Dipartimento di Matematica e Applicazioni
 “Renato Caccioppoli”

PhD Program in Mathematics and Applications

The Doctoral School in Mathematics and Applications, established in 2017 at the Department of Mathematics and Applications "Renato Caccioppoli" of University of Napoli Federico II, focuses on the following scientific areas:

  • Algebra
  • Geometry
  • Mathematical Analysis
  • Mathematical Physics
  • Numerical Analysis
  • Operations Research
  • Probability and Statistics
The courses will be given by professor of the Department and by internationally recognized researchers, moreover some courses of the Graduate School in Mathematical Engineering will be also available. All students will be asked to spend a period of study and research abroad, of at least three months.
The PhD Program is partially financed by the Institute INDAM "Francesco Severi", CIAFM-CNR consortium.

  • Admission to PhD Program 2017 - XXXIII Cycle
  • Call - Deadline: Thursday 21 September, h.12:00.
  • Activities 2017
  • Courses
  • Introduction to cyclic homology, Prof. Niels Kowalzig - University of Roma "La Sapienza"
    In this session, we will give a basic introduction to cyclic homology. In particular, we will discuss the Hochschild complex for associative algebras, define cyclic homology via a quotient of the Hochschild complex, pass to simplicial and cyclic objects to arrive at both Tsygan's bicomplex as well as Connes' mixed complex involving the Connes-Rinehart boundary B, which leads to the long exact SBI-sequence. In the second half, we will speak about the algebraic Hochschild-Kostant-Rosenberg theorem and discuss Morita invariance. Time permitting, we will also address briefly more intricate cyclic objects as for example those arising from Hopf algebras. No (serious) prior knowledge of homological algebra is needed.
  • Introduction to KK-theory, Prof. Koen van den Dungen - SISSA, Trieste
    I will give an introduction to KK-theory, with an emphasis on the unbounded picture. KK-theory is an abstract mathematical framework which encompasses both K-theory and K-homology of C*-algebras. To any pair of C*-algebras A and B corresponds an abelian group KK(A,B), which is a topological invariant of the pair of C*-algebras. Elements of these abelian groups can be thought of as generalised morphisms from A to B. The most important tool in KK-theory is the Kasparov product, which is a bilinear associative pairing on elements in KK-theory. The goal of this lecture is to give a general overview of (unbounded) KK-theory and its main properties, while avoiding the technical proofs.
  • Crash course in group representation theory with an eye on Schur-Weyl duality, Prof. Martin Evans - University of Alabama, USA
  • Un'introduzione ad alcune equazioni della meccanica quantistica, Prof. Raffaele Carlone & Gaetano Fiore - University of Napoli Federico II
  • Introduction to Alain Connes' noncommutative geometry, Prof. Francesco D'Andrea - University of Napoli Federico II
    The course is a 20 hours introduction to Alain Connes' noncommutative geometry. It includes a quick review of basic notions from operator algebras and a detailed discussion of the main tools such as cyclic and K-homology, spectral triples, K-theory and index theory.
  • The De Giorgi-Nash-Moser regularity theory, Prof. Chiara Leone - University of Napoli Federico II
  • An introduction to mean curvature flow, Prof. Carlo Mantegazza - University of Napoli Federico II
  • Modelli di crescita tumorale e problemi matematici correlati, Prof. Luigi Preziosi - Politecnico of Torino
    Scopo del corso è l'acquisizione di metodologie di costruzione di modelli matematici applicati alla biologia e alla bio-medicina. I modelli costruiti verranno analizzati sia da un punto di vista qualitativo che quantitativo e saranno lo spunto per introdurre dei metodi matematici utili per il loro trattamento.
    Programma:
    1. Processi di diffusione lineare e non lineare.
    2. Chemotassi ed equazione di Keller-Segel.
    3. Modelli di crescita tissutale e tumorale.
    4. Angiogenesi.
    5. Metastasi e motilità cellulare
    6. Individual based models

  • Seminars
  • Prof. Lucia Sanus - University of Valencia, "Sottogruppi di Hall nilpotenti e abeliani in gruppi finiti".
  • Prof. Alfredo Donno - University Niccolò Cusano, "Un'introduzione ai gruppi generati da automi".
  • Dr. Antongiulio Fornasiero, Hebrew University of Jerusalem, "Entropia algebrica".
  • Dr. Eloisa Detomi - University of Padova, "Ricoprimenti di sottogruppi verbali in gruppi profiniti".
  • Prof. Nadir Trabelsi - University of Setif, Algeria, "Groups whose proper subgroups have polycyclic-by-finite layers".
  • Dr. Francesco Spinelli - University of Roma "La Sapienza", "Varietà minimali di PI algebre graduate".


For informations:
Grazia Ieronato 081/7683665 – grazia.ieronato@unina.it
Carmine Tesone 081/675726 – carmine.tesone@unina.it