Local AWM events

The local chapter of the AWM (Association for Women in Mathematics) is holding a number of fascinating events.  We want to encourage all of our group to participate.  See https://math.unc.edu/events/awm-lecture/.  This evening’s event (Monday, October 24) is a panel discussion on jobs for mathematicians outside of academia.  There is an upcoming panel on REU opportunities.  Both of these are outstanding opportunities.

Maddie Brown’s summer work

We want to proudly highlight some of the summer work of Maddie Brown, one of our graduate students.  In addition to speaking in Bonn at the Young Women in Geometric Analysis conference and the CMS Summer Meeting in Newfoundland, she attended the Harmonic Analysis and Waves conference in Seattle and participated in the Harmonic Analysis on Manifolds Summer School in Madison.  Moreover, she volunteered as a mentor at the University of Michigan – Dearborn REU site where she led projects with Yunus Zeytuncu on Spectral Theory and CR Geometry.

We congratulate Maddie on spectacularly productive and engaged summer.

Academic Job Search Panel

The RTG invites the graduate students within UNC’s Department of Mathematics to an informal discussion on First Academic Job Searches.  We’ll field questions about the types of positions, planning for your job applications, how to prepare materials, etc.
We’ll meet on Tuesday, September 27, 3:30pm in PH332. This invitation is for all graduate students within the department.  Students from any discipline within the department are welcome.  Students not completing your degree this year are encouraged to attend to learn what to expect in the future.

Spring 2023 Topics Course

Jeremy Marzuola will offer a Graduate Topics Course (Math 891) in Spring 2023.  It will be titled: Stability of Nonlinear States in Evolution Equations.  We encourage you to enroll / watch for the course (after its completion) on the upcoming Online Topics Course Collaborative.

Description: We cover existence theory for nonlinear states in a variety of nonlinear evolution equations: 1. Dispersive models such as Korteweg-de Vries; nonlinear Schrödinger or Gross-Pitaevski, Dirac and Klein-Gordon equations, as well as other models like Density Functional Theory in quantum mechanics, Dispersion Managed models from optics, Wave and Schrödinger Maps, Schrödinger-Coulomb models, models from weak turbulence, etc.; and 2. Parabolic models such as Ginzburg-Landau equations, thin-films, and models from material science.  While these may seem disparate and unrelated, we will see that in many cases finding stationary states for such models follows from similar tools.  We will consider the existence of nonlinear states from the point of view of ode theory, the calculus of variations, and by using bifurcation theory in function spaces applied to a number of examples.  We will also introduce some numerical schemes for locating these states and discuss their convergence properties. Then, we will discuss aspects of spectral stability and address this question in a variety of examples.  Since the linearized operators around these states are non-self-adjoint, the analysis of these operators can be rather challenging, but we will consider several representative examples to identify key ideas.  In particular, we will address issues surrounding existence of stable and unstable eigenvalues, quantifying the null-space, and existence/non-existence of embedded eigenvalues.  Then, given time, we will then discuss the notions of orbital and asymptotic stability and dynamics, and how they relate to dynamical properties of the corresponding evolution equations.  Throughout we will present open problems that might be of interest for young researchers and focus on insightful computations.

Research Round-up

We will regularly announce newly posted articles and newly accepted articles within the group.  We are proud to announce the following updates from the past few months.

Yaiza Canzani (faculty)

Jeremy Marzuola (faculty)

Jason Metcalfe (faculty)

      • Newly accepted:  J. Metcalfe and A. Stewart: On a system of weakly null semilinear wave equations.  Analysis and Mathematical Physics, to appear.
      • Newly accepted:  M. Facci and J. Metcalfe: Global existence for quasilinear wave equations satisfying the null condition.. Houston Journal of Mathematics, to appear.
      • Newly accepted:  K. Hepditch and J. Metcalfe: A local energy estimate for 2-dimensional Dirichlet wave equations.  Involve, to appear.

Casey Rodriguez (faculty)

Michael Taylor (faculty)

Mark Williams (faculty)

Upcoming talks by RTG members

We proudly alert you to a number of upcoming presentations by RTG members.

  • Maddie Brown (graduate student)
  • Yaiza Canzani (faculty)
      • QMATH 15 at the University of California – Davis, September 12-16
      • Colloquium at Northwestern University, October 5
      • Chern-Weil Symposium at the University of Chicago, October 7-9
      • Panelist for “Exploring a research landscape” at the GROW conference at Duke University, October 22
      • Colloquium at Dartmouth University, October 29
  • Hans Christianson (faculty)
  • Jeremy Marzuola (faculty)
      • Attending “At the interface between semiclassical analysis and numerical analysis of wave scattering problems” at Mathematisches Forschungsinstitut Oberwolfach (Germany)
      • Applied math seminar at the University of North Carolina – Greensboro, October 3
      • SEARCDE Conference at North Carolina State University, November 12-13
  • Casey Rodriguez (faculty)