Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
19/01/24	Seminario	16:00	17:00	1201 Dal Passo	Tommaso ROSSI	Università di Roma	Algebra & Representation Theory Seminar (ARTS) "Homology operations for gravity algebras" Abstract In the early nineties Getzler discovered a nice algebraic structure on the equivariant homology of a topological conformal field theory. He called this algebraic structure a "gravity algebra" and he showed that it is governed by an operad which is closely related to the homology of M_0,n+1 , the moduli space of genus zero Riemann surfaces with n+1 marked points. A gravity algebra can be thought as a generalization of a (dg) Lie algebra, in the sense that other than the Lie bracket we also have higher arity operations which satisfies a "generalized Jacobi identity". In this talk we will first give an introduction to gravity algebras, providing many interesting examples from both algebra (cyclic cohomology of a Frobenius algebra) and topology (S¹-equivariant homology of the free loop space on a manifold). Then I will briefly explain that any class in the S¹-equivariant homology of the (unordered) configuration spaces of points in the plane H_^S¹(C_n*(R);F_p) (with coefficients in a field F_p of p elements) gives rise to an homology operation for gravity algebras. After that we will see how to compute this equivariant homology and if time permits we will see some applications.
19/01/24	Seminario	14:30	15:30	1201 Dal Passo	Riccardo ARAGONA	Università de L'Aquila	Algebra & Representation Theory Seminar (ARTS) "Normalizer chain, modular idealizer chain and partitions" Abstract In recent joint works with Civino, Gavioli and Scoppola, we studied the conjugacy classes of an elementary Abelian regular subgroup T of the symmetric group on 2ⁿ elements. In particular we computed, via GAP software package, a chain of normalizers in a Sylow 2-subgroup of this symmetric group defined iteratively, starting from T. We noticed that the logarithm of the indice of the (i-1)-th normalizer in the i-th normalizer of our chain is equal to the i-th partial sum of the sequence of the numbers of partitions of an integer in at least two distinct parts. In this talk we present some techniques developed in order to prove this result, including the notion of a special family of elements of a Sylow 2-subgroup, called rigid commutators. Finally, some generalizations to Lie algebras are given, considering similar results for an idealizer chain.
16/01/24	Seminario	14:30	16:00	1101 D'Antoni	Katharina Müller	Universität der Bundeswehr München	On towers off isogeny graphs with full level structure Abstract Let k be a finite field of chracteristic q. Let p,l be primes corpime to q and let N be a positive integer coprime to pql. In this talk we will define graphs X_l^q(Np^n) whose vertices are tuples (E,P,Q), where E/k is an elliptic curves and P,Q is a basis for E[Np^n]. The edges are given by degree l isogenies. We will discuss when X_l^q(Np^n)/X_l^q(Np^{n-1}) is Galois and will describe the structure of these graphs as volcanos. This is joint work with Antonio Lei.
11/01/24	Seminario	14:00	15:00	1200 Biblioteca Storica	Ludovico Bruni Bruno	Università di Padova	Interpolation by weights: insights and challenges Abstract Interpolation of differential forms is a challenging aspect of modern approximation theory. Not only does it shed new light on some classical concepts of interpolation theory, such as the Lagrange interpolation and the Lebesgue constant, but it also suggests that they can be extended to a very general framework. As an extent of that, it is worth pointing out that the majority of classical shape functions commonly used in finite element methods, such as those involved in Nedelec or Raviart-Thomas elements, can be seen as a specialisation of this theory. Of course, this generality brings along the evident downside of an unfriendly level of abstraction. The scope of this series of two seminars is thus twofold: presenting the main challenges of this branch of approximation theory but in a concrete manner. The first seminar will hinge on a development of a convenient one dimensional toy model that enlightens parallelisms and differences with usual nodal interpolation. In the second seminar will extend these techniques to the multi-dimensional framework, motivating our choices by a geometrical flavour. This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
09/01/24	Seminario	14:30	16:01	1101 D'Antoni	Antonio Trusiani	Chalmers University of Technology	Singular cscK metrics on smoothable varieties Abstract The study of constant scalar curvature Kähler (cscK) metrics on compact complex manifolds is a classical topic that has attracted enormous interest since the 1950s. However, detecting the existence of cscK metrics is a difficult task, which in the projective integral case conjecturally amounts to proving an important algebro-geometric stability notion (K-stability). Recent significant advancements have established that the existence of unique cscK metric in a Kähler class is equivalent to the coercivity of the so-called Mabuchi functional. I will extend the notion of cscK metrics to singular varieties, and I will show the existence of these special metrics on Q-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive. A key point in this variational approach is the lower semicontinuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact Kähler varieties with klt singularities. The latter strengthens evidence supporting the openness of (uniform) K-stability for general families of normal compact Kähler varieties with klt singularities. This is a joint work with Chung-Ming Pan and Tat Dat Tô.
09/01/24	Seminario	14:00	15:00	1201 Dal Passo	Ludovico Bruni Bruno	Università di Padova	Interpolation by weights: insights and challenges Abstract Interpolation of differential forms is a challenging aspect of modern approximation theory. Not only does it shed new light on some classical concepts of interpolation theory, such as the Lagrange interpolation and the Lebesgue constant, but it also suggests that they can be extended to a very general framework. As an extent of that, it is worth pointing out that the majority of classical shape functions commonly used in finite element methods, such as those involved in Nedelec or Raviart-Thomas elements, can be seen as a specialisation of this theory. Of course, this generality brings along the evident downside of an unfriendly level of abstraction. The scope of this series of two seminars is thus twofold: presenting the main challenges of this branch of approximation theory but in a concrete manner. The first seminar will hinge on a development of a convenient one dimensional toy model that enlightens parallelisms and differences with usual nodal interpolation. In the second seminar will extend these techniques to the multi-dimensional framework, motivating our choices by a geometrical flavour. This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
20/12/23	Seminario	16:00	17:00	1201 Dal Passo	Pierre Bieliavsky	UCLovain	Operator Algebras Seminar Geometric methods for locally compact quantum groups Abstract A result due to De Commer implies that an important source of locally compact quantum groups (I will explain this notion) is constituted by the unitary dual 2-cocycles on (classical) locally compact groups. I will present geometric methods to explicitly construct such 2-cocycles for (classical) Lie groups of Frobenius type i.e. Lie groups that admit open co-adjoint orbits. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
15/12/23	Seminario	16:00	17:00	1201 Dal Passo	Tiziano GAIBISSO	Imperial College, London	Algebra & Representation Theory Seminar (ARTS) "Nakajima quiver varieties" Abstract Nakajima quiver varieties, originally defined in '94 by H. Nakajima, form an interesting class of algebraic varieties with many applications in algebraic geometry (e.g. resolution of singularities), representation theory (e.g. Kac-Moody algebras), and string theory (e.g. Coulomb and Higgs branches). In this talk, we will begin introducing the general setting of Hamiltonian reductions via GIT, highlighting how this technique produces Poisson quasi-projective varieties in a canonical way, and, in some cases, resolutions of symplectic singularities. We will then apply this theory to quiver representations, defining Nakajima quiver varieties and illustrating how the combinatorial nature of quivers is reflected in the geometry of these varieties.
15/12/23	Seminario	14:30	15:30	1201 Dal Passo	Chetan VUPPULURY	"Sapienza" Università di Roma	Algebra & Representation Theory Seminar (ARTS) "Higher projective representations and higher central extensions" Abstract Projective representations of a group G with assigned 2-cocycle α are equivalent to (certain) representations of the central extension of G associated with α. This classical result can be seen as a piece of 2-category theory fallen into the realm of 1-categories, and in this perspective it admits natural generalizations relevant to the context of anomalous topological or Euclidean QFTs. In particular, Stolz-Teichner's Clifford field theories naturally emerge as a particular example of this construction.
13/12/23	Seminario	17:00	18:00	2001	Efthymios Sofos	University of Glasgow	Averages of multiplicative functions over integer sequences Abstract In joint work with Chan, Koymans and Pagano we prove matching upper and lower bounds for multiplicative functions when averaged over general integer sequences. We give applications to Cohen—Lenstra conjecture and Manin’s conjecture for counting solutions of Diophantine equations in a small number of variables.