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
- Physics PhD Program
- 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.

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

31 Jan 2018

Two recipients honored for dedication to Abdus Salam’s vision

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Europe/Rome
2018-04-26 14:30:00
2018-04-26 15:30:00
Studying geometry with arithmetic techniques
Abstract: See file below
ICTP
ICTP
pio@ictp.it
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26 Apr 2018

» Studying geometry with arithmetic techniques

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Europe/Rome
2018-05-03 14:30:00
2018-05-03 15:30:00
Global Existence of Solutions to Scalar Equations on Spatially Flat Universe as a Background with Non-minimal Coupling
Abstract: We prove the wellposedness of scalar wave equations on spatially at universe as a background with nonminimal coupling with the scalar potential turned on by introducing the k-order linear energy and the corresponding energy norm. In the local case, we show that both the k-order linear energy and the energy norm are bounded for finite time with initial data in Hk+1 × Hk. Whereas in the global case, we have to add three assumptions related to the nonminimal coupling constant, the scale factor of spacetimes, and the form of the scalar that has to be a polynomial with a small positive parameter. Then, we show that the solution does globally exist with a particular decay estimate that depends on the scale factor of the spacetimes. Finally, we provide some physical models that support our general setup.
ICTP
ICTP
pio@ictp.it
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3 May 2018

» Global Existence of Solutions to Scalar Equations on Spatially Flat Universe as a Background with Non-minimal Coupling

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Europe/Rome
2018-05-23 14:30:00
2018-05-23 15:30:00
BASIC NOTIONS SEMINAR: Introduction to Quantum Computation
Abstract:
I will give a very brief introduction to the concept of computation on a computer, and in particular on a quantum computer.
I will try to describe for which kind of problems we could expect a speed-up due to quantum mechanics and discuss the status of the technology in this direction.
ICTP
ICTP
pio@ictp.it
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23 May 2018

» BASIC NOTIONS SEMINAR: Introduction to Quantum Computation

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Europe/Rome
2018-05-24 14:30:00
2018-05-24 15:30:00
A Geometric View on Tsen's Theorem
Abstract:
In 1936 Tsen proved that a 1-dimensional family of hypersurfaces of degree d in projective n-space always admits a section provided that d is less than or equal to n. This simple statement has been gen- eralized in many ways, and still inspires developments in algebraic geometry. In this talk I will survey the history of Tsen’s Theorem, mostly from the geometric point of view, and describe current re- search toward new interpretations and generalizations.
ICTP
ICTP
pio@ictp.it
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24 May 2018

» A Geometric View on Tsen's Theorem

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Europe/Rome
2018-05-05 08:00:00
2018-05-10 22:00:00
TMU-ICTP School and Conference on Dynamical Systems and Ergodic Theory | (smr 3200)
Dynamical Systems and Ergodic Theory constitute a vibrant and exciting eld of current research in pure mathematics, with lots of connections to other areas such as probability theory, differential geometry, ODEs, and potential applications to such diverse areas as natural and biological sciences, economics, engineering, climate and disease modeling and many others. It can be thought of as a modern development of classical theories of Differential Equations and the fundamental concepts and guiding ideas go back more than a century to pioneering thinkers such as Poincaré, Birkhoff and Kolmogorov. Its interest and importance has only grown in time and several Fields Medals have been awarded in the area.
The ICTP-TMU School on Dynamical Systems and Ergodic Theory will consist of introductory mini-courses aimed specifically at masters and beginning PhD students who are expected to have an excellent general mathematics background but not necessarily any previous experience of the particular topics covered in the courses. The mini-courses will be complemented by a series of research-level seminars, given by internationally renowned scholars in the eld, and aimed at more advanced PhD students and local faculty and researchers. All students and researchers are welcome to all the lectures.
Scientific Committee
S. LUZZATTO, ICTP, Italy
M. NASSIRI, IPM, Iran
A. TAHZIBI, ICMC, Brazil
Lecturers
C. BONATTI, Dijon, France
P. ESLAMI, Warwick, UK
C. LIVERANI, Rome, Italy
Speakers
J.F. ALVES, Porto, Portugal
P. BERGER, Paris, France
O. BUTTERLEY, ICTP, Italy
S. LUZZATTO, ICTP, Italy
M. POLLICOTT, Warwick, UK
M. TSUJII, Kyushu, Japan
Tutor
L.D. SIMONELLI, ICTP, Italy
Tehran - Islamic Republic of Iran
ICTP
pio@ictp.it
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5 May 2018
- 10 May 2018

» TMU-ICTP School and Conference on Dynamical Systems and Ergodic Theory | (smr 3200)

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Europe/Rome
2018-05-21 08:00:00
2018-05-25 22:00:00
Workshop on Global Differential Geometry | (smr 3205)
The German Research Foundation (DFG) and the International Center for Theoretical Physics (ICTP) are organizing a Workshop on Global Differential Geometry, to be held at the African Institute of Mathematical Sciences (AIMS) in Mbour, Sénégal, May 21 - 25, 2018.
The workshop will focus on recent developments in Global Differential Geometry, in particular on symplectic and Poisson geometry, including foliations and Lie theory, as well as classical differential geometry with its connections to differential topology and global analysis. There are close relations to the index theory of elliptic operators, generalized complex geometry and geometric flows, all of which open the door to applications in mathematical physics.
Organizing Committee:
Hamidou Dathe (Dakar)
Bernhard Hanke (Augsburg)
Aissa Wade (Penn State and AIMS Mbour)
Katrin Wendland (Freiburg)
DFG Coordinators:
Carsten Balleier
Alida Höbener
Beate Wilhelm
The list of speakers includes:
Claudio Arezzo (ICTP)
Augustin Banyaga (Penn State)
Augustin Tshidibi Batubenge (South Africa)
Kai Cieliebak (Augsburg)
A. Degeratu (Stuttgart)
Hassimou Diallo (Cote d’Ivoire)
Abdoul Salam Diallo (Senegal)
Cheikh Mbacke Diop* (Senegal)
Jonathan Mboyo Esole* (Northeastern)
Urs Frauenfelder (Augsburg)
Sebastian Goette (Freiburg)
Djideme Franck Houenou (Benin)
El-Kaioum Mohamed Moutuou* (USF Florida)
Karl-Hermann Neeb (Erlangen)
Sylvie Paycha (Postdam)
Philippe Rukimbira (FIU Florida)
Thomas Schick (Göttingen)
Léonard Todjihoundé (Benin)
Joel Tossa (Benin)
Burkhard Wilking (Münster)
*to be confirmed
Mbour - Senegal
ICTP
pio@ictp.it
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21 May 2018
- 25 May 2018

» Workshop on Global Differential Geometry | (smr 3205)

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Europe/Rome
2018-06-04 08:00:00
2018-06-15 22:00:00
International School on Extrinsic Curvature Flows | (smr 3209)
NOTICE TO PARTICIPANTS
While a detaliled programme of the School will be posted at a later stage,
please be informed that foreseen daily schedule is
Monday to Friday, 9 a.m. to 5 p.m.
It is recommended that participants invited through selection process
plan their trip so to arrive in Trieste the day before the School starts,
and stay until the day after it ends, to secure continous attendance.
* * *
The School aims at introducing students both to the basic ideas and to the most recent breakthroughs in the field of extrinsic curvature flows, a fundamental research direction at the intersection of Analysis and Geometry, with deep connections to the theories of minimal surfaces and of diffusive partial differential equations.
Extrinsic flows have important applications to the geometry of submanifolds, as their study provides an effective strategy for obtaining topological classification results and for proving sharp geometric inequalities.
In a broader context, extrinsic flows arise in describing the dynamics of interfaces in physical and biological sciences, a fact that provides a strong scientific motivation for their mathematical inquiry.
Virtually all the different approaches to mean curvature flows will be accounted for, with particular emphasis on the fundamental problem of singularities formation.
A major goal of the School will indeed be putting the best students in the position of understanding the many open problems in the field.
PRELIMINARY LIST OF LECTURERS
S. Angenent, University of Wisconsin-Madison
P. Daskalopoulos, Columbia University
G. Huisken, Universität Tübingen
C. Mantegazza, Università di Napoli Federico II
F. Otto, MPI for Mathematics in the Sciences
C. Sinestrari, Università di Roma Tor Vergata
T. Souganidis, University of Chicago
Y. Tonegawa, Tokyo Institute of Technology
Interested candidates should apply online (see link "Apply here" on the left-hand menu). * DEADLINE FOR APPLICATION: EXPIRED *
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Organised in partnership with the Clay Mathematics Institute
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ICTP Secretariat contact: smr3209@ictp.it
ICTP
ICTP
pio@ictp.it
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4 Jun 2018
- 15 Jun 2018

» International School on Extrinsic Curvature Flows | (smr 3209)

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Europe/Rome
2018-06-18 08:00:00
2018-06-22 22:00:00
Summer School on Geometry of Moduli Spaces of Curves | (smr 3215)
Moduli spaces of stable pointed curves play an important role in algebraic geometry. This School will have one course on vector bundles of coinvariants and on conformal blocks and another one on their cohomology classes in relation with those of moduli of abelian varieties. The cohomology of moduli spaces of curves and abelian varieties carries several natural classes. We focus on the tautological classes and the cohomology classes related to spaces of modular forms. The problem of determining relationships between the tautological classes turns out to be particularly interesting. Moduli spaces of curves carry vector bundles of coinvariants and conformal blocks; they are invariants of a curve C attached to a Lie group G that are canonically isomorphic to global sections of an ample line bundle on the moduli stack of certain G-bundles on C. These are generalized theta functions in case C is smooth. In case g=0, the bundles of co-invariants are globally generated, and their first Chern classes are semi-ample line bundles on the moduli of curves, and shed light on its birational geometry. We can also use the moduli space of curves to learn about generalized theta functions.
TOPICS:
Cohomology classes on moduli of curves and abelian varieties
moduli spaces of curves and abelian varieties
properties of the moduli spaces and their compactifications
natural cohomology classes and their relations
tautological classes and cohomology classes related to spaces of modular forms
Vector bundles of coinvariants and conformal blocks
introduction to moduli spaces of curves
open problems and F-conjecture
vector bundles of coinvariants and conformal blocks
case g=0: global generation and semi-ample divisors
any genus: nef divisors
Chern classes of bundles of coinvariants
Global sections of ample line bundles on Bun_G(C): smooth and nodal case
PARTICIPATION:
Women are particularly encouraged to apply.
Should you come to Trieste with your child(ren), please send an e-mail to smr3215@ictp.it to describe your family needs and we will do our best to meet them.
A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.
To apply, please use the link on the left side of this web page.
The deadline for submitting applications expired on 15 March 2018.
ICTP
ICTP
pio@ictp.it
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18 Jun 2018
- 22 Jun 2018

» Summer School on Geometry of Moduli Spaces of Curves | (smr 3215)

Every year the Mathematics Group offers research opportunities for outstanding mathematicians from developing countries, for short and long-term visits, as well as postdoctoral fellowships, through the Mathematics Research Fellowships programme. A call for postdoctoral fellowships with a starting date of September 2018 is now open. The application deadline is 7 January 7 2018. Other research and education opportunities in mathematics are available through the ICTP's Postgraduate Diploma Programme as well as its Associateship Scheme.

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