Paolo Brandimarte
Online seminar - 22 December 2020 - 4:30 p.m. (duration 30-40 min)
The primary objective of the seminar is to introduce financial derivatives as risk management tools. For example, a put option on a stock index can be viewed as insurance, for which the fair price must be assessed.
The second objective is to show how, using a trivial model of uncertainty such as the classic coin toss, and assuming somewhat simplified market mechanisms, it is possible to analyse the issue using a very simple tool: the solution of a system of linear equations.
The third objective is to illustrate how, by introducing more sophisticated models of uncertainty, such as Brownian motion, the problem leads to a functional equation closely related to the physical equation of heat. The solution of this equation provides a formula for the price of simple financial options. For this result, and above all for the financial insights that justify it, Myron Scholes and Robert Merton (an engineer) were awarded the Nobel Prize in Economics in 1997.
The fourth objective is to critically analyse the model. In fact, it is based on precise assumptions from a mathematical point of view. Furthermore, from a financial point of view, options are double-edged swords: while it is true that they can be usefully employed as risk management tools, it is also true that they can be used for speculative purposes. We will conclude this brief discussion with some instructive examples of financial disasters.
Ada Boralevi
Online seminar - 12 January 2021 - 4:30 p.m. (duration 30-40 min)
In 1770, English mathematician E. Waring claimed, without proving it, that “every natural number is the sum of at most 3 cubes, at most 19 fourth powers, and so on...”. Only Hilbert, more than 100 years later, managed to prove the truth of this statement.
The natural question of whether or not a similar property applies to polynomials had to wait until 1995 for an answer.
We will talk about these great mathematicians and their ideas, and discover that these theories have surprising applications in fields such as signal processing for telecommunications.
Francesco Malaspina
Online seminar - 02 February 2021 - 4:30 p.m.
Mathematical language allows us to approach the poignant and fascinating topic of infinity from various angles.
We will take a brief look at some of these through hypercubes, meringues, and football references.
Sandra Pieraccini
Online seminar - 24 February 2021 - 4:30 p.m.
We all know that maths is everywhere in our lives, especially since we're so influenced by tech. There are loads of times when maths comes in handy. For example, you've probably noticed that pictures you get on WhatsApp are blurry until you actually download them.
During the meeting, we will briefly explain how image compression works from a mathematical point of view and carry out some simple experiments on personal photos, without using photo-editing software but only mathematical tools with scientific calculation software.
Luca Lussardi
Online seminar - 15 March 2021 - 4:00 p.m.
Starting from Einstein's brilliant ideas on space-time, we see that physics becomes geometry (non-Euclidean): Einstein versus Newton, the force of gravity exits the scene and the geometry of curved spaces answers questions that have been open for hundreds of years.
This is a formidable scientific discovery that has also raised awareness among the general public, is supported by all the experiments carried out to date (most recently the famous detection of gravitational waves), and has had important repercussions in applications to everyday life.
To request the video of the seminar, please contact web.ingmat@polito.it.
Marco Morandotti
Online activity - 07 April 2021 - 4:00 p.m.
Today's technological and social challenges require the ability to solve complex problems that at first glance seem insurmountable. We hear it everywhere: the most efficient strategy for solving a “big” problem is to break it down into “smaller” problems and assemble their solutions.
In the activity we propose, students will be faced with problems of varying complexity and will be encouraged to solve them by taking a synoptic view of the problem and identifying its basic components.
Luca Lussardi
Online seminar - 26 April 2021 - 4:00 p.m.
Why are soap bubbles round? Why do soap films seem to arrange themselves according to precise geometric laws?
We will find out together by conducting live experiments.
La.M.Po
17 May 2021 - 6:00 p.m.
Over a drink and some chips, we will discuss how mathematics is hidden in our aperitif.
Vincenzo Recupero
Online seminar - 27 May 2021 - 4:30 p.m.
Imaginary numbers and complex numbers were invented in Italy in the sixteenth century to solve third- and fourth-degree algebraic equations. We will see that these numbers are not so “imaginary” after all, and that together with their older siblings, the quaternions, they have found applications over time in a wide variety of scientific disciplines, from electrical circuits to quantum mechanics and three-dimensional graphics.