# Basic Notions in mathematical physics

Bi-weekly, Wednesdays 3:30-4:30pm hybrid online/onsite. After the talk we go out for drinks in the foodcourt.

Organisers: Roland van der Veen and Kevin van Helden

The new website for the basic notions seminar is on the fundamentals of the universe website

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
8-12-2021, 3:30-4:30PM Orlin Koop TBA/td> TBA
24-11-2021, 3:30-4:30PM Eric Pap Fiber bundles In mathematics, it is common to think of spaces as being composed of `fibers', so that the space is a `fiber bundle'. Picking an element of each fiber gives a way to unify functions, vector fields, k-forms and gauge fields. We will consider these notions of `local triviality' and `section' hands-on, in which we can recognize basics as `expressing in local coordinates' and `gauge fixing'.
10-11-2021, 3:30-4:30PM JOIN HERE or come to room 5161.0289 Jann Aschersleben Neural networks Machine learning algorithms can appear as black boxes that magically return the correct answers of a complex problem. I will introduce the very basic principles of artificial neural networks and how they learn to solve a problem from labelled training data.
27-10-2021, 3:30-4:30PM Jorge Becerra My name is Theory, Category Theory I will give a down-to-earth, non-technical overview of some basic concepts of category theory that are transversal in mathematics and physics, giving many different examples. I will also illustrate how this framework arises naturally in physics.
13-10-2021, 3:30-4:30PM Martijn Kluitenberg Tensors Some might say a tensor is "something that transforms like a tensor," while others might say that it's "an element of a tensor space." I will not try to answer the question "What is a tensor?" but I will try to explain the relationship between the previous two useless answers.
29-9-2021, 3:30-4:30PM Jeffrey Weenink Quantum calculus Quantum calculus, is first your university year of math without limits. A lot of easy results can be restated in this simple formalism. It's especially useful in non-commutative (i.e. quantum) settings, where it is a more natural language instead of the standard calculus and algebra.
13-9-2021, 3:30-4:30PM Roland van der Veen Space according to the functions on it. Think of some space X. How will you describe it? How can you communicate what's happening inside? How can you do calculations with it? In answering such questions you will probably have used certain functions on X. In fact the outcome of any measurement you do on X would be a function on X, so I will argue that the space of functions Fun(X) is more fundamental than X itself. If that is so then it seems a good idea to reformulate basic notions of geometry on X directly in terms of Fun(X). Taking this to the extreme we can forget about X and just work with some set of functions Fun(X). This point of view is especially useful if X is behaving badly and/or we want to quantize. One of the founders of this subject is Shahn Majid and he will tell us less basic things about it in our September 24 fundamentals of the universe symposium.
8-6-2021, 2PM Nikolay Martynchuk Partitioning an n-cube
17-6-2021, 2PM Ema Dimastrogiovanni
3-6-2021, 2PM Bram Brongers The Geometric Nature of Fundamental Physics We will explore the Wu-Yang dictionary, which established a deep connection between the geometry of principal bundles and particle physics, in the 1970s. The primary aim is to explain the mathematical/geometric perspective of what a gauge theory is.
20-5-2021, 2PM NO SEMINAR -
6-5-2021, 2PM Jelmar de Vries The Solvability of the Hard Problem of Consciousness In this presentation, we will explore a proof showing that no theory (physical or otherwise) can explain the qualitative experience that humans have. We will also have a brief look at the implications of this proof.
22-4-2021, 2PM Dijs de Neeling (Super-)Integrable Planetary Systems We'll talk about Liouville integrability in the context of planetary systems. How is integrability defined? And what is super-integrability? What are the consequences for systems that posses these properties?
8-4-2021, 2PM 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?