### General

### Program Description

The GSSI offers 31 PhD fellowships and invites applications for fellowships for the PhD Programmes in Astroparticle Physics, Mathematics in Natural, Social and Life Sciences, Computer Science, Urban Studies and Regional Science.

The official language for all PhD courses is English.

The fellowships are awarded for 4 years and their yearly amount is € 16.159,91 gross. All PhD students have free accommodation at the GSSI facilities and use of the canteen.

The application must be submitted through the online form available at www.gssi.it/phd/ by 18 June 2019 at 6 pm (Italian time zone, 6pm).

The Gran Sasso Science Institute (GSSI) is an international PhD school and a center for research and higher education in the areas of Physics, Mathematics, Computer Science and Social Sciences. Founded in 2012 in L’Aquila (Italy) as Center for Advanced Studies of the National Institute for Nuclear Physics (INFN) and then established in March 2016 as a School of Advanced Studies providing post-graduate education. Through a day-to-day collaboration and interaction, researchers and students have the opportunity to build a sound knowledge of the research methods and to experiment contamination of interests, innovative approaches and multicultural exchanges in all the GSSI activities. In addressing the complexity of today’s world, we are committed to removing all barriers between the GSSI areas of study and research, where interdisciplinarity and cross-fertilization underlie everything we do. Among our goals are the dissemination of scientific results towards society and the promotion of cultural events for generic public, citizens and schools.

For more information, please consult the Call for Applications at www.gssi.it/phd/ or write an email to info@gssi.it or call +39 0862 4280262.

The PhD curriculum in Mathematics of Natural, Social and Life Sciences at Gran Sasso Science Institute will lead the students to deal not only with the more traditional aspects of this discipline, such as Pure Mathematics, Partial Differential Equations and Mathematical Physics, but also with entirely new problems, requiring the development of the most appropriate tools to deal with the complexity, such as stochastic analysis and computational mathematics.

The curriculum consists of 4 years of study and research. During the first year, after initial training classes, students will be offered three main courses and a wide number of short courses, covering a large spectrum of topics. By the beginning of the second year students select a research project under the supervision of one (or more) of the mathematicians affiliated to GSSI.

**Governing Board**

**Paolo Antonelli** (GSSI), **Piermarco Cannarsa** (Università Roma TorVergata), **Gianluca Crippa** (Universität Basel), **Camillo De Lellis** (Universität Zürich), **Nicola Guglielmi** (GSSI - Università L'Aquila), **Pierangelo Marcati** (Chair, GSSI), **Errico Presutti** (GSSI), **Gigliola Staffilani** (MIT), **Angelo Vulpiani** (Sapienza Università di Roma)

**Past Committee (2013-2016)**

**Paolo Antonelli** (GSSI), **Stefano Bianchini** (SISSA), **Gianni Dal Maso** (SISSA), **Camillo De Lellis** (Universität Zürich), **Antonio De Simone** (SISSA), **Pierangelo Marcati** (Chair, University of L'Aquila and GSSI), **Errico Presutti** (GSSI), **Gigliola Staffilani** (MIT)

**The Gran Sasso Science Institute offers 34 Ph.D. fellowships in Physics, Mathematics, Computer Science and Social Sciences.**

http://www.gssi.it/phd/

The Gran Sasso Science Institute (GSSI), founded in 2012 in L’Aquila (Italy) as Center for Advanced Studies of the National Institute for Nuclear Physics (INFN) and then established in March 2016 as a School of Advanced Studies providing post-graduate education, offers 34 Ph.D. positions for the academic year 2018/19.

The GSSI (www.gssi.it) invites applications for 10 fellowships in “Astroparticle Physics”, 8 in “Mathematics in Natural, Social and Life Sciences”, 8 in “Computer Science” and 8 in “Urban Studies and Regional Science”. The official language for all Ph.D. courses is English.

The fellowships are awarded for 4 years and their yearly amount is € 16.159,91 gross. All Ph.D. students have free accommodation at the GSSI facilities and use of the canteen.

The application must be submitted through the online form available at www.gssi.it/phd/ by June 20, 2018, at 18.00 (Italian time zone).

For more information, please consult the Call for Applications at www.gssi.it/phd/ or write an email to info@gssi.it

**Courses Mathematics**

**A.A. 2017-2018**

ANALYSIS AND PDEs

- P. Marcati (GSSI and University of L’Aquila) - Mathematical problems in Fluid dynamics
- P. Antonelli (GSSI) - Introduction to harmonic analysis and dispersive equations
- A. Muntean (Carlstadt University) - Reaction-diffusion systems with distributed microstructures
- G. Crippa (Basel University) - Exponential Mixing and Loss of Regularity for Incompressible Flows
- L. Forcella (EPFL Lausanne) - Nonlinear Schrödinger Equations

STATISTICAL MECHANICS AND DYNAMICAL SYSTEMS

- E. Presutti (GSSI) - Probability and Statistical Mechanics (Presutti)
- A. Vulpiani (Sapienza University of Rome) - Chaos, transport, and reaction-diffusion
- T. Funaki (University of Tokio) – Probability and Statistical Mechanics
- C. Marchioro (Sapienza, University of Rome) – Topic in fluid mechanics
- S. Poghosyan (National Academy of Sciences of Armenia) – Cluster expansion in statistical mechanics
- M. Pulvirenti (Sapienza, University of Rome) - Some mathematical aspects of the Boltzmann equation

NUMERICAL METHODS

- N. Guglielmi (L’Aquila U.), V. Protasov (L’Aquila U. & Moscow St.U.) - Advanced Topics on Numerical Methods
- D. Boffi (Pavia University) TBA
- M. Lopez Fernandez (Sapienza University of Rome) - Contour integral methods for evolutionary PDEsContour integral methods for evolutionary PDEs
- C. Lubich (Universität Tübingen) – Dynamical low-rank approximation
- G. Russo (Catania University) - Numerical methods for hyperbolic problems

CONTINUUM MECHANICS

- R. Verzicco (Rome 2) - Introduction to Continuum Mechanics

MATHEMATICAL PROBLEMS IN QUANTUM MECHANICS

- A.Teta (Sapienza, University of Rome) - Introduction to quantum mechanics and scattering theory
- S. Cenatiempo (GSSI) - Introduction to quantum many-body problems
- M. Griesemer (University of Stuttgart) - Quantum electrodynamics for atoms and molecules

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A.A. 2016-2017

ANALYSIS AND PDEs

- P. Antonelli (GSSI) - Dispersive equations
- T.-Y. Wang (GSSI) - Mathematical Theory of Compressible Euler Equations
- P. Marcati (GSSI) - Introduction to the Incompressible Navier Stokes equation and the mathematical theory of Turbulence
- S. Kawashima (Kyush Univ.) - Hyperbolic Systems
- S. Spirito (University of L’Aquila) - Tutorial on Convex Integration
- S. Daneri (Erlangen) - Dissipative Hölder solutions to the incompressible Euler equations
- A. Muntean (Carlstadt Univ.) - Reaction-diffusion systems with distributed microstructures
- Antonietti (PoliMI) - Discontinuous Galerkin
- A. Vulpiani (Sapienza Univ. Roma) - Anomalous Diffusions

STATISTICAL MECHANICS

- R. Fernadez (Utrecht) - Introduction to equilibrium mathematical statistical mechanics
- E. Presutti (GSSI) - Mass transport and applications to Markov chains and Gibbs processes
- Pulvirenti (Sapienza Univ. Roma) - Scaling Limits and Effective Equations in Kinetic Theory
- Galves (São Paulo - Brasil) - Markov chains with infinite memory

NUMERICAL METHODS

- N. Guglielmi (L’Aquila Univ.) – V. Protasov (L’Aquila Univ. & Moscow St.U.) - Advanced Topics on Numerical Methods
- D. Boffi (Pavia Univ.) - Introduction to Finite Element

CONTINUUM MECHANICS

- R. Verzicco (Rome 2) - Introduction to Continuum Mechanics

MATHEMATICAL PROBLEMS IN QUANTUM MECHANICS

- A. Teta (Sapienza Univ. Roma) - Introduction to quantum mechanics
- S. Cenatiempo (GSSI) - Introduction to Quantum many body problems
- B. Schlein (Zürich Univ.) - Quantum many body problems
- M. Correggi (Sapienza Univ. Roma) - Vortices in Bose-Einstein condensates

*Last updated July 2019*

### About the School

The Gran Sasso Science Institute (GSSI) is an international PhD school and a center for research and higher education.