I - 34151 Trieste Italy

*(+39) 040 2240 111*

*pio@ictp.it*

- Joint ICTP/SISSA PhD Programme in Physics and Mathematics
- Joint PhD Programme, Earth Science and Fluid Mechanics
- Joint Masters in Physics
- Joint ICTP/Collegio Carlo Alberto Program in Economics
- International Master, Physics of Complex Systems
- Master of Advanced Studies in Medical Physics
- Masters in High Performance Computing

Contacts:

Since 1986 the Mathematics section at ICTP has played an important role in fostering mathematics research and education in developing countries. Research is carried out in various fields of Mathematics by the permanent staff, postdocs, and graduate students, as well as by scientific visitors from all over the world.

Typically, the section organizes from 5 to 10 focused activities a year involving an average of 100 participants. These activities are the core of the section's activities and are crucial for disseminating current mathematics knowledge of the highest level as widely as possible.

In addition the Mathematics section, like all the other sections at ICTP, participates in the Diploma program. Since 2011 Diploma students can apply to stay on to work on a PhD in Mathematics in a joint program with SISSA.

The Mathematics section also offers opportunities for postdocs and research fellows; click here for latest announcements.

The ICTP Mathematics section maintains a Math Blog, where you can read the latest updates written by the section members.

Once a month, the section organises The Basic Notions Seminar Series to broaden the understanding of some mathematical concepts.

26 Aug 2016

Vahatra Rabodonandrianandraina: The Joy of Applied Mathematics

5 Jul 2016

Breakthrough Prize winner Ian Agol on knots and what to do with a million dollars

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Europe/Rome
2017-06-01 15:30:00
2017-06-01 16:30:00
The many aspects of hyperbolic volume (Basic Notions Seminar)
Abstract:
First I shall briefly present the basic notions of hyperbolic space and volume in n dimensions. Then I shall explain why the study of non-euclidean and especially hyperbolic polyhedral volume is an important but difficult topic. Several aspects, results and open questions of analytical, topological and arithmetic nature are presented.
ICTP
ICTP
pio@ictp.it
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1 Jun 2017

» The many aspects of hyperbolic volume (Basic Notions Seminar)

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Europe/Rome
2017-05-22 08:00:00
2017-06-02 22:00:00
Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability | (smr 3118)
The Abdus Salam International Centre for Theoretical Physics (ICTP) is organizing this School and Workshop above, to take place at the ICTP from 22 May to 2 June 2017.
The study of partial differential equation with nonlocal features is an extremely active area of research in analysis, with strong ties to other parts of mathematics, like differential geometry and probability theory, and with motivations in the most diverse scientific contexts: kinetic theory, fluid dynamics, quantum mechanics, materials science, biology etc.
The goal of the proposed activity is bringing together leading mathematicians working on different aspects of nonlocal PDEs in order to disseminate the state of the art on the subject through a mix of courses and talks. The activities will include:
• courses by: Laurent Desvillettes (Université Paris Diderot), Yanyan Li (Rutgers University), Michael Loss (Georgia Tech), Enrico Valdinoci (University Melbourne);
• short courses by: Josè Carrillo (Imperial College London), Alessio Figalli (ETH Zürich), Daniela Tonon (CEREMADE-U Paris-Dauphine)
• regular talks by: Anton Arnold (TU Wien), Xavier Cabre (ICREA and UP Catalunya), Irene Gamba (University of Texas at Austin), Maxime Hauray (Université d'Aix-Marseille), Mikaela Iacobelli (University Cambridge), Jan Maas (IST Austria), Giuseppe Mingione (Università Parma), Stéphane Mischler (CNRS-U Paris-Dauphine), Yannick Sire (Johns Hopkins University), Giuseppe Toscani (Università Pavia), Alexis Vasseur (University of Texas at Austin), Juan Luis Vazquez (Universidad Autónoma de Madrid).
Topics: Kinetic theory, Boltzmann and Landau equations, conformally invariant elliptic PDE, fractional diffusion and fractional minimal surfaces, symmetry and symmetry breaking in variational problems.
GRANTS: A limited number of grants are available to support the travel and living expenses of selected participants, with priority given to participants working in a developing country and who are at the early stages of their career.
Co-sponsored by the
NSF-RNMS (Ki-Net) at University of Texas at Austin
MIUR SIR-grant “Geometric Variational Problems’ (RBSI14RVEZ)
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ICTP
ICTP
pio@ictp.it
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22 May 2017
- 2 Jun 2017

» Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability | (smr 3118)

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Europe/Rome
2017-06-19 08:00:00
2017-07-07 22:00:00
ICTP-EAUMP School on Modern Functional Analysis | (smr 3133)
The summer school is intended to provide a thorough introduction to various topics in functional analysis, from introductory to more advanced, and with a particular focus on functional analytic methods used in current research.
The two introductory courses in the first week cover some of the fundamentals of functional analysis and of operator theory, before two more advanced courses in the second week will introduce ideas which establish a link between the methods of classical functional analysis and the modern theory of partial differential equations.
Finally, the two courses in week three will expose participants to some more advanced topics which tie together the areas of functional analysis, differential equations and geometry. Each of the courses will consist of a series of lectures and accompanying classes, which are intended to give participants an opportunity to deepen their understanding of the material introduced in the lectures.
All of the lecture courses will be delivered by internationally recognised researchers in analysis.
In the final week of the summer school, participants will have a chance to work independently on a small topic of their choice.
COURSES
Week 1, 19-23 June - Introductory courses
Course 1: An introduction to function spaces
Lecturer: Dr Lassi Paunonen (Tampere, Finland)
Description: An overview of the basic theory of Banach and Hilbert spaces, with a focus on function spaces which play a part in modern applications of functional analysis
Syllabus: Overview of basic properties of Banach and Hilbert spaces (completeness, separability, reflexivity, etc), some fundamental theorems in functional analysis (e.g. the Riesz Representation theorem and the Hahn-Banach theorem), examples with relevance to modern applications of functional analysis (Sobolev spaces, Bergman spaces, Hardy spaces etc)
Course 2: An introduction to operator theory
Lecturer: Prof. Charles Batty (Oxford, UK)
Description: An overview of some of the central theorems on linear operators between normed vector spaces, touching on the theory of unbounded linear operators
Syllabus: Overview of the basic theory of bounded linear operators between Banach spaces, spectral theory, some fundamental results in classical operator theory (uniform boundedness theorem, closed graph theorem, open mapping theorem, inverse mapping theorem), introductory material on the theory of closed unbounded operators (as time permits)
Week 2, 26-30 June - Advanced courses
Course 3: Advanced operator theory
Lecturer: Dr David Seifert (Oxford, UK)
Description: An overview of some more advanced topics in operator theory, making the connection with modern PDE theory
Syllabus: Compactness in normed vector spaces, compact operators (characterisation, properties, spectral theory, examples), operators with closed range, the closed range theorem, Fredholm theory (Fredholm index, Fredholm alternative, perturbation results), existence and uniqueness for simple elliptic PDEs via the Fredholm alternative
Course 4: The theory of operator semigroups and their applications
Lecturer: Dr Sachi Srivastava (University of Delhi)
Description: An introduction to the theory of strongly continuous operator semigroups and their applications
Syllabus: C0-semigroups, infinitesimal generators, spectral theory of generators, Lumer-Phillips theorem, Hille-Yosida theorem, examples, abstract Cauchy problems, mild solutions, applications to simple PDEs (heat equation, wave equation) and quantum systems
Week 3, 3-7 July - Modern applications of functional analysis
Course 5: The Laplacian on a Riemannian manifold
Lecturers: Prof Claudio Arezzo and Dr Luca Di Cerbo (ICTP)
Syllabus: Basic theory of differential and Riemannian manifolds. Differential forms and integration. L2 functions and forms. Gradient, divergence and Laplacian on a Riemannian manifold. Towards Hodge Theorem, as much as time permits.
Course 6: Distribution solutions to ordinary differential equations
Lecturer: Dr Ismail Mirumbe (Makerere, Uganda)
Local organizing committee
• James Katende (University of Nairobi)
• Damian Maingi (University of Nairobi)
• Bernard Nzimbi (University of Nairobi)
• Jared Ongaro (University of Nairobi, Chair)
• Patrick Weke (University of Nairobi)
Scientific advisory committee
• Leif Abrahamson (University of Uppsala, Sweden)
• Rikard Bogvad (Stockholm University, Sweden)
• Damiani Maingi (University of Nairobi, Kenya)
• Fernando Rodrigues Villegas (ICTP)
• David Ssevviiri (Makerere University, Uganda)
• Balazs Szendroi (University of Oxford, UK, main International Organizer)
• Patrick Weke (University of Nairobi, Kenya)
EAUMP Country Coordinators
• Juma Kasozi (Makerere University, Uganda)
• Sylvester E. Rugeihyamu (Dar es Salaam University, Tanzania)
• Jared Ongaro (University of Nairobi, Kenya)
• Michael Gahirima (University of Rwanda)
• Mubanga Lombe (University of Zambia)
Nairobi - Kenya
ICTP
pio@ictp.it
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19 Jun 2017
- 7 Jul 2017

» ICTP-EAUMP School on Modern Functional Analysis | (smr 3133)

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Europe/Rome
2017-06-19 08:00:00
2017-06-23 22:00:00
Workshop on Hyperbolic Dynamics | (smr 3126)
The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste is organizing a Workshop in Hyperbolic Dynamics with an emphasis on topics that have benefited from the seminal contributions of Yakov Pesin, on the occasion of his 70th birthday.
The workshop will take place at ICTP, Trieste on 19-23 June 2017 and will include lectures by internationally renowned speakers who have led the progress in the field over several decades. There will be ample opportunities for interaction and discussion amongst participants of all levels of experience.
The workshop is organized in conjunction with a school in Hyperbolic Dynamics which will be held on 12-16 June 2017 at the Centro di Ricerca Matematica Ennio de Giorgi, Pisa, with mini-courses by D. Dolgopyat (Maryland), S. Luzzatto (ICTP), Y. Pesin (Penn State), F. Rodriguez-Hertz (Penn State) and some invited seminars. Details can be found on the website of the school at: http://crm.sns.it/event/410/
Registration, participation and funding for the two events are independent of each other.
Topics:
Uniform and nonuniform hyperbolicity
Partial hyperbolicity
Lyapunov exponents
Ergodic Theory
Thermodynamical formalism
Dimension Theory
Statistical properties of deterministic dynamical systems
Decay of correlations
Markov extensions and structures
Preliminary list of Speakers:
Aaron Brown
Leonid Bunimovich
Keith Burns
Jerome Buzzi
Manfred Denker
Dmitry Dolgopyat
Andrey Gogolev
Mike Hochman
Huyi Hu
Michael Jakobson
Anatole Katok
Svetlana Katok
Konstantin Khanin
Carlangelo Liverani
Stefano Luzzatto
Stefano Marmi
Mark Pollicott
Federico Rodriguez-Hertz
Omri Sarig
Jeorg Schmeling
Samuel Senti
Mike Shub
Domokos Szasz
Sandro Vaienti
Amie Wilkinson
Ke Zhang
ICTP
ICTP
pio@ictp.it
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19 Jun 2017
- 23 Jun 2017

» Workshop on Hyperbolic Dynamics | (smr 3126)

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Europe/Rome
2017-07-19 08:00:00
2017-07-22 22:00:00
Mediterranean Youth Mathematical Championship 2017 (La Sapienza University, Rome) - (smr 3171)
An initiative to encourage Mediterranean youth, both male and female, to develop an interest in Mathematics, a discipline which has been of great importance for the growth of the cultural community of the Mediterranean, with its many nations and religions.
Working language of the championship: English
Some 20 teams involved, one for each of the Mediterranean countries.
Each team consisting of 4 people, 2 boys and 2 girls, presently attending the last three years of high school (and at most nineteen years old).
Each team selected by appropriate local entities (e.g., the local entities in charge of the IMO).
Program:
July 19, 2017 - Arrival in Rome
July 20, 2017 - Opening ceremony and contest on the premises of Roma Tre university
July 21, 2017 - Awards ceremony and visit of Rome
July 22, 2017 - Departure from Rome
Contest operating methods:
July 20 in the morning
1. A common list of problems for all teams
2. Preliminary ranking of the teams according to their score
July 20 in the afternoon (direct clashes)
1. First round – direct clashes between 1st and 2nd ranked teams, 3rd and 4th ranked teams, 5th and 6th ranked teams, etc.
2. Second round – direct clashes between randomly coupled teams
3. Each direct clash carries some points to the teams
4. The points accumulated in the afternoon are added to those scored in the morning.
Description of a direct clash
Each team receives two lists of problems and decides which one to keep, the other being passed to the opponent. Thus every team has two lists of problems to solve in a fixed amount of time. The winner is the team able to solve more problems (hence a tie is possible).
July 20 in the afternoon (final problem)
A common problem is given to each team, to be solved in at most 10 minutes. The team which first provides the correct answer is awarded 3.5 points; all the other teams providing a correct answer are awarded 1 point. If a team provides an incorrect answer, it is awarded 0 points. If a team does not provide an answer, it is awarded 0.5 points. The points awarded are added to those already accumulated.
The final ranking of the MYMC is decided by the Jury based on the final score obtained by the various teams, at the conclusion of the competitions described above.
Local Organizing Committee:
Claudio Bernardi, Sapienza Università di Roma
Luca Biasco, Università degli Studi Roma Tre
Giandomenico Boffi, Università degli Studi Internazionali di Roma
Corrado Falcolini, Università degli Studi Roma Tre
Marta Menghini, Sapienza Università di Roma
Marina Monsurrò, Università Europea di Roma
Francesco Pappalardi, Università degli Studi Roma Tre
Maria Grazia Proietti, Università degli Studi Roma Tre
Valerio Talamanca, Università degli Studi Roma Tre
Francesca Tovena, Università degli Studi di Roma Tor Vergata
- Italy
ICTP
pio@ictp.it
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19 Jul 2017
- 22 Jul 2017

» Mediterranean Youth Mathematical Championship 2017 (La Sapienza University, Rome) - (smr 3171)

Every year the Mathematics Group offers research opportunities for outstanding mathematicians from developing countries, for short and long-term visits, as well as Post-doctoral Fellowships, through the Mathematics Research Fellowships programme.

The ICTP Mathematics Section collaborates with organizations from around the world.

Differential Geometry

Claudio Arezzo studies the geometry of complex algebraic varieties using techniques from analysis and differential geometry.

Algebraic Geometry

Lothar Goettsche is interested in moduli spaces in algebraic geometry and interactions with theoretical physics.

Dynamical Systems

Stefano Luzzatto studies dynamical systems and is particularly concerned with the geometric and statistical properties of chaotic systems as well as the use of rigorous use of numerical techniques to study them.

Number Theory

Fernando Rodriguez Villegas has research interests in representation theory, combinatorics and symmetric functions as well as computational algebra and number theory.

ICTP is governed by UNESCO, IAEA, and Italy, and is a UNESCO Category 1 Institute

http://library.ictp.it/ejds.aspx