Basic Notions in mathematical physics

Bi-weekly, Thursdays 2pm online

Organisers: Roland van der Veen and Kevin van Helden

What is basic knowledge to one person may be rather mysterious to another. The plan of this seminar is to promote the communication between mathematics and physics by having some informal discussions on basic notions relevant to mathematical physics. The topic is intentionally rather broad but since this is part of the fundamentals of the universe program a few examples that come to mind could be 'duality', 'field', 'tensor', 'quantization', 'distribution', 'action', 'representation',...

Everybody is busy so the point is not to prepare a great and impressive presentation. Rather the converse, if you cannot speak about it unprepared then it may not be a basic notion for you. At any rate the level should not be higher than what a good bachelor student in her/his 3rd year can understand (at least for the first 15 minutes!).

Schedule

date speaker title Notes
22-4-2021, 2PM Dijs de Neeling Integrable systems
8-4-2021, 2PM JOIN HERE Oliver Lorscheid What is a tropical variety?
25-3-2021, 2PM Martine Schut Quantum entanglement I'll discuss quantum entanglement. How do we define it? How is it useful? And how do we measure it? To answer these questions we will probably talk a bit about the density matrix formalism as well.
11-3-2021, 2PM Giovanni van Marion Meta-stable quantum mechanics A hot particle is trapped in the local minimum of some potential and is trying to tunnel out. How can we compute its decay rate? I will discuss this problem from various angles and how it connects to my research.
25-2-2021, 2PM Myrthe Scheepers Reduction in physics The notion of reduction is of great importance in describing the relation between different theories in physics, but different examples seem to indicate different characteristics of that relation. So what are our requirements for theory reduction?
11-2-2021, 2PM Nico Moro Dynamics of the Kuramoto model We will discuss the synchronization of coupled oscillators.
28-1-2021, 2PM Kevin van Helden Geometry of Maxwell's equations In physics, everybody is familiar with the theory of electromagnetism. The equations behind this theory are known as the Maxwell equations, and they relate the electric and the magnetic field by derivatives, divergences and rotations. There is also a different approach to writing those equations, and that involves exterior derivatives and differential forms. We will explore this path and see how these approaches are related.
7-1-2021, 2PM Roland van der Veen Group theory To kick off the new year let's have a chat about symmetry. Here's a fun fact to get us started: take the multiplication table of any group and interpret it as a square matrix with whose entries are independent variables. The determinant of that matrix will factor into the "elementary particles of the group", the irreducible representations.
10-12-2020 (1PM not 2PM!) Johannes Lahnsteiner Field theory I will give a short overview of field theory and its significance in theoretical physics. I will sketch how to define, organize, and use field theories by reviewing the hallmark examples of 20th-century physics: Einstein gravity, the standard model of particle physics, and effective field theories in condensed matter physics. The focus will lie on unpacking the jargon and the general structure of these examples.
19-11-2020 Eric Pap Conjugation and adjoint actions How does conjugation appear in practice? What groups are connected to conjugation? How does a bracket relate to conjugation? Handout available here
5-11-2020 Frederico Zadra Hamiltonian Mechanics I will explain how this construction appears to be the natural choice in some physical problem, how symplectic geometry and in other geometrical frameworks enter in physics.
22-10-2020 Diederik Roest Active vs passive
8-10-2020 Roland van der Veen The dual of a vector space Some topics we may to touch on: Is the dual of the dual the same as the original? How do you raise an index? What is the transpose? and why not just pick a metric/inner product? What is the Dirac delta function? What happens when you tensor with the dual?

Literature and links