Courses

Courses a.y. 2020-2021

 

 

Course: :  
Teacher:

 

Courses by Type
(click on type to see its courses)

BASIC   ▾  N : 26

Course nameNotePeriodTime
Table

semester I
 
  • ( - To be defined )  
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 semester II
 
  • Vito Michele ABRUSCI ( michele.abrusci@tlc.uniroma3.it, vitomichele.abrusci@uniroma3.it - Universita degli Studi Roma TRE )  
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INTERMEDIATE   ▾  N : 13

Course nameNotePeriodTime
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semester I
 
  • Alexandre STAUFFER ( astauffer@mat.uniroma3.it - Dipartimento di Matematica e Fisica )  
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 semester I
 
  • ( paolo.delgiudice@roma1.infn.it - Universita La Sapienza )  
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IRRATIONALITY, TRANSCENDENCE AND DIOPHANTINE EQUATIONS (TN520) -

Irrationality, transcendence and diophantine equations (TN520) -

Introduction to algebraic number theory:
Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.

The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.

Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.

Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.

Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.

Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.


 


Semester II
 
  • Fabrizio BARROERO ( barroero@mat.uniroma3.it - Dipartimento di Matematica e Fisica )  
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 semester II
 
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 semester II
 
  • Roberto MAIELI ( maieli@uniroma3.it - Dipartimento di Matematica e Fisica )  
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 semester II
 
  • Elisabetta SCOPPOLA ( scoppola@mat.uniroma3.it - Dipartimento di Matematica e Fisica )  
  • Luciano TERESI ( luciano.teresi@uniroma3.it - Dipartimento di Matematica e Fisica )  
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 semester II
 
  • Fabio LA FRANCA ( lafranca@fis.uniroma3.it - Dipartimento di Matematica e Fisica )  
  • Giorgio MATT ( matt@fis.uniroma3.it - Dipartimento di Matematica e Fisica )  
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 semester II
 
  • Alessandro VERRA ( verra@mat.uniroma3.it - Dipartimento di Matematica e Fisica )  
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SPECIAL   ▾  N : 4

Course nameNotePeriodTime
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CURVES AND BUNDLES ON CURVES WITH TRIVIAL CANONICAL BUNDLE

Curves and bundles on curves with trivial canonical bundle

Starting from March 2021, two 2 hours lectures per week
PROGRAM

Review of Brill-Noether Theory. Brill-Noether theory for curves on a K3 surface. The Lazarsfeld-Mukai bundle. Lazarsfeld proof of Brill-Noether-Petri Theorem.
Constancy of Clifford index for curves on a K3 surface: Donagi-Morrison Conjecture. Clifford dimension and exceptional curves: Eisenbud-Lange-Martens-Schreyer Conjecture.
Mukai’s Program: non-abelian Brill-Noether Theory of curves on a K3 surface. Reconstruction of a K3 surface from its hyperplane section.
The Wahl map and Wahl Conjectures: characterization of Brill-Noether-Petri general curves on a K3 surface.
Brill-Noether Theory of curves on an abelian surface. The second Gauss-Wahl map and hyperplane sections of abelian surfaces.
Severi Varieties on K3 and abelian surfaces.

PREREQUISITES: basic knowledge of algebraic geometry (schemes and sheaf cohomology); curves (Arbarello-Cornalba-Griffiths-Harris, volume 1)


March, 2021
 
  • Andrea BRUNO ( bruno@mat.uniroma3.it - Dipartimento di Matematica e Fisica )  
  • Margherita LELLI CHIESA ( margherita.lellichiesa@uniroma3.it - Dipartimento di Matematica e Fisica )  
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INTRODUCTION TO KAC'S MODEL AND ITS RELATIONS WITH STATISTICAL MECHANICS

Introduction to Kac\'s model and its relations with Statistical Mechanics

The aim of the course is to present basic problems of kinetic theory and statistical mechanics using Kac's model as a starting point and testing ground for physical ideas and rigorous results. In the first part, Kac's model will be introduced and its classic results will be discussed, in particular:
relaxation towards equilibrium and derivation and solutions of the Boltzmann-Kac equation.
After that the evolution of Kac's model will be studied, when in contact with a thermostat or with a thermal bath.
Finally the recent attempts to extend the results to systems in
contact with more than one thermostat or thermal bath initially at different temperatures, will be presented so as to arrive at a situation of actual non-equilibrium.


May, June 2021
 
  • Bonetto Federico ( bonetto@math.gatech.edu - Georgia Institute of Technology, Atlanta )  
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ONLINE COURSEES IN OTHERS UNIVERSITIES   ▾  N : 1

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THE THEORY OF THE DEFECT AND ITS APPLICATION TO THE PROBLEM OF LOCAL UNIFORMIZATION

The theory of the defect and its application to the problem of local uniformization

Doctoral Program in Mathematical Science Univ. Padova, Dept Math "“Tullio Levi-Civita”


Il 1oincontro sara' Venerdi' 19/2 alle ore 15, via zoom. Poi ci sara' un
incontro a settimana, il Venerdi' mattina, sempre via zoom secondo questo
calendario:

19 febbraio - ore 15:00-17:00
26 febbraio - ore 11:00-13:00
5 marzo - ore 11:30-13:00
12 marzo - ore 11:00-13:00
19 marzo - ore 11:00-13:00
 26 marzo - ore 11:00-13:00
 2 aprile - ore 11:00-13:00
 9 aprile - ore 11:00-13:00

Per iscriversi:

https://dottorato.math.unipd.it/current-activity/FutureActivities

 

Feb-April, 2021
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Admin 04 Settembre 2019