Theses

Proposed Thesis

Groebner basis and zero-dimensional schemes / 2018
Bachelor/Master

Let f_1, ..., f_m be polynomials in Q [x_1, ..., x_n] with only a finite number of zeros in common in C^n. Then the ideal I = (f_1, ... f_m) is zero-dimensional. How to use Groebner bases to calculate I's zeros?

Tuesday 08 May 2018 - 16:47
Bach and mathematics / 2018
Bachelor

A mathematical apprach to Bach music is possible.

Monday 07 May 2018 - 10:56
Tensor Network / 2018
Bachelor/Master/PhD

Understanding quantum many-body systems is probably the most  challenging problem in condensed matter physics. The standard approach to understand these systems is based on proposing simplified models that are believed to reproduce the relevant interactions responsible for the observed physics. As far as numerical simulation algorithms are concerned, Tensor Network methods have become increasingly popular in recent years to simulate strongly correlated systems. Describing this phenomena from a mathematical point of view requires the usage of secant varieties of Segre varieties and tensor decomposition techniques.

Monday 07 May 2018 - 10:56
Blind source separtion / 2018
Bachelor/Master/PhD

The big brother wants to know the position of enemy radio antennas. The big brother has to solve a Waring problem.

Monday 07 May 2018 - 10:55
Mathematics and Phylogenetics / 2018
Bachelor/Master/PhD

Given a group of species with a common ancestor, we are interested in reconstructing the phylogenetic tree from the species known to the common ancestor. To do this we need algebraic varieties called secant varieties of Segre varietis.

Monday 07 May 2018 - 10:55
Complexity of Matrix Multiplication / 2018
Bachelor/Master/PhD

Strassen was convinced that it was not possible to improve the classical algorithm for the multiplication of matrices. In an attempt to prove this fact, he found a simpler algorithm for multiplying 2x2 matrices. This algorithm is shown to be the best possible one. For matrix nxn with n> 2 only bounds the complexity are known.

Monday 07 May 2018 - 10:55
Multiplication of numbers and digital music / 2018
Bachelor/Master

Fast Fourier Transform is the fastest way to multiply two numbers. It is used whenever multiplication of large numbers is needed. This happens in cryptography, in the separation of musical traces, in the reconstruction of images...

Monday 07 May 2018 - 10:55

GIVEN THESES

 

Master Thesis

- Daniele Taufer. Symmetric Tensor Decomposition. (Galileian School of Higher Education - University of Padova), 2017.

PEM (Excellence CV)

- Federico Mazzone, Il crivello quadratico. 2018
- Lorenzo Barban Sistemi inversi di Macaulay. 2018

Bachelor Theses

- Francesco Grigoli, Trattazione della musica da un punto di vista matematico - Luglio 2018.
- Federico Mazzone,
Number field sieve: Introduzione storica, strategia di base, analisi della complessità asintotica e alcune varianti del metodo - Luglio 2018.
- Lorenzo Stefanello, Sul lavoro di Kummer riguardo l’Ultimo Teorema di Fermat - Luglio 2018.
- Stefano Pellegrini, AKS, the proof of "PRIMES is in P", Correctness and time complexity analysis, along with Java implementation - Marzo 2018.
- Tommaso Granziol, Risoluzione di immagini con matrici di rango basso - Marzo 2018.
- Luca Dal Bianco, Frazioni Continue - Marzo 2018.

- Michele Battagliola, Il teorema dei Numeri Primi - Novembre 2017.
- Davide Teroni, Il grande problema di Waring - Novembre 2017.
- Nicolò Insalaco,
Algoritmo di Sylvester - Marzo 2017.
- Gabriella Bettonte, Formule per i numeri primi
- Marzo 2017.
- Giulia Biasi,
Il teorema dell'elemento primitivo - Marzo 2017.
- Thomas Chiozzi,
Test di primalità e curve ellittiche - Marzo 2017.

- Luca Girardi, Half-factorial Domain, Other Half-factorial Domain. Settembre 2016.
- Maria Ricci, 
Teorema della base di Hilbert e basi di Gröebner, Settembre 2016.