Seminari/Colloquia

Pagina 10


DateTypeStartEndRoomSpeakerFromTitle
19/01/24Seminario16:0017:001201 Dal Passo
Tommaso ROSSI
Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Homology operations for gravity algebras"

  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 M0,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(Cn(R);Fp) (with coefficients in a field Fp 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.
19/01/24Seminario14:3015:301201 Dal Passo
Riccardo ARAGONA
Università de L'Aquila
Algebra & Representation Theory Seminar (ARTS)
"Normalizer chain, modular idealizer chain and partitions"

  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.
16/01/24Seminario14:3016:001101 D'AntoniKatharina MüllerUniversität der Bundeswehr MünchenOn towers off isogeny graphs with full level structure

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.
11/01/24Seminario14:0015:001200 Biblioteca StoricaLudovico Bruni BrunoUniversità di PadovaInterpolation by weights: insights and challenges

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).
09/01/24Seminario14:3016:011101 D'AntoniAntonio TrusianiChalmers University of TechnologySingular cscK metrics on smoothable varieties

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.
09/01/24Seminario14:0015:001201 Dal PassoLudovico Bruni BrunoUniversità di PadovaInterpolation by weights: insights and challenges

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).
20/12/23Seminario16:0017:001201 Dal PassoPierre Bieliavsky UCLovain
Operator Algebras Seminar
Geometric methods for locally compact quantum groups

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)
15/12/23Seminario16:0017:001201 Dal Passo
Tiziano GAIBISSO
Imperial College, London
Algebra & Representation Theory Seminar (ARTS)
"Nakajima quiver varieties"

  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.
15/12/23Seminario14:3015:301201 Dal Passo
Chetan VUPPULURY
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Higher projective representations and higher central extensions"

  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.
13/12/23Seminario17:0018:002001Efthymios SofosUniversity of GlasgowAverages of multiplicative functions over integer sequences

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.

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