Scuola tematica "Modern Trends in Pure and Applied Mathematics"

Contribution List

1. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

26/05/2025, 09:00

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

2. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

26/05/2025, 09:55

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

3. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

26/05/2025, 11:15

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

4. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

26/05/2025, 12:10

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

5. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi"

26/05/2025, 14:30

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

6. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi"

26/05/2025, 15:25

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

7. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

27/05/2025, 09:00

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

8. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

27/05/2025, 09:55

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

9. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

27/05/2025, 11:15

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

10. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

27/05/2025, 12:10

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

11. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi"

27/05/2025, 14:30

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

13. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi"

27/05/2025, 15:25

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

14. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

27/05/2025, 16:45

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

15. A. Sorrentino (University of Roma Tor Vergata) - Minicourse "When Mathematicians play... billiards"

28/05/2025, 09:00

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

16. A. Sorrentino (University of Roma Tor Vergata) - Seminar "Dynamical and spectral rigidity of mathematical billiards"

28/05/2025, 09:55

Abstract
Mathematical billiards offer a rich and fascinating playground where geometry, dynamics, and analysis theory meet. In its simplest form, a billiard system consists of a point particle moving freely within a domain, undergoing elastic reflections off the boundary according to the classical law of reflection. Despite the apparent simplicity of the model, the resulting dynamics are...

17. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

28/05/2025, 11:15

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

18. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

28/05/2025, 12:10

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

19. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

29/05/2025, 09:00

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

20. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

29/05/2025, 09:55

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

21. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

29/05/2025, 11:15

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

22. V. Agostiniani (University of Trento) - Minicourse "Rigidity phenomena arising in Riemannian Geometry and in General Relativity"

29/05/2025, 12:10

In geometric analysis, rigidity phenomena occur when specific conditions, typically expressed in terms of partial differential equations, are imposed on a family of mathematical objects, such as functions or tensor fields, leading to the conclusion that solutions can exist only on a distinguished subclass of manifolds, typically characterised by a high number of symmetries.

In this...

23. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi".

29/05/2025, 14:30

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

24. A. Vistoli (Scuola Normale Superiore) - Minicourse "Di quanti parametri abbiamo bisogno per definire un oggetto algebrico? Problemi vecchi e risultati nuovi".

29/05/2025, 15:25

Abstract
La dimensione essenziale, un invariante che si può definire in grande generalità; risponde alla domanda: quanti parametri indipendenti sono necessari per definite un oggetto algebrico in una certa classe? Fu introdotta, nel caso delle estensioni di Galois, nel 1997 da Z. Reichstein e J. Buhler nell'articolo "On the essential dimension of a finite group". Le sue radici sono in...

25. S. Cenatiempo (Gran Sasso Science Institute, L’Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

29/05/2025, 16:45

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

26. V. Agostiniani (University of Trento) - Seminar "Green's functions and positive mass theorems"

30/05/2025, 09:00

Abstract
In this concluding seminar, we will illustrate some geometric and relativistic applications of the study of Green's functions on asymptotically flat 3-manifolds with nonnegative scalar curvature. Time permitting, we will also discuss some more recent results concerning the case of compact 3-manifolds with boundary and strictly positive scalar curvature.

27. A. Vistoli (Scuola Normale Superiore) - Seminar "Sulla dimensione di Cremona di un gruppo finito"

30/05/2025, 09:55

Abstract
La dimensione di Cremona è un invariante di un gruppo finito, che fornisce un limite inferiore per la sua dimensione essenziale. Illustrerò tre dei risultati noti, dovuti a Prokhorov e Shramov, a Haution, e a Bresciani, Reichstein e me stesso.

28. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Minicourse "Large scale limits of the interacting Bose gas"

30/05/2025, 11:15

Abstract
While the theory of quantum mechanics describes interactions between the fundamental constituents of matter at microscopic scales, these interactions can lead to fascinating effects at the macroscopic level. Understanding the emergence of these phases from the microscopic description of quantum systems is a fundamental yet highly challenging mathematical problem. In this course, we...

29. S. Cenatiempo (Gran Sasso Science Institute, L'Aquila) - Seminar "Macroscopic behaviour of dilute Bose gases: the Gross-Pitaevskii equation"

30/05/2025, 12:10

Since the early experiments on Bose-Einstein condensation in cold atomic gases, the Gross-Pitaevskii equation has emerged as a unique tool for describing both the equilibrium and dynamical properties of dilute Bose gases at low temperature. From a mathematical perspective, pioneering works by Lieb, Seiringer and Yngvason (2000) and Erdös, Schlein and Yau (2010) have shown that the...