English

This course examines venture capital and private equity investments. In particular, it focuses on issues surrounding the funding of entrepreneurial firms that are financed by venture capital or private equity funds. The course departs from conventional investment approaches that examine risk and return of publicly listed securities and analyzes issues associated with financing growing, innovation intensive private businesses.

This course introduces the basic principles and techniques in genetics (in the context of oncology), to develop basic competences in the planning and performance of experiments and the evaluation of results, as well as writing reports. The course consists of 6 sessions of approx. 4 hours and covers topics such as DNA isolation/purification, gel electrophoresis, staining procedures, protein detection, and basic bioinformatics (commonly used databases, finding the genetic location of a specific gene and its gene sequences, design amplification primers for a specific genetic region, etc) using online available tools. Furthermore, this course provides basic knowledge on Good Laboratory Practice (GLP) and Laboratory Safety Regulations. Besides the hands-on time in the lab, each session requires preparation beforehand and reporting afterwards. Students work in pairs. Lab experience is not required, although biological and chemical background knowledge at secondary school level is recommendable for full understanding of the provided techniques. If necessary, in the first lab session, pipetting skills will be trained or refreshed. This course is designed to be taken in combination with SCI2022 Genetics and Evolution. Students who wish to take this course should concurrently enroll in SCI2022 Genetics and Evolution or have taken SCI2022 Genetics and Evolution before. 

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. This course covers the theoretical understanding and working knowledge of the principal gravitational phenomena determining the structure, the dynamics and the evolution of stellar systems, from open and globular clusters, to galaxies, to galaxy clusters. At the end of the course, the student is able to use in autonomy some of the advanced mathematical techniques needed in potential theory and in epicyclic theory. The course content is divided into 2 parts:

1. GENERALS

Gravitational field of point particles, principle of superposition. Integral representation for any distributions. Most important properties of the divergence operator and its coordinate-free representation starting from Gauss's Theorem. Operational introduction to the one-dimensional and multidimensional Dirac Delta in Cartesian and curvilinear coordinates. Calculation of the divergence of the field of extended distributions, Poisson's equation for the field. Direct proof of the First and Second Newton's theorem (homogeneous spherical shells). Alternative demonstration using Gauss's theorem. Coordinate-free representation of the gradient, curl, and Laplacian operators. Notes on differential forms. Exact fields and their properties, potential and work. Closed fields. Stokes' theorem, closed fields in simply and non-simply connected domains. Existence of the potential and its connection with the total energy of a particle. Potential difference as a line integral. Formal calculation of the potential of a point mass. Potential of extended distributions, general expression and discussion of the meaning of the additive constant. Poisson and Laplace equations. First and second Green's identities, uniqueness of the solution of the Poisson equation in bounded volumes with prescribed boundary conditions. Field inside cavities with equipotential boundary. Helmholtz Decomposition Theorem. Definition of concentric and similar ellipsoids. Definition of homoeoid. Statement of the Third Newton's Theorem for finite homoeoids. Field inside a heterogeneous hollow homoeoid from the principle of superposition. Co-area theorem, relationship with the field of homoeoids. Definition of confocal ellipsoidal coordinates. Classification of the three families of associated quadrics. Ellipsoidal coordinates: orthogonality, gradient, Laplacian. Application to the problem of the ellipsoidal layer with zero internal field. Potential of the heterogeneous ellipsoid. Chandrasekhar's formula. Introduction to the multipole expansion of potential in the far field. Monopole, dipole and quadrupole terms.

Introduction to the concept of Green's function for linear differential operators and their use in solving nonhomogeneous problems. The potential of a material point as an explicit example of a Green's function for the Laplacian. Separation of variables for the Laplacian in Cartesian coordinates. Fourier transform and inverse transform in Rn, the case of the Dirac Delta. Green's function in Cartesian coordinates. Green's function in spherical coordinates. Separation of variables. Rotational invariance and the azimuthal quantum number m. Orthogonality of azimuthal functions. Associated Legendre equation for the latitude angle, transformation into an algebraic equation. Outline with examples of singularities of ODEs, both mobile and fixed. Fuchs' theorem, regular points, regular singularities, and essential singularities. Classification for the Legendre equation. Frobenius method and polar quantum number. Legendre functions and associated functions P and Q. Legendre polynomials. Rodrigues formulas, norm of associated polynomials. Orthogonality of solutions with Sturm-Liouville theory. Spherical harmonics as eigenfunctions of the angular part of the Laplacian. Systems with cylindrical symmetry. Generating function for Legendre polynomials, multipole moments. Gegenbauer polynomials. Addition theorem for spherical harmonics. Separation of variables for the vacuum solution of the Laplacian in cylindrical coordinates. Bessel equation and its properties: orthogonality of solutions, singular points. Asymptotic analysis of Bessel functions for large values of the argument. Closure relation and Hankel transform. Green's function in cylindrical coordinates for the Laplacian. Any density potential with Fourier-Bessel transforms. Case of axisymmetric systems. Infinitely thin axisymmetric disks, potential in the plane of the disk, homogeneous rings. Thin disk rotation curve. Mestel's disc and exponential, implications for the dark matter halos. Potential of axisymmetric systems using elliptical integrals.

2. COLLISIONLESS SYSTEMS

Introduction to the epicyclic approximation. Notes on curvilinear coordinates, velocity and acceleration in cylindrical coordinates. Newtonian equations of motion in general axisymmetric potentials, conservation of energy and Jz. Deduction of equations from the Euler-Lagrange equations. The meridional plane, its motion, and effective potential. Equations of motion in the meridional plane, orbital families, circular orbits and their (equivalent) equations. Interpretation of total energy as energy for motion in the meridional plane, extremum properties for the energy of circular orbits, centrifugal barrier, zero-velocity curves. Development of the effective potential to second order. Frequency of vertical and radial epicycles. Radial and vertical motion on the epicycle in the case of stable orbits, zero-velocity ellipses. Rayleigh criterion and examples of applications. First-order angular motion, coordinates on the equatorial plane referred to the deferent, equation of the epicycle on the equatorial plane, and determination of the axes for the epicyclic ellipse. Epicycles in Coulomb, harmonic, and flat rotation potentials: frequency and shape. Relation of Oort constants to the radial epicyclic frequency. Closed, rosette, and open orbits: closure conditions, pattern angular velocity, Lindblad kinetic waves, and the dynamical phenomenology of disks.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. This advanced course focuses on the main theoretical approaches to promote well-being across the life-span, tools for assessing the quality of life and psychological well-being in children and adults with typical and atypical development, and interventions aimed at improving well-being in developmental and learning contexts. 

The course presents theories, methods, and assessment and intervention tools to promote wellbeing, quality of life and learning in a development and education perspective in the lifecycle. The course involves the following integrated and complementary modules:

The first module is designed to provide the principal theoretical approach of the course concerning the wellbeing promotion in children, students, youth, and adults. The module also explores the role of technologies in human development, by considering both their functional use to develop knowledge, skills and their dysfunctional effects on lifecycle development.

The second module provides an advanced theoretical and empirical approach to understand the developmental and educational consequences of social stigma on children’s health, quality of life and psycho-social well-being, and cognitive functioning. Evidence-based interventions to reduce stigma and its consequences in educational settings are illustrated.

The Scandinavian countries (Sweden, Norway, Denmark) are often seen as global models of welfare, good governance, and high quality of life, successfully combining social protection with entrepreneurial success. Historically associated with consensus politics, trust, and moral leadership - through figures such as Olof Palme or Norway's peace diplomacy - the region has long defied conventional wisdom about global pressures for deregulation, showing how social protection can coexist with global competitiveness. Recent narratives of decline, however, point to rising crime, economic stagnation, and populism. This course revisits the evolving politics of the "Nordic model," exploring its institutions, challenges, and relevance for Europe through history, politics, economics, and sociology.

This course examines information theory, including error-correcting codes, data compression and cryptography. Each of these subtopics are enhanced by the application of entropy functions, and more sophisticated error-correcting codes are provided by way of brief introduction to number theory and finite fields. 

This course examines philosophical and conceptual issues in the life sciences. Topics may include the units and levels of selection, adaptationism, the evolution of altruism, biology and ethics, sociobiology and evolutionary psychology, cultural evolution, evolution versus creationism, and the origin and nature of life. It addresses questions including: What is life? Why do living things inevitably die? Could artificial life (for example, synthetic cells made in a laboratory) ever be genuinely alive? How should we understand the role of our genes in shaping who we are? We're told that it's important to conserve biodiversity, but what exactly is biodiversity, and should it be the main target of conservation efforts? How do (and how should) social values relate to life scientists' study of human behavior, sexuality, and other topics? How does our increasing knowledge of microbial life, including the bacteria and other microorganisms living inside our own bodies, affect our understanding of the living world and of what it means to be human?

This course examines the region of Mesopotamia and the Mediterranean between 1500 BCE to 100 CE. Topics include an introduction to Mesopotamia and the Mediterranean world, the Neo Assyrians and their Empire – 900 to 600 BCE, the Neo Babylonians and their rule – 600 to 537, and the Achaemenid Persian Empire – 537-333BCE. The Hellenistic Empires, Seleucid and Ptolemaic Empires, and the Romans and Parthians are also covered.

This course focuses on practical statistics and computation in real-world scenarios. It covers how statistics are used, how to turn data into information, how to create statistical graphics, how to obtain data from surveys and designed experiments, probability theory, and random variables.

This advanced course is especially designed in the format of seminars and guest lecturers to expose the student to the frontier of knowledge of climate and apprehend what are the topics available for the final thesis. Students are able to grasp what are the emerging areas on climate science and be able to select the topic for future deepening of the knowledge.

The course is structured with 1- or 2-hours long time slots and with three types of offers:

1) Seminars: >=1 hour on current research/technological challenges, delivered by specialist.

2) Lecture: >=2 hours on a more general topic of broader relevance and less technical details.

3) Short course: >=3 hours on an additional supplementary skill. Examples may include a focus on programming or on an area of transversal interest.

The exact schedule changes every year. Students are asked to check the program frequently given that it is usually updated in the course of the year based on availability of speakers.