Prerequisites and Corequisites

Recently I have taught three courses:

MAT244H1 – Introduction to Ordinary Differential Equations.

  • Prerequisite:
    • Calculus I: (MAT135H1 & MAT136H1)/ MAT137Y1 or Analysis II (MAT157Y1)
    • Linear Algebra I: MAT223H1 or Algebra I: MAT240H1
  • Corequisite:
    • Calculus II (MAT235Y1/​ MAT237Y1) or Analysis II​ MAT257Y1

I believe that

  • MAT135/MAT136 and MAT235Y1 are too weak and should be quashed and
  • Linear Algebra II: MAT244H1 or Algebra II: MAT247H1 should be Recommended.

MAT334H1 – Complex variables

  • Prerequisite:
    • Calculus II: MAT235Y1/​ MAT237Y1/​ or /Analysis II: MAT257Y1
    • Linear Algebra I: MAT223H1 or Algebra I:​ MAT240H1

I strongly believe that

  • MAT235 is too weak and should be quashed, while
  • Linear Algebra I/ Algebra I is not needed.

APM346H1 – Partial Differential Equations

  • Prerequisite:
  • Calculus II: MAT235Y1/​ MAT237Y1 or Analysis II: MAT257Y1,
  • Ordinary Differential Equations: MAT244H1/​ MAT267H1

I very strongly believe that

  • MAT235 is too weak and should be quashed, and
  • Linear Algebra II: MAT244H1 or Algebra II: MAT247H1 should be added as a prerequisite, and
  • Complex Variables: MAT334H1 or Complex Analysis I: MAT354H1 should be added as a corequisite.

I also very strongly believe that MAT334 and APM346 are excessive for economists etc and should be replaced by a single one semester class

Elements of the Complex Variables an d Partial Differential Equations

Spectral Methods in Mathematical Physics

Programme “Spectral Methods in Mathematical Physics”

14 January—26 April 2019, Mittag Leffler Institute, Djursholm, Sweden

(I participate February 15—24)

My talk: Complete Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Coefficients Operators and Bethe-Sommerfeld Conjecture in Semiclassical Settings, February 19, 2019

My talk at Analysis Seminar (McGill University University, January 26, 2018)

Spectral asymptotic for Steklov’s problem in domains with edges (work in progress)

We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacles for deriving a sharper (two-term) asymptotics

Slides

Aftermath

My Research Monograph is almost ready (in January I plan to edit Introduction, Preface and add some references, after which I pronounce it “Done” and I am not going to add any new material, at least for several years).

Meanwhile I started several new topics:

My talk at PDE & Analysis Seminar (Hebrew University, December 6, 2017)

Asymptotics of the ground state energy for relativistic heavy atoms and molecules

We discuss sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, without magnetic field or with the self-generated magnetic field, and, in particular, relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. In particular, we conclude that the Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.

Slides