12/03/24  Seminario  14:30  15:30  1201 Dal Passo  Alessandro Scagliotti  TU Munchen  Seminario di Equazioni Differenziali
Controltheoretic approach for the approximation of the optimal transport map
In this presentation, we tackle the problem of reconstructing the optimal transport map $T$ between two absolutely continuous measures $mu,
u in mathcal{P}(mathbb{R}^n)$, and for this approximation we employ flows generated by linearcontrol systems in $mathbb{R}^n$.
We first show that, under suitable assumptions on the measures $mu,
u$ and on the controlled vector fields, the optimal transport map is contained in the $C^0_c$closure of the flows generable by the system.
In the case that discrete approximations $mu_N,
u_N$ of the measures $mu,
u$ are available, we use a discrete optimal transport plan to set up an optimal control problem. With a $Gamma$convergence argument, we prove that its solutions corresponds to flows that provide approximations of the optimal transport map $T$.
Finally, in virtue of the Pontryagin Maximum Principle, we propose an iterative numerical scheme for the resolution of the optimal control problem, resulting in an algorithm for the practical computation of approximations of the optimal transport map. This approach can be interpreted as the construction of a ''Normalizing Flow'' by means of a Residual Neural Network (ResNet). Based on a joint work with Sara Farinelli.
[1] A. Scagliotti, S. Farinelli. Normalizing flows as approximations of optimal transport maps via linearcontrol neural ODEs. arXiv preprint, 2023.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

12/03/24  Seminario  14:30  16:00  1101 D'Antoni  Andrea Di Lorenzo  Humboldt University (Berlin)  The importance of being a weighted blowup
Blowups are fundamental tools in algebraic geometry, and there are several results (e.g the famous Castelnuovo's theorem) that can be used to determine when a variety is obtained as a blowup of a smooth variety along a smooth center. Weighted blowups play a similar role for stacks. In this talk I will present a criterion for finding out if a smooth DM stack is a weighted blowup. I will apply this result for showing that certain alternative compactifications of moduli of marked elliptic curves are obtained via weighted blowups (and blowdowns). This in turn will prove to be useful in order to compute certain invariants, like Chow rings or Brauer groups. First part of this talk is a joint work with Arena, Inchiostro, Mathur, Obinna and Pernice; the second part of this talk is a joint work with L. Battistella. 
05/03/24  Seminario  14:30  16:01  1101 D'Antoni  Víctor González Alonso  Leibniz Universität Hannover  Embedded deformations of curves with maximal variation of Hodge structure
Given a family of complex (smooth projective) manifolds, one can measure its nontriviality by looking at how much the Hodge structures of the fibres change. This leads to the notion of maximal (infinitesimal) variation of Hodge structure (IVHS).
In the case of families of curves, results of LeePirola and of myself with Torelli imply that a general deformation of any curve has maximal IVHS. This is however not so clear if one wants the deformation to keep some further structure, such as the gonality of the curve or an embedding into a given surface. For example, it was only recently proved by Favale and Pirola that every smooth plane curve admits a deformation as a plane curve with maximal IVHS, and the question remains open for deformations of curves inside any other surface.
In this talk I will present a joint work in progress with Sara Torelli extending this result to curves in P^1 x P^1, which turns out to be way more involved than the plane case. 
05/03/24  Seminario  14:30  15:30  1201 Dal Passo  Stefano Baranzini  Università di Torino  Seminario di Equazioni Differenziali
Chaotic phenomena for singular systems on surfaces
The main focus of the talk will be a class of 2d singular mechanical systems on a surface
S with a potential V having a finite number of singularities C := {c_1,..., c_n} of the form
V(q) ~ C_i d(c_i,q)^{a_i}
where C_i>0, a_i >= 1 and q in O(c_i).
The first result I will present is an existence one: there are periodic solutions in (infinitely) many conjugacy classes of pi_1(S,C).
Using this fact, I will construct an invariant set for the system which admits a semiconjugation with a Bernoulli shift.
The second result I will discuss aims at identifying some situation in which the semiconjugation is actually a conjugation and the invariant set constructed displays a chaotic behaviour. This happens, for instance, under some negativity condition on the curvature of S and for large values of the energy. Much emphasis will be put on the interplay between geometry, topology and variational methods.
This is a joint work with Gian Marco Canneori.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
01/03/24  Seminario  16:00  17:00  1201 Dal Passo  Matteo MICHELI  “Sapienza” Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"Degenerations of the classical Grassmannians and their isotropic subvarieties"
This talk is based on joint work in progress with E. Feigin, M. Lanini and A. Pütz.
We analyze a family of Quiver Grassmannians for the equioriented cycle, which are degenerations of the classical Grassmannians: for each one, we describe its irreducible components, find a cellular decomposition in terms of attracting sets, and give an overview of the underlying combinatorics. Then we introduce symplectic conditions and try to understand the associated subvarieties, which are degenerations of the classical isotropic Grassmannians.

01/03/24  Seminario  14:30  15:30  1201 Dal Passo  Timm PEERENBOOM  RuhrUniversität  Bochum 
Algebra & Representation Theory Seminar (ARTS)
"CoHas of extended Dynkin quivers"
In this talk I give a description of the semistable Cohomological Hall algebra (CoHa) for extended Dynkin quivers with central slope in terms of generators and relations.
This extends work of FranzenReineke who dealt with the case of the Kronecker quiver. 
28/02/24  Seminario  16:00  17:00  1201 Dal Passo  Giovanni Landi  University of Trieste 
Operator Algebras Seminar
On Atiyah sequences of braided Lie algebras and their splittings
To an equivariant noncommutative principal bundle one
associates an Atiyah sequence of braided derivations whose
splittings give connections on the bundle. There is an explicit
action of vertical braided derivations as infinitesimal gauge
transformations on connections. From the sequence one
derives a Chern—Weil homomorphism and braided Chern—
Simons terms.
On the principal bundle of orthonormal frames over the
quantum sphere S^{2n}_theta, the splitting of the sequence
leads to a LeviCivita connection on the corresponding
module of braided derivations. The connection is torsion free
and compatible with the 'round' metric. We work out the
corresponding Riemannian geometry.
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

27/02/24  Seminario  16:00  17:00  1201 Dal Passo  Dario Darji  University of Louisville (US)  Applications of Local Entropy Theory
Local entropy theory is a culmination of deep results in dynamics, ergodic theory and combinatorics. Given a dynamical system with positive entropy, it gives, in some sense, the location of where the entropy resides. It is a powerful tool that can be applied in a variety of settings. In this talk, we will show how the speaker (with his coauthors) has been able to apply local entropy theory to settle some problems in continuum theory, and in dynamics of maps on the space of finite measures.

27/02/24  Seminario  14:30  16:00  1101 D'Antoni  Sam Molcho  ETH  Equivariant localization in the absence of a group action
Consider the moduli space of stable, nmarked curves M and the tautological subring R^*(M) of its Chow ring. The standard calculus for R^*(M) is based on the ''strata algebra" SA(M), which is constructed via the inductive structure of the boundary of M and the excess intersection formula, and in which calculations are expressed in terms of ''graph sums". In this talk I will discuss a new calculus for R^*(M), based on the introduction of a new ring L^*(M), built out of tropical geometry, and in which several standard calculations simplify significantly. I will explain how the comparison between SA and L is analogous to the comparison between equivariant cohomology and equivariant cohomology of the fixed locus in GKM theory.
Finally, I will sketch how this idea can be used to give explicit formulas for the BrillNoether cycles  informally, the cycles on M parametrizing curves on which a line bundle of the form omega^k(sum a_ix_i) has at least r+1 linearly independent sections.
This is a joint work with M. Abreu and N. Pagani. 
21/02/24  Seminario  17:15  18:15  1201 Dal Passo  Alexander Stottmeister  University of Hannover 
Operator Algebras Seminar
Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras
We discuss the embezzlement of entanglement and its relation to the
classification of the latter, as well as its application to relativistic
quantum field theory. Embezzlement (of entanglement), introduced by van
Dam and Hayden, denotes the task of producing any entangled state to
arbitrary precision from a shared entangled resource state, the
embezzling state, using local operations without communication while
perturbing the resource arbitrarily little. We show that Connes'
classification of type III von Neumann algebras can be given a
quantitative operational interpretation in terms of embezzlement. In
particular, this quantification implies that all type III factors, apart
from some type III_0 factors, host embezzling states. In contrast,
semifinite factors (type I or II) cannot host embezzling states.
Specifically, type III_1 factors are characterized as 'universal
embezzlers', meaning every normal state is embezzling. The latter
observation provides a simple explanation as to why relativistic quantum
field theories maximally violate Bell inequalities.
To understand the connection between embezzlement of entanglement and
the classification of von Neumann algebras, we use a technique
introduced by Haagerup and Størmer that associates to each normal state
on a von Neumann algebra a state on the flow of weights. Our results
then follow by quantifying the invariance of states on the flow of
weights on the restriction of the dual modular flow.
If time permits, we will also discuss the connection between embezzling
states and embezzling families, as used by van Dam and Hayden.
This is joint work with Lauritz van Luijk, Reinhard F. Werner, and
Henrik Wilming. 