SEMINARIO DI GEOMETRIA
Lunedì 29 ottobre 2018
ore 15:30
*Scuola Normale Superiore*
Pisa
Aula Mancini
*Mirko Mauri*
*(University College London)*
terrà un seminario dal titolo:
*“**The essential skeletons of pairs and the geometric P=W conjecture**”*
*Abstract:*
The geometric P=W conjecture is a conjectural description of the asymptotic
behavior of the celebrated Nonabelian Hodge correspondence. In particular,
it is expected that the dual boundary complex of the compactification of
character varieties has the homotopy type of a sphere. In a joint work with
Enrica Mazzon and Matthew Stevenson, we compute the first non-trivial
examples of these dual boundary complexes in the compact case. This
requires to develop a new theory of essential skeletons over a
trivially-valued field. As a byproduct, inspired by these constructions, we
show that certain character varieties appear in degenerations of compact
hyper-Kähler manifolds. In this talk I will explain how these new
non-archimedean techniques can shed new light into classical algebraic
geometry problems.
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani(a)sns.it
E-mail: classi(a)sns.it
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SEMINARIO DI GEOMETRIA
Lunedì 29 ottobre 2018
ore 14:30
*Scuola Normale Superiore*
Pisa
Aula Mancini
*Enrica Mazzon*
*(Imperial College)*
terrà un seminario dal titolo:
*“**Berkovich approach to degenerations of hyper-Kähler varieties**”*
*Abstract:*
To a degeneration of varieties, we can associate the dual intersection
complex, a topological space that encodes the combinatoric of the central
fiber and reflects the geometry of the generic fiber. In this talk I will
show how the techniques of Berkovich geometry give an insight in the study
of the dual complexes. In this way, we are able to determine the
homeomorphism type of the dual complex of some degenerations of
hyper-Kähler varieties. The results are in accordance with the predictions
of mirror symmetry, and the recent work about the rational homology of dual
complexes of degenerations of hyper-Kähler varieties, due to Kollár, Laza,
Saccà and Voisin. This is joint work with Morgan Brown.
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani(a)sns.it
E-mail: classi(a)sns.it
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*Colloqui della Classe di Scienze*
Anno Accademico 2017/2018
Mercoledì 24 ottobre 2018
ore 15:00
*Scuola Normale Superiore*
Pisa
(Sala Stemmi)
*Hermann Nicolai*
(Max Planck Institute for Gravitational Physics)
Terrà un seminario dal titolo:
*“Symmetry and Unification -- can Physics be reduced to a single formula?*
*”*
*Abstract:*
"Attempts to `unify' all of known physics have a long history. Since the
mid-seventies, these attempts have been considerably re-invigorated with
ongoing efforts to reconcile Einstein's theory of General Relativity and
Quantum Mechanics into a unified theory of quantum gravity. In this talk I
will review the motivation as well as some more recent developments at an
introductory level and discuss prospects for the future."
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani(a)sns.it
E-mail: classi(a)sns.it
<Colloquio della Classe di Scienze 3.docx>
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SEMINARI DI MATEMATICA
Giovedì 18 ottobre 2018
*Scuola Normale Superiore*
Pisa
Sala Conferenze, Collegio Puteano
si terranno i seguenti seminari:
14:30 *Paolo Buttà* ( Università di Roma "La Sapienza"),
*“On the large deviations of interface motions in statistical mechanics
models”*
*Abstract:*
*In this talk, I consider the sharp interface limit of the action
functional associated to either the Glauber dynamics for Ising systems with
Kac potentials or the Glauber+Kawasaki process. The corresponding limit
functionals provide, in the sense of large deviations theory, the
probability of deviations from the mean curvature flow. I discuss, in the
case of smooth interfaces, the derivation of these functionals, for which
explicit formulae of the mobility and transport coefficients are given.
This is joint work with L. Bertini and A. Pisante.*
15:20 *Michela Ottobre* (Heriot-Watt University, Edimburgh),
*“Beyond the Hoermander condition”*
*Abstract:*
*The study of diffusion processes of elliptic and hypoelliptic type has by
now produced a fully-fledged theory, involving several branches of
mathematics: stochastic analysis, analysis of differential operators,
(sub-)Riemannian geometry and control theory, just to mention the main
players. One of the key steps in the development of such a theory has been
the seminal paper of Hoermander and a large body of work has been dedicated
for over 40 years to the study of diffusion processes under the Hoermander
Condition (HC), which is a sufficient condition for hypoellipticity. We
propose to study processes that do not, in general, satisfy the HC. In
place of the HC, we wish to enforce a weaker condition, the so-called UFG
condition, introduced by Kusuoka and Strook with probabilistic motivations,
and, independently, by Sussman, Hermann and Lobry, this time in the field
of control theory. In particular, Kusuoka and Strook showed that it is
still possible to build a solid PDE theory for diffusion semigroups even in
absence of the Hoermander condition. We will present new results on the
geometry and long time behaviour of diffusion semigroups that do not
satisfy the Hoermander condition. Our interest in UFG diffusions stems from
the observation that they constitute a large class of SDEs which exhibit
multiple invariant measures and such that it is possible to determine in a
systematic way the basin of attraction of each equilibrium state. This is
a joint work with P. Dobson (Maxwell Institute), T. Cass and D. Crisan
(Imperial College).*
16:10 *Boguslaw Zegarlinski* (Imperial College London),
*“Hypoelliptic diffusion in noncommutative setup”*
*Abstract:*
*I will review results and problems concerning hypoelliptic diffusion and
coercive (Poincare and Log-Sobolev) inequalities.*
Tutti gli interessati sono invitati a partecipare.
Classe di Scienze
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani(a)sns.it
E-mail: classi(a)sns.it
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