Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
21/01/25	Seminario	14:30	16:00	1101 D'Antoni	Francesca Carocci	Università di Roma Tor Vergata	Geometry Seminar A logarithmic approach to linear series Abstract Maps to projective space are given by basepoint-free linear series, thus these are key to understanding the extrinsic geometry of algebraic curves. How does a linear series degenerate when the underlying curve degenerates and becomes nodal? Eisenbud and Harris gave a satisfactory answer to this question when the nodal curve is of compact type. I will report on a joint work in progress with Luca Battistella and Jonathan Wise, in which we review this question from a moduli-theoretic and logarithmic perspective. The logarithmic prospective helps understanding the rich polyhedral and combinatorial structures underlying degenerations of linear series; these are linked with the theory of matroids and Bruhat-Tits buildings. 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
17/01/25	Seminario	14:30	15:30	1201 Dal Passo	Frédéric PATRAS	Université Côte d'Azur	Algebra and Representation Theory Seminar (ARTS) How to recognize free Lie algebras? Abstract Structure properties of free Lie algebras are a fundamental tool in group theory and its many applications. However, it is not always easy in practice to recognize that a Lie algebra is free. The talk will survey various results that allow to conclude to freeness, and various concrete examples. Based on joint work with L. Foissy.
14/01/25	Seminario	14:30	15:30	1201 Dal Passo	Riccardo Montalto	Università degli Studi di Milano Statale	Seminario di Equazioni Differenziali Small and large amplitude quasi-periodic waves in Fluid Mechanics Abstract In this talk I shall discuss some recent results about the construction of small and large amplitude quasi-periodic waves in Euler equations and other hydro-dynamical models in dimension greater or equal than two. I shall discuss quasi-peridic solutions and vanishing viscosity limit for forced Euler and Navier-Stokes equations and the problem of constructing quasi-periodic traveling waves bifurcating from Couette flow (and connections with inviscid damping). I also discuss some results concerning the construction of large amplitude quasi-periodic waves in rotating fluids. The techniques are of several kinds: Nash-Moser iterations, micro-local analysis, analysis of resonances in higher dimension, normal form constructions and spectral theory. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
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
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).