in view of possibility of “quadruplets” of complex eigenvalues, with nonzero real and imaginary parts. We finally show that in 1D this never happens; the spectral stability is completely characterized by the Vakhitov–Kolokolov condition (dQ/d\omega<0) and the energy vanishing condition (E>0). This is the introductory talk; no prior acquaintance with Dirac is assumed.

  • September 24, 2026

    Andrew Comech, TAMU

    Title: Complete characterization of linear stability for nonlinear Dirac equation in 1D

    Abstract: One says that a solitary wave solution is “spectrally stable” if the operator of linearization at this wave has no eigenvalues with positive real part. In the case of the nonlinear Dirac equation, this question becomes very convoluted in view of possibility of “quadruplets” of complex eigenvalues, with nonzero real and imaginary parts. We finally show that in 1D this never happens; the spectral stability is completely characterized by the Vakhitov–Kolokolov condition (dQ/d\omega<0) and the energy vanishing condition (E>0). This is the introductory talk; no prior acquaintance with Dirac is assumed.