17/11/17  Seminario  14:30  15:30  1101 D'Antoni  Michael Ehrig  University of Sydney  TBA
TBA 
24/10/17  Seminario  14:30  15:30  1201 Dal Passo  Daniele Castorina  John Cabot University (Roma)  Ancient solutions of superlinear heat equations on Riemannian manifolds.
We study the qualitative properties of ancient solutions of superlinear heat equations in a Riemannian manifold, with particular attention to positivity and triviality in space. This is joint work with Carlo Mantegazza (Napoli ''Federico II'')

17/10/17  Seminario  14:30  15:30  1201 Dal Passo  Carlo Nitsch  Universita' di Napoli  Problemi di ottimizzazione in isolamento termico
In questo seminario affrontiamo il problema di isolare
termicamente un corpo conduttore di calore dall'ambiente circostante,
avendo a disposizione una certa quantità di isolante da distribuire sulla
sua superficie. La definizione di "isolamento ottimo" dipenderà dalla
presenza o meno di una sorgente di calore e darà luogo a due formulazioni
distinte. Dimostreremo che la maniera migliore di disporre l'isolante
sulla superficie del conduttore non è sempre ovvia e a volte addirittura
controintuitiva. Anche nel caso più semplice, in cui il conduttore sia una
palla, e ci troviamo in assenza di sorgente di calore, distribuire
l'isolante uniformemente sulla superficie sferica non é sempre la cosa
migliore da fare. 
10/10/17  Seminario  14:30  15:30  1201 Dal Passo  Roberto Peirone  Universita' di Roma "Tor Vergata"  Existence of selfsimilar energies on finitely ramified fractals
An important problem in analysis on fractals is the construction of a selfsimilar energy on the fractal. An old conjecture is whether on a specific important class of finitely ramified selfsimilar fractals there exists a selfsimilar energy.
In this talk, it is shown a recent example where we have no selfsimilar energy. On the other hand, a selfsimilar energy always exists if the
selfsimilarity is considered with respect to a suitable set of maps that define the fractal. 
10/10/17  Seminario  13:00  14:00  1201 Dal Passo  Israel Vainsencher  Universidade Federal de Minas Gerais  Counting singular surfaces
How many surfaces of a given degree present singularities of some specified type and pass through an appropriate number of points?
We focus on counting singular surfaces with certain non isolated singularities: e.g., Whitney's umbrella, quartics singular along atwisted cubic, etc. We give a proof for the polynomial nature of the formulae and make it explicit in a few cases. Conjecturally the degree of the formula is twice the dimension of the family of curves imposed in the singular locus. We manage to bound it by thrice that dimension. We draw essentially from previous joint work with Angelo Lopez and Fernando Cukierman. 
03/10/17  Seminario  16:00  17:00  1101 D'Antoni  Peter Heinzner  RuhrUniversitaet Bochum  KAEHLERIAN REDUCTION
In this talk we will consider Hamiltonian actions of groups of holomorphic Kaehler
isometries on Kaehlerian manifolds. In the rare cases where the orbit spaces are
smooth it is well known that the corresponding quotient spaces in the sense of Marsen
Weinstein are Kaehler manifolds as well.
We will show that in the general case the quotient has a natural structure of a
Kaehler space. The main tool in the proof is the construction of invariant Kaehler
potentials for not necessarily compact group actions.

26/09/17  Seminario  15:00  16:00  1101 D'Antoni  Lara BOSSINGER  University of Cologne  Toric degenerations of Grassmannians: birational sequences and the tropical variety
As toric varieties are well understood due to their rich combinatorial structure, a toric degeneration allows to deduce properties of the original variety. For Grassmannians, such degenerations can be obtained from birational sequences and the tropical Grassmannian.
The first were recently introduced by Fang, Fourier, and Littelmann. They originate from the representation theory of Lie algebras and algebraic groups. In our case, we use a sequence of positive roots for the Lie algebra sl_{n} to define a valuation on the homogeneous coordinate ring of the Grassmannian. Nice properties of this valuation allow us to define a filtration whose associated graded algebra (if finitely generated) is the homogeneous coordinate ring of the toric variety.
The second was defined by Speyer and Sturmfels and is an example of a tropical variety: a discrete object (a fan) associated to the original variety that shares some of its properties and in nice cases, as the one of Grassmannians, provides toric degenerations. In this talk, I will briefly explain the two approaches and establish a connection between them.

20/09/17  Seminario  16:00  17:00  1201 Dal Passo  Michael Magee  Durham University  Word measures on unitary groups
I'll talk about joint work with Doron Puder (Tel Aviv University).Fix a positive integer r, and fix a word w in the freegroup on r generators.Let G be any group. One obtains a 'word map' from the product of r copies of G to G by substituting in elements of G for occurrences of generators in w. We also call this map w.The pushforward of Haar measure under w is called the wmeasure on G. We are interested in the case G = U(n), the compact Lie
group of n dimensional unitary matrices. A motivating question of our work is to what extent the wmeasures on U(n) determine algebraic properties of the word w. We proved in our first paper that one can detect the 'stable commutator length' of w from these measures. One of our main tools is a formula for Fourier coefficients of
wmeasures, which happen for deep reasons to be rational functions of the dimension parameter n. We can now explain all the Laurent coefficients of these rational functions in topological terms. I'll explain all this in my talk, which should be broadly accessible and of general interest. I'll also outline some remaining open questions and explain what we know so far about them.

26/07/17  Seminario  16:00  17:00  1201 Dal Passo  Marco Oppio  Universita' di Trento  Quantum theory in real or quaternionic Hilbert space: How the
complex Hilbert space structure emerges from Poincare'
Joint work with: Valter Moretti
In principle, the lattice of elementary propositions of a generic quantum system admits a representation in real, complex or quaternionic Hilbert spaces as established by Soler's theorem (1995) closing a long standing problem that can be traced back to von Neumann's mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in Hilbert spaces whose scalar field is different from the set of complex numbers. We show that elementary relativistic systems (in Wigner's approach) cannot be described in real/quaternionic Hilbert spaces as a consequence of some peculiarity of continuous unitary projective representations of SL(2,C) related with the theory of polar decomposition of operators. Indeed such a "naive" attempt leads necessarily to an equivalent formulation on a complex Hilbert space. Although this conclusion seems to give a definitive answer to the real/quaternionicquantummechanics issue, it lacks consistency since it does not derive from more general physical hypotheses as the complex one does. Trying a more solid approach, in both situations we end up with three possibilities: an equivalent description in terms of a Wigner unitary representation in a real, complex or quaternionic Hilbert space. At this point the "naive" result turns out to be a definitely important technical lemma, for it forbids the two extreme possibilities. In conclusion, the real/quaternionic theory is actually complex. This improved approach is based upon the concept of von Neumann algebra of observables. Unfortunately, while there exists a thorough literature about these algebras on real and complex Hilbert spaces, an analysis on the notion of von Neumann algebra over a quaternionic Hilbert space is completely absent to our knowledge. There are several issues in trying to define such a mathematical object, first of all the inability to construct linear combination of operators with quaternionic coeff 
19/07/17  Seminario  14:00  15:00  1201 Dal Passo  Francesco Polizzi  Universita' della Calabria  A pair of rigid surfaces with p_g=q=2 and K^2=8 whose universal
cover is not the bidisk.
We construct two complexconjugated rigid surfaces with p_g=q=2 and K^2=8, whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces with these invariants and Albanese map of degree 2, apart a family of productquotient surfaces constructed by Penegini. This is a joint work with C. Rito and X. Roulleau. 