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 Programme
- 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.

14 Mar 2019

N.S. Narasimhan reflects on the late mathematician's contributions

28 Nov 2018

New partner institute with University of the Chinese Academy of Sciences inaugurated

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Europe/Rome
2019-04-18 14:30:00
2019-04-18 17:30:00
Mathematics Seminar Afternoon
14:30 - 15:30 Roman O. Popovych (Faculty of Mathematics, University of Vienna, Austria & Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine)
Computation of contractions of Lie algebras
Abstract: Limiting processes (contractions) of Lie algebras appear in different areas of physics and mathematics, where Lie algebras arise, e.g., in the study of representations, invariants and special functions. The algebraic counterpart of the notion of contractions of Lie algebras is given by degenerations of Lie algebras.
The main attention in the talk is paid to the practical computation of contractions of Lie algebras. We present a wide list of necessary conditions for the contraction existence. Particular ways for realizing contractions, which are relevant to physics and includes simple and generalized Inönü–Wigner contractions and Saletan (linear) contractions, are discussed and the limitation for using them is clarified. We also plan to present the complete description of contractions of Lie algebras of dimension not greater than four, of five- and six-dimensional nilpotent algebras and of almost Abelian Lie algebras over both the complex and real field.
15:30 - 16:00 break
16:00 - 17:00 Célestin Kurujyibwami (University of Rwanda, Kigali, Rwanda)
Group classification of multidimensional nonlinear Schrödinger equations
Abstract: We describe the equivalence groupoid and the equivalence group of the class N of generalized multidimensional Schrödinger equations with variable mass and show that this class is not normalized. We then partition this class into two disjoint normalized subclasses and derive their corresponding equivalence groups. Restricting to the case of constant mass equal to one, we characterize the point transformations of the subclasses of the class N with respect to specific values of the arbitrary elements, in particular we do this for the class V of multidimensional nonlinear Schrödinger equations with potentials and modular nonlinearities. This class also turns out not to be normalized. We partition it into three normalized subclasses, and this allows us to apply the algebraic method and solve each subclass completely for space dimension two. The group classification in each involves three integers that are invariant with respect to the adjoint action of the equivalence transformations. As a result, a full list of Lie symmetry extensions together with their corresponding families of potentials in the class V is presented.
Everyone is welcome to attend
ICTP
ICTP
pio@ictp.it
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18 Apr 2019

» Mathematics Seminar Afternoon

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Europe/Rome
2019-04-23 16:00:00
2019-04-23 17:00:00
Five-term relations
Abstract: I will review how the five term relation for the Fadeev-Kashaev's quantum dilogarithm arises in the Hall algebra context, and sketch a simple proof. Then I will explain how this proof can be transported to the elliptic Hall algebra situation, where the five term relation implies identities between Macdonald polynomials conjectured by Bergeron and Haiman. This is a joint work with Adriano Garsia.
ICTP
ICTP
pio@ictp.it
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23 Apr 2019

» Five-term relations

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Europe/Rome
2019-04-24 14:30:00
2019-04-24 15:30:00
Refinement of Kool-Thomas invariants via Equivariant K-theoretic invariants
Abstract: Please see attached.
ICTP
ICTP
pio@ictp.it
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24 Apr 2019

» Refinement of Kool-Thomas invariants via Equivariant K-theoretic invariants

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Europe/Rome
2019-05-02 16:00:00
2019-05-02 17:00:00
Quantized pseudo-fixed-point subalgebras and the reflection equation
ICTP
ICTP
pio@ictp.it
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2 May 2019

» Quantized pseudo-fixed-point subalgebras and the reflection equation

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Europe/Rome
2019-06-17 08:00:00
2019-06-28 22:00:00
1st Latin American School in Applied Mathematics | (smr 3301)
All lessons will be held in English at the
Universidad San Francisco de Quito Campus Cumbaya
http://www.usfq.edu.ec/Paginas/Inicio.aspx and
Escuela Politécnica Nacional
https://www.epn.edu.ec/
**DEADLINE for requesting participation is 24 MARCH 2019**
Topics:
Optimal Control and Applications to Biology
Fluid Mechanics
Machine Learning
Cancer Dynamics Description continued
This activity serves as an opportunity to highlight current research topics and real-world applications in applied mathematics. Students exposed to the mini-courses will learn mathematical tools used to efficiently solve real world problems. Specifically, the intention is to highlight the applications of mathematics in other disciplines as well as in industry in an effort to illustrate mathematics as a useful and necessary tool as well as a lucrative career option.
Courses aim to address both theoretical aspects as well as real world applications. The courses will be complemented by additional computer lab sessions where students will solve relevant problems and be given an opportunity to run simulations and learn computational skills. In addition, students will be provided with mentoring regarding jobs in industry as well as opportunities for advanced studies in mathematics.
Lecturers include:
M. S. Aronna, Escola de Matemática Aplicada (FGV), Brazil
J. Bedrossian, University of Maryland, U.S.A.
R. Cóbe, Sao Paulo State University, Brazil
D. Levy, University of Maryland, U.S.A.
Organizers:
M. Calahorrano, EPN, Ecuador
M. G. Delgadino, Imperial College, U.K.
D. C. Ramirez, USFQ, Ecuador
L. D. Simonelli, ICTP, Italy
G. Violini, Emeritus, CIF, Colombia
Local Organizer:
C. Arezzo, ICTP, Trieste, Italy
Quito - Ecuador
ICTP
pio@ictp.it
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17 Jun 2019
- 28 Jun 2019

» 1st Latin American School in Applied Mathematics | (smr 3301)

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Europe/Rome
2019-07-01 08:00:00
2019-07-05 22:00:00
Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306)
A growing number of researchers use algebraic geometry in industrial and applied mathematics: applications include biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear PDE, optimization, and robotics.
Algebraic Geometry of data clouds
- density of cloud data
- reach of a manifold and topological data analysis
- classical theory of polar classes of a variety
- the nearest points to a variety
- the EDD degree of a manifold and its properties
- the Bottleneck degree of varieties
Biochemical reaction networks modeled by mass-action kinetics
- basics on reaction networks with mass-action kinetics: biochemical notions, algebraic notions, dynamical notions
- steady state invariants and computational algebraic geometry
- networks with toric steady states
- counting the number of positive steady states and real solutions to polynomial
systems
Grants:
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.
Women are particularly encouraged to apply.
ICTP
ICTP
pio@ictp.it
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1 Jul 2019
- 5 Jul 2019

» Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306)

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Europe/Rome
2019-07-15 08:00:00
2019-08-02 22:00:00
EAUMP - ICTP Summer School on Algebraic Topology and its Applications | (smr 3310)
The Eastern Africa Universities Mathematics Programme (EAUMP) courtesy of the International Science Programme (ISP) of Sweden; jointly with ICTP, Trieste, Italy; Sida; CIMPA, DAAD, LMS/AMMSI, COMPOSITIO is organizing a three weeks summer School on Algebraic Topology and its Applications to be held at Makerere University, Kampala, Uganda from 15th July to 2nd August, 2019.
It is intended that the School will take the audience comprising young academic staff members and advanced graduate students (M.Sc, Ph.D and Postdoctoral Students) of Mathematics from the Eastern African region and beyond. The school is the next one in a series of schools organized under the Eastern African Universities Mathematics Programme (EAUMP). The most recent EAUMP schools were organized in 2015 at Makerere University, Uganda, on Experimental Pure Mathematics; in 2016 at the University of Rwanda on Number Theory; in 2017 at the University of Nairobi on Modern Functional Analysis; and in 2018 at the University of Dar es Salaam on Homological methods in Algebra and Geometry. All the schools are within one of the main aims of EAUMP which is to improve the pure mathematics in the region.
The member Universities of the EAUMP are University of Dar es Salaam, Tanzania; University of Nairobi, Kenya; University of Zambia, Zambia; Makerere University, Uganda; University of Rwanda, Rwanda.
GOALS OF THE SCHOOL
To introduce participants to current trends in Algebraic Topology and its applications, including knot theory and Topological Data Science, and provide research topics for masters and PhD studies.
To provide a forum for African mathematicians to interact, exchange ideas and initiate collaborations.
Identify talented students for possible PhD programs.
To produce digital lecture material for dissemination, which contributes to the training of master students in the Eastern Africa region.
STURCTURE AND PROGRAMME
As in the years 2013-2017, participants will be asked to submit mini-projects on the material studied at the School, with the best submissions receiving prizes/awards. They will work on their projects after the end of the School and will submit them during the third week of the school.
Here is the detailed course plan for the School.
Week 1: Introductory courses
Course 1: Introductory Topology
Lecturers: Balazs Szendroi (University of Oxford) and Venuste Nyagahakwa (University of Rwanda)
Description: This course will introduce the basic ideas of topology, starting with an abstract definition of topological space, and treating many examples.
Course 2: The Fundamental Group
Lecturer: Jean-Baptiste Gatsinzi (Botswana Institute of Science and Technology)
Description: The fundamental group is a basic but key algebraic invariant of a topological space. This course will define this group and give some interesting examples of how to compute it.
Week 2: Intermediate courses
Course 3: Manifolds
Lecturer: Claudia Scheimbauer (NTNU, Trondheim)
Description: Manifolds provide a very interesting class of examples of topological spaces, of great interest in applications to geometry, physics and elsewhere. This course will introduce this notion with many examples, mainly from dimensions 1, 2 and 3.
Course 4: Introduction to persistent homology
Lecturer: Ulrike Tillmann (University of Oxford)
Description: Persistent homology, a method for computing topological features of a space at different spatial resolutions, will be explained in this course, with a view towards applications.
Week 3: Advanced courses
Course 5: Introduction to Knot Theory
Lecturer: Mehdi Yazdi (University of Oxford)
Description: A knot is a tangled piece of rope in the three dimensional space, with the two loose ends glued together. Knot theory asks questions such as: can this knot be untangled by continuously deforming the rope? Are there ways to tell two knots apart? This course will discuss the basic invariants and quantities defined for knots, together with the connection with the theory of 3-dimensional manifolds.
Course 6: Topological Data Analysis
Lecturer: Vidit Nanda (University of Oxford)
Description: Topological data analysis is a recent and fast-growing field providing a set of new topological and geometric tools to infer global features from complex data. This course will give an introduction to this circle of ideas.
SCHOOL PARTICIPATION
Online application form is available at http://indico.ictp.it/event/8699/, and will close on 28th April, 2019. Alternative request for participation can be done by originating an email to kasozi@cns.mak.ac.ug copied to ssevviiri@cns.mak.ac.ug, szendroi@maths.ox.ac.uk. Only those applicants who will be successful shall be contacted. Letters of invitation will be issued to participants upon request for the processing of travel documents or soliciting for funding.
INTERNATIONAL ORGANISING COMMITTEE
Leif Abrahamson (University of Uppsala, Sweden), Prof. Bengt-Ove Turesson (Linkoping University, Sweden), Fernando Rodriguez Villegas (ICTP, Italy), Balazs Szendroi (University of Oxford, UK), Patrick Weke (University of Nairobi, Kenya).
LOCAL ORGANIZING COMMITTEE
David Ssevviiri (Makerere University), Juma Kasozi (Makerere University), John Mango Makerere University), Patrick Weke (University of Nairobi), Jared Ongaro (University of Nairobi), Eunice Mureithi (University of Dar es Salaam), James Makungu (University of Dar es Salaam), Michael Gahirima (UR-CST, Nyarugenge), Wellars Banzi (UR-CST, Nyarugenge), Mubanga Lombe (University of Zambia), Isaac D. Tembo (University of Zambia).
Kampala - Uganda
ICTP
pio@ictp.it
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15 Jul 2019
- 2 Aug 2019

» EAUMP - ICTP Summer School on Algebraic Topology and its Applications | (smr 3310)

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Europe/Rome
2019-07-15 08:00:00
2019-07-26 22:00:00
ICTP School on Geometry and Gravity | (smr 3311)
The purpose of the School is to expose graduate students and young researchers to a variety of topics, techniques and lines of research of common interest to geometers and physicists. The activity is intended for theoretical physicists and mathematicians with knowledge of Differential geometry and General Relativity.
Topics:
Black Holes,
Modified Gravity Theories,
AdS/CFT Correspondence,
Einstein Constraint Equations,
Mass in General Relativity,
Cosmological Solutions.
School Lectures:
C. CEDERBAUM, University of Tubingen, Germany
P. CHRUSCIEL, University of Vienna, Austria
M. DAFERMOS, Princeton University, USA and University of Cambridge, UK
H. REALL, DAMTP, University of Cambridge, UK
R. SCHOEN, University of California Irvine, USA
R. WALD, University of Chicago, USA
T. WISEMAN, Imperial College London, UK
N. YUNES, Montana State University, USA
Grants:
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.
ICTP
ICTP
pio@ictp.it
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15 Jul 2019
- 26 Jul 2019

» ICTP School on Geometry and Gravity | (smr 3311)

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 2019 is now open. The application deadline is 7 January 2019. Other research and education opportunities in mathematics are available through the ICTP's Postgraduate Diploma Programme as well as its Associateship Scheme.

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

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