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.

5 Jul 2018

New SISSA-ICTP institute unites physics and geometry for innovation

1 Jun 2018

James Yorke, father of chaos, on the usefulness of defining disorder

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Europe/Rome
2018-11-19 16:00:00
2018-11-19 17:00:00
D-brane masses and the motivic Hodge conjecture
Abstract:
We consider one complex structure parameter mirror families W of Calabi-Yau 3-folds with Picard-Fuchs equations of hypergeometric type. By mirror symmetry the even D-brane masses of the orginal Calabi-Yau M can be identified with four periods w.r.t. to an inte- gral symplectic basis of H3(W, Z) at the point of maximal unipotent monodromy. It was discovered by Chad Schoen in 1986 that the sin- gular fibre of the quintic at the conifold point gives rise to a Hecke eigen form of weight four f4 on Γ0(25) whose Fourier coefficients ap are determined by counting solutions in that fibre over the finite field Fpk . The D-brane masses at the conifold are given by the transition matrix Tmc between the integral symplectic basis and a Frobenius basis at the conifold. We predict and verify to very high precision that the entries of Tmc relevant for the D2 and D4 brane masses are given by the two periods (or L-values) of f4. These values also deter- mine the behaviour of the Weil-Petersson metric and its curvature at the conifold. Moreover we describe a notion of quasi periods and find that the two quasi period of f4 appear in Tmc. We extend the analy- sis to the other hypergeometric one parameter 3-folds and comment on simpler applications to local Calabi-Yau 3-folds.
ICTP
pio@ictp.it
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19 Nov 2018

» D-brane masses and the motivic Hodge conjecture

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Europe/Rome
2018-11-21 14:30:00
2018-11-21 15:30:00
On noncommutative cubic surfaces and their moduli
Abstract: This is based on joint work with Shinnosuke Okawa and Kazushi Ueda. The zero loci of a cubic equations in three dimensional projective space are pretty cool! As varieties, they may be deformed in four directions. However, they may also be deformed as "noncommutative" spaces in an extra four dimensions. Here we realise these noncommutative deformations as certain quiver algebras. We then go on to study their moduli and compare them to existing theories of noncommutative cubic surfaces. Time permitting we will discuss generalisations of these ideas to other del Pezzo surfaces.
ICTP
ICTP
pio@ictp.it
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21 Nov 2018

» On noncommutative cubic surfaces and their moduli

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Europe/Rome
2018-11-22 14:30:00
2018-11-22 15:30:00
New complex analytic methods in the theory of minimal surfaces
Abstract:
In this talk, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained as applications of both classical and modern complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces, including the Calabi-Yau problem, constructions of properly immersed and embedded minimal surfaces in R^n and in minimally convex domains of R^n, results on the complex Gauss map, and isotopies of conformal minimal immersions.
ICTP
ICTP
pio@ictp.it
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22 Nov 2018

» New complex analytic methods in the theory of minimal surfaces

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Europe/Rome
2018-11-26 11:00:00
2018-11-26 12:00:00
Endomorphism rings of Jacobians
Abstract:
Over the last two centuries mathematicians have developed a very rich theory of abelian varieties; however, certain kinds of explicit calculations have remained out of reach of our computational power until quite recently, when theoretical and technological advances have led to a renewed interest in the computational side of the theory. In this talk I will discuss one of the fundamental algorithmic problems one would like to solve, namely that of determining the endomorphism ring of the Jacobian of an explicitly given curve over a number field. I will describe a method to compute the endomorphism ring of such a Jacobian, starting with the case of genus-2 curves, and show the connection between this problem and a certain local-global principle for the center of the endomorphism algebra. If time permits, I will also outline how to prove the necessary local-global principle for abelian surfaces and, under the assumption of the Mumford-Tate conjecture, for all abelian varieties.
ICTP
ICTP
pio@ictp.it
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26 Nov 2018

» Endomorphism rings of Jacobians

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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)
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)
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
2019 EAUMP School on Algebraic Topology and its Applications | (smr 3310)
Kampala - Uganda
ICTP
pio@ictp.it
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15 Jul 2019
- 2 Aug 2019

» 2019 EAUMP 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)
ICTP
ICTP
pio@ictp.it
`
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