I - 34151 Trieste Italy

*(+39) 040 2240 111*

*pio@ictp.it*

- Conferences, workshops and schools
- Junior Associates
- Regular Associates
- Senior Associates
- Federated Institutes
- The Kuwait Programme at ICTP
- APS-EPS-ICTP Travel Award Fellowship Programme (ATAP)
- CIMPA-ICTP Research in Pairs for mathematicians in developing countries
- Researchers Mobility for Sustainable Development

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.

12 May 2022

ICTP celebrates International Year of Basic Sciences for Sustainable Development

23 Mar 2022

Don Zagier named the first holder of ICTP's Ramanujan International Chair

`
Europe/Rome
2022-12-05 14:00:00
2022-12-08 16:00:00
CIMPA/ICTP Course on "Introduction to Optimization and Operator Theory"
This is a recurring meeting, therefore please register just once for all 4 sessions:
https://zoom.us/meeting/register/tJUodOihqDMvE9fOe6s-MziaNCKeZeoaVSDt
Venue (for in-person attendees):
Luigi Stasi Seminar Room
Timetable:
Monday 5 December: 14:00 - 16:00
Tuesday 6 December: 14:00 - 16:00
Wednesday 7 December: 14:00 - 16:00
Thursday 8 December: 14:00 - 16:00
Abstract:
An introductory lecture on operator and optimization theory will be given. To be specific, various notions of derivatives for mappings between Normed spaces will be discussed, with a special emphasis on mappings taking values in <span lang="EN-GB" style="font-size:12.0pt;font-family:Times;mso-fareast-font-family:
Times;mso-bidi-font-family:Times;mso-ansi-language:EN-GB;mso-fareast-language:
IT;mso-bidi-language:AR-SA">R
connecting derivatives with optimization problems. We discuss the continuity, lower semicontinuity, differentiability, and, most importantly, optimization properties of convex functions in normed spaces. We will also go over the Fenchel conjugate and biconjugate for convex functions, as well as their properties. With these tools at our disposal, we move on to the duality methods in optimization, which allows us to solve unconstrained and constrained minimization problems (called the primal) by relating them to their dual problems obtained via the Fenchel conjugate. Finally, after discussing the Moreau proximity operator in Hilbert spaces, we will look at a popular class of optimization algorithms.
References:
[1] Kravvaritis, D. C., & Yannacopoulos, A. N. (2020). Variational methods in nonlinear analysis: with applications in optimization and partial differential equations. Walter De Gruyter Gmbh & Co Kg.
[2] Bauschke, H. H., & Combettes, P. L. (2011). Convex analysis and monotone operator theory in Hilbert spaces (Vol. 408). New York: Springer.
Hybrid
ICTP
pio@ictp.it
`
5 Dec 2022
- 8 Dec 2022

» CIMPA/ICTP Course on "Introduction to Optimization and Operator Theory"

`
Europe/Rome
2022-12-09 16:00:00
2022-12-09 17:30:00
Basic Notions Seminar - What is a moduli space?
Venue: for in-person attendees (Leonardo da Vinci, Luigi Stasi Seminar Room).
For virtual attendees:
https://zoom.us/meeting/register/tJ0od-ihrTIjH9F3K0rVN45vAwYwC2diqLtL
After registering, you will receive a confirmation email containing information about joining the meeting.
Abstract: There is a beautiful connection between the prime numbers and the zeros of Riemann zeta-function in the complex plane, and understanding the distribution of these zeros can lead to remarkable consequences in our understanding of the primes. A famous open problem, known as the Riemann Hypothesis, states that the non-real zeros of the Riemann zeta-function lie on a vertical line. I will motivate this conjecture, describe some evidence for it, and describe some of the consequences it would lead to in our understanding of the primes. In particular, I will describe how to bound on the maximum gap between prime numbers assuming the Riemann Hypothesis (which is based on joint work with Carneiro and Soundararajan).
hybrid
ICTP
pio@ictp.it
`
9 Dec 2022

» Basic Notions Seminar - What is a moduli space?

`
Europe/Rome
2022-12-09 16:00:00
2022-12-09 17:00:00
BASIC NOTIONS SEMINAR: What is a moduli space?
Register in advance for this meeting:
https://zoom.us/meeting/register/tJ0od-ihrTIjH9F3K0rVN45vAwYwC2diqLtL
After registering, you will receive a confirmation email containing information about joining the meeting.
Abstract: Given a certain set of mathematical objects, a guiding question is often the classification problem. In algebraic geometry, the objects that you would like to classify have usually some geometry interests, like for instance manifolds, vector bundles, algebraic curves. The attempt to reach a meaningful classification often leads to the construction of a moduli space: a parameter space whose points correspond to all the objects you would like to study. In the talk, I will give a very gentle introduction to the notion of parameter space focusing on elementary examples. If time permits, at the end I will give some hints towards more complicated but also more interesting examples.
hybrid seminar
ICTP
pio@ictp.it
`
9 Dec 2022

» BASIC NOTIONS SEMINAR: What is a moduli space?

`
Europe/Rome
2023-02-27 07:00:00
2023-03-03 21:00:00
Learning Workshop on BPS States and 3-Manifolds | (smr 3818)
The main scientific theme of the workshop is counting BPS states in physical systems associated to 3-manifolds or links, and interpretation of these counts as old or new topological invariants.
Although the ideas behind such relations appeared already in the late 90s, the recent years have seen some dramatic new developments. The goal of this learning workshop is to bring together physicists and mathematicians who are experts in the subject and also those who would like to enter the field. In particular, the talks will be given both by senior scientists and junior ones, including PhD students who only recently began working on the subject. The talks will be supplemented by dedicated discussion sessions where experts can answer questions that will be submitted by participants to the moderator in advance, or asked directly during the session.
Topics:
"Z-hat" and F_K invariants counting BPS states in 6d superconformal field theory compactified on 3- manifolds, and their relation to known invariants of 3-manifolds and links
Knots-quivers correspondence and its generalization to knot complements
Properties of generating functions counting BPS states, including: modularity, relation to characters of (logarithmic) Vertex Operator Algebras, GW/DT invariants
Speakers:
R. AKHMECHET, Columbia University
*M. CHENG, University of Amsterdam
H-J. CHUNG, Jeju National University
F. COSTANTINO, Toulouse University
T. EKHOLM, Uppsala University
B. HAGHIGHAT, Tsinghua University
S. HARICHURN, Bonn University
J. JANKOWSKI, Wrocław University
P. JOHNSON, Michigan State University
S. KRUSHKAL, University of Virginia
H. LARRAGUIVEL, Jagiellonian University
P. LONGHI, Uppsala University
D. NOSHCHENKO, University of Amsterdam
S. PARK, University of Texas at Austin
D. PASSARO, University of Amsterdam
*D. PEI, University of Southern Denmark
P. RAMADEVI, Indian Institute of Technology, Mumbai
S.J. RI, ICTP
M. STOSIC, Instituto Superior Técnico
P. SULKOWSKI, Warsaw University
J. SVOBODA, University of Miami
*C. VAFA, Harvard University
* to be confirmed
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
`
27 Feb 2023
- 3 Mar 2023

» Learning Workshop on BPS States and 3-Manifolds | (smr 3818)

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. 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