Home Analysis, PDEs, differential geometry and applications seminar
Analysis, PDEs, differential geometry and applications seminar
Spring 2021 (Thursdays 3 pm through Zoom)
Date: Thursday February 11
Speaker: Dr. John Holmes
Title: New results on weakly dispersive PDEs
Abstract: We will discuss two models for water waves. The first models waves near the equator, where the coriolis effect is important. The second equation is the FORQ equation, which is related to the celebrated KdV equation. Together with Feride Tiglay and Ryan Thompson, we study these equations in Besov spaces and show that the data-to-solution map is not better than continuous. In this talk we will motivate and introduce Besov spaces based on the Littlewood-Paley decomposition. We will also outline the proofs of nonuniform dependence and present some new estimates in Besov spaces.
Date: Thursday February 18
Speaker: Dr. Jeremy Marzuola
Title: Some recent progress on nodal domains
Abstract: We will first discuss some recent work on characterizing the number of nodal sets for an eigenfunction that was initiated with Graham Cox and Chris Jones, then has been further developed with Greg Berkolaiko and Graham Cox. The work of Berkolaiko-Cox-M gives an especially nice means of quantifying nodal sets for separable problems. Then, time permitting we will discuss more closely properties of nodal sets for low energy eigenfunctions on nearly rectangular domains that we looked at in joint with with Tom Beck and Yaiza Canzani.
Date: Thursday February 25
Speaker: Dr. John Gemmer
Title: Gamma-convergence for novices: Part 1
Abstract: Gamma convergence provides an asymptotic description for the behavior of a family of minimization problems and has been used to provide a rigorous framework for studying singular perturbation problems that arise in homogenization theory, phase transitions, free discontinuity problems, and elasticity theory to name a few. In 2002 Andrea Braides wrote a book entitled “Gamma convergence for beginners” which requires a solid foundation in measure theory and functional analysis to read in depth which is not my definition of a beginner. My goal in these three lectures is to introduce the topic of gamma convergence to a broad audience somewhere at the novice level, i.e. a Wake Forest student taking MST 711. Part 1 of the lecture will serve as an introduction to weak convergence and the direct method of the calculus of variations. Part 2 will focus on gamma convergence with respect to the weak topology and contain several examples of computing gamma limits. Finally part 3 will focus on a collaboration with Kaitlin Hill in which we apply gamma-convergence techniques to understand noise induced tipping in piecewise-smooth dynamical systems.
Date: Thursday March 4
Speaker: Dr. John Gemmer
Title: Gamma-convergence for novices: Part 2
Abstract: Gamma convergence provides an asymptotic description for the behavior of a family of minimization problems and has been used to provide a rigorous framework for studying singular perturbation problems that arise in homogenization theory, phase transitions, free discontinuity problems, and elasticity theory to name a few. In 2002 Andrea Braides wrote a book entitled “Gamma convergence for beginners” which requires a solid foundation in measure theory and functional analysis to read in depth which is not my definition of a beginner. My goal in these three lectures is to introduce the topic of gamma convergence to a broad audience somewhere at the novice level, i.e. a Wake Forest student taking MST 711. Part 1 of the lecture will serve as an introduction to weak convergence and the direct method of the calculus of variations. Part 2 will focus on gamma convergence with respect to the weak topology and contain several examples of computing gamma limits. Finally part 3 will focus on a collaboration with Kaitlin Hill in which we apply gamma-convergence techniques to understand noise induced tipping in piecewise-smooth dynamical systems.
Date: Thursday March 11
Speaker: Dr. John Gemmer
Title: Gamma-convergence for novices: Part 3
Abstract: Gamma convergence provides an asymptotic description for the behavior of a family of minimization problems and has been used to provide a rigorous framework for studying singular perturbation problems that arise in homogenization theory, phase transitions, free discontinuity problems, and elasticity theory to name a few. In 2002 Andrea Braides wrote a book entitled “Gamma convergence for beginners” which requires a solid foundation in measure theory and functional analysis to read in depth which is not my definition of a beginner. My goal in these three lectures is to introduce the topic of gamma convergence to a broad audience somewhere at the novice level, i.e. a Wake Forest student taking MST 711. Part 1 of the lecture will serve as an introduction to weak convergence and the direct method of the calculus of variations. Part 2 will focus on gamma convergence with respect to the weak topology and contain several examples of computing gamma limits. Finally part 3 will focus on a collaboration with Kaitlin Hill in which we apply gamma-convergence techniques to understand noise induced tipping in piecewise-smooth dynamical systems.
Date: Thursday March 18
Speaker: Dr. Irfan Glogic
Title: TBD
Abstract: TBD
Date: Thursday March 25
Speaker: Dr. Marco Lopez
Title: TBD
Abstract: TBD
Date: Thursday April 1
Speaker: Dr. Nsoki Mavinga
Title: TBD
Abstract: TBD
Date: Thursday April 8
Speaker: Dr. Mostafa Rezapour
Title: TBD
Abstract: TBD
Date: Thursday April 15
Speaker: Dr. Mostafa Rezapour
Title: TBD
Abstract: TBD
Date: Thursday April 22
Speaker: Dr. Kate Meyer
Title: TBD
Abstract: TBD
