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.

9 May 2019

Join the effort to inspire and train the next generation

14 Mar 2019

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

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Europe/Rome
2019-09-19 14:30:00
2019-09-19 15:30:00
Analysis Seminar: On the Strichartz inequalities for the Schroedinger equation
Abstract: In this talk we will discuss some mixed Lp estimates obtained by Robert Strichartz in 1977 for a large class of dispersive PDEs, restricting our attention to the special case of the Schroedinger equation. Starting with simple facts about the Fourier transform, we will show how Harmonic Analysis can be applied in order to obtain a complete proof of these estimates. It is worth to mention that such estimates also have strong connections with the theory of restriction estimates for Fourier transform, and we could see the main result of this talk as the base for the companion talk of Mateus Sousa (about sharp restriction estimates for the Fourier transform).
ICTP
ICTP
pio@ictp.it
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19 Sep 2019

» Analysis Seminar: On the Strichartz inequalities for the Schroedinger equation

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Europe/Rome
2019-09-19 15:30:00
2019-09-19 16:30:00
Analysis Seminar: On sharp Strichartz inequalities
Abstract: In this follow-up talk we will discuss a little bit about the concept of sharp inequalities with a focus on the particular case of Strichartz inequalities. We will discuss questions related to sharp constants, existence of extremizers and characterization of extremizers.
ICTP
ICTP
pio@ictp.it
`
19 Sep 2019

» Analysis Seminar: On sharp Strichartz inequalities

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Europe/Rome
2019-09-24 13:00:00
2019-09-24 14:00:00
DIPLOMA Seminar: The sphere packing problem and the construction of magic functions
Abstract: How densely can one pack identical balls that do not overlap in $R^n$? Although it looks like an innocent question, this turns out to be one of the most difficult problems in geometry. Before 2016, the answer for the problem was known only in dimensions 1, 2 and 3. In 2003, Cohn and Elkies found a connection between this problem and a Fourier optimization one. Using Cohn and Elkies result, Viazovska constructed magic functions that solve the sphere packing problem in dimension 8 and, later on, she and her collaborators also solved the problem in dimension 24 using similar techniques. In this talk, we introduce the sphere packing problem and discuss Viazovska's construction and the role played by modular forms in it.
ICTP
ICTP
pio@ictp.it
`
24 Sep 2019

» DIPLOMA Seminar: The sphere packing problem and the construction of magic functions

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Europe/Rome
2019-09-16 08:00:00
2019-09-20 22:00:00
School and Workshop on Mixing and Control | (smr 3324)
This activity is part of a two-week event consisting of
Week 1: School and Workshop on Mixing and Control (16 - 20 September)
Week 2: School and Workshop on Random Matrix Theory and Point Processes
(23 - 27 September)
To participate in both activities you need to submit two distinct applications.
Week 1: Please click on the link "Apply here" on the left hand-side column
Week 2: Please apply at: http://indico.ictp.it/event/8900/
DEADLINE for requesting participation for both weeks: 15 MAY 2019
==========================================================
Organizers:
A. Agrachev, SISSA, Trieste
A. Bufetov, Marseille & Steklov Institute
T. Grava, SISSA & Bristol
A. Guionnet, ENS Lyon
S. Kuksin, Paris & Shandong University
Local Organizer:
S. Luzzatto, ICTP, Trieste
The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory.
One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars.
The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers.
Week 1: Mixing and Control
Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics.
Week 2: Random Matrix Theory and Point Processes
The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes.
Topics:
Point process;
Random matrices;
Integrable probability;
Integrable systems;
Mixing;
Stationary measure;
Markov systems;
Nonholonomic constraints;
Controllability;
Lecturers:
A. Agrachev, SISSA, Trieste
A. Bufetov, Marseille & Steklov Institute
A. Guionnet, ENS Lyon
S. Kuksin, Paris & Shandong University
Speakers:
F. Augeri, Weizmann, Israel
F. Baudoin, Purdue Univ.
C. Bordenave, Toulose, France
U. Boscain, CNRS, Sorbonne Univ.
A. Bufetov, MIT
M. Cafasso, Angers, France
*I. Corwin, Columbia University
N. Cuneo, University Paris-Diderot
A. de Bouard, Ecole Polytechnique
A. Debussche, ENS Rennes
A. Dymov, Steklov Insitute, Moscow
J-P. Eckmann, University of Geneva
*L. Erdoes, Wien, Austria
N. Glatt-Holtz, Tulane University
H. Guan, Tsinghua University
V. Jaksitch, McGill University
I. Krasovsky, Imperial College
M. Krishnapur, Bangalore, India
*A. Kupiainen, University of Helsinki
K. Mc Laughlin, Colorado State University
V. Nersesyan, University of Versailles
P. Nikitin, Steklov, St. Petersburg
G. Olshanski, ITP, RAS, Russia
S. Peche, LPSM, Paris, France
Y. Qiu, CNRS, France
A. Ramirez, Pontificia Universidad Catolica de Chile
R. Raquepas, University Grenoble Alpes (Institut Fourier)
T. Sasamoto, Chiba, Japan
M. Shcherbina, Kharkov, Ukraina
A. Shirikyan, Cergy-Pontoise
N. Tzvetkov, University of Cergy Pontoise
A. Veselov, Loughbourogh University
*H-T. Yau, Harvard
* to be confirmed
ICTP
ICTP
pio@ictp.it
`
16 Sep 2019
- 20 Sep 2019

» School and Workshop on Mixing and Control | (smr 3324)

`
Europe/Rome
2019-09-23 08:00:00
2019-09-27 22:00:00
School and Workshop on Random Matrix Theory and Point Processes | (smr 3382)
This activity is part of a two-week event consisting of
Week 1: School and Workshop on Mixing and Control (16 - 20 September)
Week 2: School and Workshop on Random Matrix Theory and Point Processes (23 - 27 September)
To participate in both activities you need to submit two distinct applications.
Week 1: Please apply at: http://indico.ictp.it/event/8720/
Week 2: Please click on the link "Apply here" on the left hand-side column
DEADLINE for requesting participation for both weeks: 15 MAY 2019
=======================================================
Organizers:
A. Agrachev, SISSA, Trieste
A. Bufetov, Marseille & Steklov Institute
T. Grava, SISSA & Bristol
A. Guionnet, ENS Lyon
S. Kuksin, Paris & Shandong University
Local Organizer:
S. Luzzatto, ICTP, Trieste
The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory.
One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars.
The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers.
Week 1: Mixing and Control
Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics.
Week 2: Random Matrix Theory and Point Processes
The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes.
Topics:
Point process; Random matrices;
Integrable probability;
Integrable systems; Mixing;
Stationary measure;
Markov systems;
Nonholonomic constraints;
Controllability.
Lecturers:
A. Agrachev, SISSA, Trieste
A. Bufetov, Marseille & Steklov Institute
A. Guionnet, ENS Lyon
S. Kuksin, Paris & Shandong University
Speakers:
F. Augeri, Weizmann, Israel
F. Baudoin, Purdue Univ.
C. Bordenave, Toulose, France
U. Boscain, CNRS, Sorbonne Univ.
A. Bufetov, MIT
M. Cafasso, Angers, France
*I. Corwin, Columbia University
N. Cuneo, University Paris-Diderot
A. de Bouard, Ecole Polytechnique
A. Debussche, ENS Rennes
A. Dymov, Steklov Insitute, Moscow
J-P. Eckmann, University of Geneva
*L. Erdoes, Wien, Austria
N. Glatt-Holtz, Tulane University
H. Guan, Tsinghua University
V. Jaksitch, McGill University
I. Krasovsky, Imperial College
M. Krishnapur, Bangalore, India
*A. Kupiainen, University of Helsinki
K. Mc Laughlin, Colorado State University
V. Nersesyan, University of Versailles
P. Nikitin, Steklov, St. Petersburg
G. Olshanski, ITP, RAS, Russia
S. Peche, LPSM, Paris, France
Y. Qiu, CNRS, France
A. Ramirez, Pontificia Universidad Catolica de Chile
R. Raquepas, University Grenoble Alpes (Institut Fourier)
T. Sasamoto, Chiba, Japan
M. Shcherbina, Kharkov, Ukraine
A. Shirikyan, Tzvetkov, University of Cergy Pontoise
A. Veselov, Loughbourogh University
*H-T. Yau, Harvard
* to be confirmed
PLEASE NOTE:
Additional funds are available for participants based in the US through the National Science Foundation. Please complete and submit the application at the following link in ADDITION to the regular online request for participation to the activity.
https://www.dropbox.com/s/m0ra2m0j2oomz2s/NSF_application.docx?dl=0
ICTP
ICTP
pio@ictp.it
`
23 Sep 2019
- 27 Sep 2019

» School and Workshop on Random Matrix Theory and Point Processes | (smr 3382)

`
Europe/Rome
2019-09-23 08:00:00
2019-10-04 22:00:00
School on Smooth and Homogeneous Dynamics | (smr 3271)
Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to ga ther top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics.
Special Lectures:
Infosys-ICTS Ramanujan lectures - by Elon Lindenstrauss
ICTS Distinguished lecture - by Marcelo Viana.
List of invited Speakers
Speakers week 1:
Alex Blumenthal, Maryland, USA
Sylvain Crovisier, Paris Sud
Carlangelo Liverani, Rome, Italy
Federico Rodriguez-Hertz, Penn State, USA
Jana Rodriguez-Hertz, Shenzen, China
Marcelo Viana, IMPA
Khadim War, IMPA, Brazil
Zhiyuan Zhang, Princeton
Speakers week 2:
Victor Beresnevich, University of York
S. G. Dani, University of Mumbai
Manfred Einsiedler, ETH Zurich
Alexander Gorodnik, University of Zurich
Seonhee Lim, Seoul National University
Elon Lindenstrauss, Hebrew University of Jerusalem
Jens Marklof, University of Bristol
Shahar Mozes, Hebrew University of Jerusalem
Amos Nevo, Technion, Haifa
Sanju Velani, University of York
Barak Weiss, Tel Aviv University
Minicourse Lecturers
Sylvain Crovisier, Paris Sud, France
Stefano Luzzatto, ICTP
Both weeks will feature research talks by leading mathematicians as well as mini courses. A number of slots will be available in the program for younger participants to present their research and a poster session will also be organized.
A number of slots will be available in the programme for younger participants to present their research and a poster session will also be organized.
The program is jointly organised and supported by ICTS and IMPA.
Program link: https://www.icts.res.in/program/etds2019
General Information: https://www.icts.res.in/program/Information-for-Participants
Bangalore - India
ICTP
pio@ictp.it
`
23 Sep 2019
- 4 Oct 2019

» School on Smooth and Homogeneous Dynamics | (smr 3271)

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Europe/Rome
2019-09-30 08:00:00
2019-10-11 22:00:00
School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)
The main focus is on recent developments in gauge theories, both in theoretical physics and in mathematics. This area is very fruitful for active interplays between Mathematics and Physics.
In theoretical physics exact results in supersymmetric quantum field theories and superstrings on curved backgrounds prompted the interest in explicit calculations of (equivariant) Donaldson invariants also in higher rank and the possible definition of new invariants for four manifolds using non-Lagrangian theories. On the mathematical side, new results have been obtained for higher rank Donaldson invariants and Vafa-Witten invariants. A key role is played by the interplay of with representation theory and quantum integrable systems. These developments are also expected to have impact on enumerative geometry, knot theory and representation theory of infinite dimensional algebras. A key technical tool in these developments is equivariant localization which allows the extraction of exact results.
Topics :
higher rank Donaldson invariants
Vafa-Witten invariants
Donaldson-Thomas invariants
study of the BPS spectra of (non Lagrangean) N=2 Gauge Theories and new four-dimensional invariants
relation to matrix models and topological strings
quantum Hitchin systems and character varieties
gauge theories on complex toric surfaces and their instanton moduli spaces
surface operators in gauge theory and moduli spaces of principal bundles with parabolic structure
quantum cohomology of the instanton moduli space
K-theory of quiver varietes
quantum integrability, quantum Yang-Baxter equations
relations to knot theory and Khovanov Homology
higher dimensional supersymmetric gauge theories and M-theory
Lecturers:
L. GÖTTSCHE, ICTP
G. MOORE, Rudgers (tbc)
H. NAKAJIMA, Kavli IPMU
N. NEKRASOV, Simons Center (tbc)
P. PUTROV, ICTP
Speakers include:
A. DAEMI, Simons Center
A. GOLAMPOUR, University of Maryland
S. GUKOV, Caltech
S. JEONG, Stony Brook
A. KLEMM, Universität Bonn
M. KOOL, Utrecht University
J. MANSCHOT, Trinity College Dublin
A. MELLIT, Universität Wien
D. OPREA, University of California, San Diego
D. PEI, Caltech
Z. RUIDONG, Tokyo University
A. SHESHMANI, Harvard University
Y. TANAKA, Oxford University
K. YOSHIOKA, Kobe Unversity
ICTP
ICTP
pio@ictp.it
`
30 Sep 2019
- 11 Oct 2019

» School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)

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