Teaching
Introduction to Lattice QCD (Liverpool, 2016-2017)
This course is targeted for the post-graduate students, but is open to everyone.
It consists of black board lectures and the goal is to discuss the various concepts of Lattice QCD, the methods, the advantages and the limitations.
In the first part of the course, I will introduce the basics ideas of lattice QCD:
the lattice regularization, formulation of the pure gauges theory, relation to the continuum one, gauge invariance, fermion discretizations and chiral symmetry.
0. Introduction, motivations and example:
we define a simple correlator (2-point function<P P^d>)
and show how to relate the quark mass to a hadron mass though Wick theorem
1. Path Integral of Euclidean QCD and Monte-Carlo
We discuss the meaning of the average over the gauge ensembles,
we show how to "separate" the fermionic from the gluonic part,
and defined the sea and the valence quarks
2. Wilson formulation of the Gauge action
we see how gauge invariance is maintained on the lattice
(without having to fix the gauge) at finite lattice spacing,
and show that how the lattice action tends to the continuum one
3. The Fermionic part.
How to discretize the Dirac action while keeping gauge invariance,
naive fermions and doubling problem
Wilson formulation and chiral symmetry breaking
4. Choosing the Lattice discretization, physics or politics ?
Symmetries, in the continuum and on the lattice
Lattice regularization and uv cutoff, continuum limit, O(a)-improvement
Several discretization of the Dirac operator
In the second part, I will discussed more advanced topics,
the synopsis is not fixed, it will depend on what the audience want to hear.
A possible list of topics is
Exact and approximate chiral symmetry, Ginsparg-Wilson relation and Domain wall fermions
Non-Perturbative Renormalization, MOM schemes or Schroedinger functional
Heavy Quarks on the Lattice
Computing four-quark operators matrix elements
More about Monte-Carlo methods
Finite density, sign Problem and potential solutions
...
Symmetries Fields and Particles. Part III maths, DAMTP (2014-2015)
Maths, Calculus, Statistics, Numerical Simulations. Trinity College Dublin (2012-2014)
I was a lecturer at the school of maths of TCD, in charge of three modules
(mainly lectures but also tutorial, labs, marking, admin, etc.)
MAM01: Calculus for the life scientist (first year)
MA22S6: Numerical and Data analysis techniques (second year science students)
Stat, proba, minimizing chi^2, Markov chain
MA3469: Practical Numerical Simulations (final year maths and theoretical physics)
Solving mathematical and physical problem numerically. On hands course.
Differential Equations (ODE, PDE), MonteCarlo, etc. in C/C++ using open-source (linux) environment