Seminari/Colloquia
Pagina 10
Date  Type  Start  End  Room  Speaker  From  Title 

19/01/24  Seminario  16:00  17:00  1201 Dal Passo  "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 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 (S^{1}equivariant homology of the free loop space on a manifold). Then I will briefly explain that any class in the S^{1}equivariant homology of the (unordered) configuration spaces of points in the plane H_{*}^{S1}(C_{n}(R  
19/01/24  Seminario  14:30  15:30  1201 Dal Passo  "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 2^{n} elements. In particular we computed, via GAP software package, a chain of normalizers in a Sylow 2subgroup of this symmetric group defined iteratively, starting from T. We noticed that the logarithm of the indice of the (i1)th normalizer in the ith normalizer of our chain is equal to the ith 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 2subgroup, 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
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^{n1}) 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
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 RaviartThomas 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 multidimensional 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
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 algebrogeometric stability notion (Kstability). Recent significant advancements have established that the existence of unique cscK metric in a Kähler class is equivalent to the coercivity of the socalled Mabuchi functional. I will extend the notion of cscK metrics to singular varieties, and I will show the existence of these special metrics on QGorenstein 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) Kstability for general families of normal compact Kähler varieties with klt singularities. This is a joint work with ChungMing 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
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 RaviartThomas 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 multidimensional 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  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 2cocycles on (classical) locally compact groups.
I will present geometric methods to explicitly construct such 2cocycles for
(classical) Lie groups of Frobenius type i.e. Lie groups that admit
open coadjoint 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  "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. KacMoody 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 quasiprojective 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  "Higher projective representations and higher central extensions"
Projective representations of a group G with assigned 2cocycle 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 2category theory fallen into the realm of 1categories, and in this perspective it admits natural generalizations relevant to the context of anomalous topological or Euclidean QFTs. In particular, StolzTeichner'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
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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