Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
14/01/25	Seminario	14:30	16:00	1101 D'Antoni	Francesco Tropeano	Università di Roma Tre	Geometry Seminar Relative monodromy of ramified sections on abelian schemes Abstract Let us consider a complex abelian scheme endowed with a section. On some suitable open subsets of the base it is possible to define the period map, i.e. a holomorphic map which marks a basis of the period lattice for each fiber. Since the abelian exponential map of the associated Lie algebra bundle is locally invertible, one can define a notion of abelian logarithm attached to the section. In general, the period map and the abelian logarithm cannot be globally defined on the base, in fact after analytic continuation they turn out to be multivalued functions: the obstruction to the global existence of such functions is measured by some monodromy groups. In the case when the abelian scheme has no fixed part and has maximal variation in moduli, we show that the relative monodromy group of ramified sections is non-trivial and, under some additional hypotheses, it is of full rank. As a consequence we deduce a new proof of Manin's kernel theorem and of the algebraic independence of the coordinates of abelian logarithms with respect to the coordinates of periods. (Joint work with Paolo Dolce, Westlake University.) Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027), Prin 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
08/01/25	Seminario	16:00	17:00	1201 Dal Passo	Jacopo Bassi	IM PAN, Warsaw, PL	Operator Algebras Seminar Applications of measurable dynamics to analytic group theory Abstract Biexactness and the (AO)-property can be considered as analytic counterparts of hyperbolicity for discrete groups. Motivated by the problem of determining whether they are equivalent, I will discuss an approach to the study of regularity properties of boundary actions/representations based on measurable dynamics. This approach will be used to study SL(3,Z) and to answer a question posed by C. Anantharaman-Delaroche. Some bibliography: https://arxiv.org/abs/2111.13885 https://arxiv.org/abs/2305.16277 https://arxiv.org/abs/2410.01447
01/01/25	Seminario	08:00	09:00	1016 Master	speaker	Affil	titolo Abstract abstract
19/12/24	Seminario	14:30	15:30	1101 D'Antoni	Marco Castronovo	U Columbia	Topology Seminar Decoupling Fukaya categories Abstract A basic problem in symplectic topology is the classification of Lagrangian submanifolds up to Hamiltonian isotopy. There is growing evidence that this is impossible to solve, but one can hope to have a coarser classification by proving that finitely many Lagrangians generate the Fukaya category. I will illustrate some concrete examples where we know how to do this, some in which we do not, and a new technique called decoupling that could partially bridge the gap.
18/12/24	Seminario	16:00	17:00	1201 Dal Passo	Kasia Rejzner	University of York	Operator Algebras Seminar Quantum reference frames and operator algebras Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) Abstract In this talk I will present the recent paper by Fewster, Janssen, Loveridge, Waldron and myself: "Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory." In this work we show how mathematically rigorous notion of quantum reference frames allows to generalize the results of Chandrasekaran, Longo, Penington and Witten on observables in de Sitter space. The main idea is to study the joint algebra associated to the system together with the reference frame in the presence of symmetries. If both the system and the reference frame are covariant under some symmetry group, the construction of the invariant joint algebra very naturally involves crossed products.
17/12/24	Seminario	14:30	15:30	1201 Dal Passo	Paolo Cosentino	Università di Roma "Tor Vergata"	Seminario di Equazioni Differenziali A Harnack type inequality for singular Liouville type equations Abstract We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actually more delicate and results in a nontrivial variation of the regular case. Part of the arguments of Chen-Lin can be adapted to the singular case by means of an isoperimetric inequality for surfaces with conical singularities. The rest of the proof actually requires a different approach, due to the loss of translation invariance of the problem. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
17/12/24	Seminario	14:30	16:00	1101 D'Antoni	Davide Gori	Sapienza Università di Roma	Geometry Seminar Alternative Modular Compactifications of M_{g,n} via Cluster Algebras with applications to the MMP of overline{M}_{g,n} Abstract We will discuss modular compactifications of M_{g,n} (the moduli space of smooth curves) and their birational geometry within the framework of the Hassett-Keel program. We classify the open substacks of canonically polarized curves with nodes, cusps, and tacnodes having a proper good moduli space. Using the S- and Theta-completeness criteria, we transform the problem into a combinatorial one where compactifications and flips can be described using cluster algebra theory. This approach yields a complete description of the Q-factorialization fan of (overline{M}_{g,n}(7/10)) as a cluster fan.
13/12/24	Seminario	16:00	17:00	1101 D'Antoni	Paolo ANTONINI	Università del Salento	Algebra and Representation Theory Seminar (ARTS) Optimal Transport between Algebraic Hypersurfaces Abstract I will report on a recent work in collaboration with F. Cavalletti and A. Lerario, where we study complex projective hypersurfaces seen as probability measures on the projective space. Our guiding question is: “What is the best way to deform a complex projective hypersurface into another one?" Here the word best means from the point of view of measure theory and mass optimal transportation. In particular, we construct an embedding of the space of complex homogeneous polynomials into the probability measures on the projective space and study its intrinsic Wasserstein metric.The Kähler structure of the projective space plays a fundamental role and we combine different techniques from symplectic geometry to the Benamou-Brenier dynamical approach to optimal transportation to prove several interesting facts. Among them we show that the space of hypersurfaces with the Wasserstein metric is complete and geodesic: any two hypersurfaces (possibly singular) are always joined by a minimizing geodesic. Moreover outside the discriminant locus, the metric is induced by a Kähler structure of Weil-Petersson type. In the last part I will give an application to the condition number of polynomial equations solving. This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).
13/12/24	Seminario	14:30	15:30	1101 D'Antoni	Maxime RAMZI	Universität Münster	Joint Topology & Algebra and Representation Theory Seminar (T-ARTS) Induced character formulae and the Becker-Gottlieb transfer Abstract The induced character formula in classical representation theory can be used, among other things, to describe the dimension of coinvariants of a representation in terms of its character. In this talk, I will explain how this formula is related to the multiplicativity of Euler characteristics in algebraic topology, and, in a more homotopy-coherent context, to the composability of so-called Becker-Gottlieb transfers, which are "wrong-way maps" in singular (co)homology; by describing a general formula to compute "dimensions of homotopy colimits". If time permits, I will discuss the most general case in which composability of Becker-Gottlieb transfers is now known. This is based on joint works with Carmeli-Cnossen-Yanovski, Klein-Malkiewich (and the last part with Volpe-Wolf). This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).
10/12/24	Seminario	14:30	15:30	1201 Dal Passo	Felice Iandoli	Università della Calabria	Seminario di Equazioni Differenziali Strong ill-posedness in L^∞ of the 2D Boussinesq equations Abstract In this talk I will present a recent work in which the strong ill-posedness of the two-dimensional Boussinesq system is proven. I will show explicit examples of initial data with vorticity and density gradient in L^∞ (R²) for which the horizontal density gradient has a strong norm inflation in infinitesimal time. This is a joint work with Roberta Bianchini (CNR) and Lars Eric Hientzsch (Bielefeld University). NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006