Let k be a knot (i.e. an embedding of S^1into S^3). Once S^3is seen as the boundary of D^4, one can ask which kind of (properly) embedded surfaces in D^4have k as boundary. Finding the minimal genus of such a surfaces (called slice genus) is a…
Eventi
Large deviations for the Allen-Cahn approximation of the mean curvature flow – Adriano Pisante (Universita’ di Roma La Sapienza)
We consider the sharp interface limit for the Allen-Cahn equation on the three dimensional torus with deterministic initial condition and deterministic or stochastic forcing terms. In the deterministic case, we discuss the convergence of solutions…
Flussi geometrici su varietà con bordo – Giovanni Mascellani (Scuola Normale Superiore)
I flussi geometrici sono oggetti geometrici che, a partire dalla loro introduzione da parte di Hamilton nel 1981, si sono rivelati strumenti molto potenti per risolvere problemi di analisi geometrica (particolarmente nota è la dimostrazione della…
Non-stationary substitutive dynamics and Pisot cocyles – Milton Minervino (Aix-Marseille Université)
We work with shift spaces defined by infinite sequences of simple combinatorial rules called substitutions. To such a system we associate a renormalization cocycle, intimately related with a multidimensional continued fraction algorithm. Under…
Continuous family of conserved energies for NLS, KdV and mKdV – Herbert Koch (Bonn)
InthistalkbasedonjointworkwithKienzlerandVazquezIwill explainhowCaffarelli’sstrategyofprovingregularityforfree boundaryproblemscanbeimplementedfortheporousmediumequation. ElementsoftheproofisaglobalexistenceresultforLipschitz…
Coarse algebraic topology – Luigi Caputi (University of Regensburg)
Coarse geometry was born from the informal idea of studying the large scale structure of metric spaces. As the abstraction of continuous functions between them led to the concept of open sets and topological spaces, the study of the large scale…
Knots, Galois groups and Massey products – Claudio Quadrelli (Università di Firenze)
Cohomological Massey products were defined in the ’50s as higher cohomology operations generalizing the cup product, to provide a “cohomological translation” of the Milnor invariants, which describe the higher linking properties of the knots in a…
Nonlocal phase transitions and minimal surfaces – Enrico Valdinoci
We present some recent results on a nonlocal version of the Allen-Cahn equation, which is also related, at a large scale, to surfaces which minimise a nonlocal perimeter functional. We discuss some features, such as symmetry property, regularity and…
Gruppi Kac-Moody, minori generalizzati e rappresentazioni di quiver – Salvatore Stella (Sapienza Università di Roma)
La teoria delle rappresentazioni dei gruppi Kac-Moody e quella dei quiver aciclici presentano entrambe, nel caso generale, una struttura tripartita. Le rappresentazioni di un gruppo Kac-Moody G sono divise naturalmente in tre classi (peso più alto,…
How to “synthesize” sub-fixed point sets into the global one just by looking inside groups? – Masato Mimura (Tohoku university e EPF Lausanne)
Consider a group G action on a metric space X by isometries, andsubgroups M_1,…, M_l. One interesting and important problem isto studyconditions underwhichnon-emptyness of each M_i-fixed points ensures thatof global (G-)fixed points. One extreme…