Teaching, supervisor and examiner experience
My teaching experience ranges from advanced PhD courses to first-year courses devoted to science students or future high school teachers. For what concerns the topic of the courses I taught, they are briefly summarized below.
PhD Level
2022
- Lecturer of the special lecture:
“The BV formalism: from ghost fields to the quantum master equation”,
Göttingen University.
Course description:
The concept of ghost fields was first introduced by Faddeev and Popov in 1967. Their aim was to construct the perturbative path integral for the Yang-Mills theory. Indeed, although the discovery of the perturbative approach to the path integral and the introduction of the Feynman graphs revolutionised the field, still a major problem had to be faced: the divergency of the integral in the presence of a gauge symmetry. Here is where the ghost fields enter the game: these extra (non-physical) fields are used to eliminate the divergences appearing in the path integral, which are caused by the presence of (gauge) symmetries in the theory. This groundbreaking idea opened the way to a very fruitful line of research, whose physical motivation disclosed a very rich mathematical structure, currently known under the name of BV formalism. In this series of lessons, we will start with a brief overview of the physical motivation that determined the creation of this field of research. Then we will mainly focus on the advanced mathematical tools that play a key role in this formalism: this will include elements of symplectic and supergeometry. The final goal will be to present a cohomological approach to quantisation based on the so-called quantum master equation. - Lecturer of the special lecture:
“Spectral triple and gauge theory”, Göttingen University.
Course description:
In the last years, noncommutative geometry has emerged as a very active field of research. Lying at the intersection between operator algebras and differential geometry, noncommutative geometry has shown itself to be a very effective mathematical framework for crucial results in many areas, from spectral theory, index theorems and foliations to field theories and gravity models in physics. In particular, the relation with physics has been clear from the very beginning: indeed, the Heisenberg uncertainty relations clearly call for the use of noncommutative algebras. In this series of lessons we will focus on what is a central concept in noncommutative geometry, that is the notion of a spectral triple. Our aim will be to introduce this notion and to explain why a spectral triple could be seen as a noncommutative generalisation of the concept of spin manifold. Starting with the Gelfand-Naimark theorem, we will explain the correspondence between commutative C∗-algebras and locally compact Hausdorff spaces. Then, metric and differential aspects will be taken into account, arriving to Connes’ reconstruction theorem, where the equivalence between canonical spectral triples and compact Riemannian spin manifolds has been established. Finally, the intrinsic relation between spectral triples and gauge theory will be explained, showing how any spectral triple naturally induces a gauge theory. If time allows, the description of the full Standard Model as almost-commutative spectral triple will be quickly illustrated.
2018
- Lecturer and scientific organizer of the Masterclass:
“Noncommutative geometry: spaces, bundles and connections”,
Aarhus University.
Course description:
The central notion in noncommutative geometry is that of a spectral triple. In this part of the masterclass, we aim to introduce this notion and to explain why a spectral triple could be seen as a noncommutative generalisation of the concept of spin manifold. Starting with the Gelfand-Naimark theorem, we will explain the correspondence between commutative C* algebras and locally compact Hausdorff spaces. Then, metric and differential aspects will be taken into account, arriving to Connes’ reconstruction theorem, where the equivalence between canonical spectral triples and compact Riemannian spin manifolds has been established. Finally, the intrinsic relation between spectral triples and gauge theory will be explained, showing how any spectral triple naturally induces a gauge theory. If time allows, the description of the full Standard Model as almost-commutative spectral triple will be quickly illustrated.
Master Level
2022
- Assistant for the 3rd year Bachelor/1st year Master course
“Operator Theory and Quantum Physics II”,
Göttingen University. - Assistant for the 1st year Master course
“Operator Theory and Quantum Physics III”,
Göttingen University.
2017
- Lecturer for the 2nd year Master/PhD course “Gauge Theory”,
Aarhus University.
2011
- Teaching Assistant (TA) for the course “Harmonic analysis”,
Radboud University Nijmegen.
Bachelor Level
2024
- Assistant and coordinator of the tutors for the course “Mathematics for physicists II”
Göttingen University. - Tutor for the 1st year course “Differenzial- und Integralrechnung II”,
Göttingen University.
2023
- Assistant and coordinator of the tutors for the course “Mathematics for physicists I”
Göttingen University. - Lecturer and coordinator of the course/seminar “Complex algebraic geometry”
Göttingen University. - Tutor for the 1st year course “Differenzial- und Integralrechnung II”,
Göttingen University.
2022
- Lecturer and coordinator of the course/seminar “Differential Geometry”
Göttingen University. - Tutor for the 1st year course “Differenzial – und Integralrechnung II”,
Göttingen University.
2020
- Lecturer for the 2nd year course “Differential equations”,
Aarhus University.
2019
- Lecturer for the 1st year course “Calculus B”
University of Toronto.
2013
- TA for 2nd year course “Complex functions”,
Radboud University Nijmegen.
2012
- TA for 2nd year course “Complex functions”,
- TA for 3rd year course “Functional analysis”,
Radboud University Nijmegen.
2011
- TA for 2nd year course “Complex functions”,
- TA for 3rd year course “Functional analysis”,
Radboud University Nijmegen.
Student with special needs
2009 & 2010
- Lecturer for undergraduate students with physical disabilities (severe visual impairment, blindness, severe impaired hearing, deafness) and learning disabilities (especially dyslexia and dysgraphia), preparing suitable visual/audio material.
University of Milan (Italy).
Supervising experience
2023
- Bachelor project: “Noncommutative geometry and gauge theories: the almost-commutative case”
Göttingen University [End: January 2024]
Service as committee member
2022
- Member of the doctoral thesis committee for the thesis “Noncommutative geometry and gauge theories on AF Algebras”, by G. Nieuviarts at Centre de Physique Théorique,
Aix Marseille Université, CPT, Marseille, France
Teaching qualifications and pedagogical development
2018
- “Teacher Training Programme”, track on Supervision, Aarhus University [150 hours].
Course description:
The programme is mandatory for anyone wishing to apply for a tenured position at Aarhus University. The aim of the programme is to contribute to the professionalisation and quality of university teaching through the development of the participants’ practical teaching skills and by fostering a scholarly approach to teaching. By the end of the course the participants will be able to:
− Analyse and discuss teaching based on knowledge about quality teaching, didactics, assessment,
evaluation, and students as learners.
− Plan, execute, and evaluate well-aligned teaching and assessment activities within their own disciplines and organisational contexts.
− Use and evaluate educational technologies to promote learning activities for groups and individual students.
− Demonstrate practical teaching skills.
− Collect data, analyse, and communicate information about their teaching practices and experiences to colleagues and other stakeholder in a teaching portfolio.
The programme comprises altogether four modules:
Module 1: Introduction to teaching and learning in research-based education;
Module 2: Educational TI – The use of educational technology;
Module 3: (Re-)designing a course within one of the following tracks: lecturing, small class teaching or supervision;
Module 4: Final workshop on teaching portfolio, knowledge sharing and the teaching practice.
2017
- “Introduction to Teaching and Learning”, Aarhus University [50 hours].
Roberta Iseppi 