Basic Notions

Basic Notions is a bi-weekly seminar at Wednesdays from 3:30pm to 4:30pm. Its format is hybrid (online/onsite). After the talk we go out for drinks in the Foodcourt.

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.

Fiber Bundles

November 24th 2021

Eric Pap

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'.

Time: 3:30pm - 4:30pm

Location: room 5115.0014 or online

Neural networks

November 10th 2021

Jann Aschersleben

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.

Time: 3:30pm - 4:30pm

Location: room 5161.0289 or online

My name is Theory, Category Theory

October 27th 2021

Jorge Becerra

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.

Time: 3:30pm - 4:30pm

Location: room 5161.0289 or online

Tensors

October 13th 2021

Martijn Kluitenberg

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.

Time: 3:30pm - 4:30pm

Location: room 5161.0289 or online

Quantum calculus

September 29th 2021

Jeffrey Weenink

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.

Time: 3:30pm - 4:30pm

Location: room 5161.0289 or online

Space according to the functions on it.

September 13th 2021

Roland van der Veen

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.

Time: 3:30pm - 4:30pm

Location: room 5161.0041b or online

Partitioning an n-cube

July 8th 2021

Nikolay Martynchuk

Time: 2:00pm - 3:00pm

Location: online

Basics of General Relativity

June 17th 2021

Ema Dimastrogiovanni

Time: 2:00pm - 3:00pm

Location: online

The Geometric Nature of Fundamental Physics

June 3rd 2021

Bram Brongers

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.

Time: 2:00pm - 3:00pm

Location: online

The Solvability of the Hard Problem of Consciousness

May 6th 2021

Jelmar de Vries

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.

Time: 2:00pm - 3:00pm

Location: online

(Super-)Integrable Planetary Systems

April 22nd 2021

Dijs de Neeling

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?

Time: 2:00pm - 3:00pm

Location: online

What is a tropical variety?

April 4th 2021

Oliver Lorscheid

Time: 2:00pm - 3:00pm

Location: online

Quantum entanglement

March 25th 2021

Martine Schut

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.

Time: 2:00pm - 3:00pm

Location: online

Meta-stable quantum mechanics

March 3rd 2021

Giovanni van Marion

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.

Time: 2:00pm - 3:00pm

Location: online

Reduction in physics

February 25th 2021

Myrthe Scheepers

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?

Time: 2:00pm - 3:00pm

Location: online

Dynamics of the Kuramoto model

February 2nd 2021

Nico Moro

We will discuss the synchronization of coupled oscillators.

Time: 2:00pm - 3:00pm

Location: online

Geometry of Maxwell's equations

January 28th 2021

Kevin van Helden

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.

Time: 2:00pm - 3:00pm

Location: online

Group theory

January 7th 2021

Roland van der Veen

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.

Time: 2:00pm - 3:00pm

Location: online

Field theory

December 10th 2020

Johannes Lahnsteiner

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.

Time: 1:00pm - 2:00pm

Location: online

Conjugation and adjoint actions

November 19th 2020

Eric Pap

How does conjugation appear in practice? What groups are connected to conjugation? How does a bracket relate to conjugation? Handout available here

Time: 2:00pm - 3:00pm

Location: online

Hamiltonian Mechanics

November 5th 2020

Federico Zadra

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.

Time: 2:00pm - 3:00pm

Location: online

Active vs passive

October 22th 2020

Diederik Roest

Time: 2:00pm - 3:00pm

Location: online

The dual of a vector space

October 8th 2020

Roland van der Veen

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?

Time: 2:00pm - 3:00pm

Location: online

Actions and Angles

December 8th 2021

Orlin Koop

Actions and Angles constitute a system of phase-space coordinates that is widely used in Galactic studies to describe orbits of bodies in a Galactic Gravitational potential.
In this talk I will introduce what Actions and Angles are and why they are of interest, and I will point out the intricacies and problems we currently still have while using Actions and Angles with our current datasets.

Time: 3:30pm - 4:30pm

Location: room 5115.0020 or online