| 26/09/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Alberto AVITABILE | Università di Roma "Tor Vergata" |
Topology, Algebra & Representation Theory Seminar (T-ARTS)
"E∞-algebra structure on singular cochains"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
Singular cohomology of a space carries a natural CDGA structure induced by cup product at the level of cochains. While cup product is a well-defined operation on singular cochains, commutativity only holds after passing to cohomology, due to the presence of non-trivial Steenrod operations. This fact will be the motivating example for introducing E∞-algebras and to explain how the E∞-structure on cochains encodes this phenomenon in a precise way. Since the theory of E∞-algebras needs the notion of operad, general recollections on the basics of operad theory will be provided.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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| 26/09/25 | Seminario | 11:30 | 12:30 | 1101 D'Antoni | Alessandro Scagliotti | Technical University of Munich and Munich Center for Machine Learning | Optimal Control and Machine Learning:
Machine Learning through the lens of sub-Riemannian Geometry
In this talk we illustrate the link between Deep Neural Networks and flows
induced by control systems (Neural ODEs), and we relate the ''expressivity'' of a Residual Neural Network (ResNets) to the controllability properties of the corresponding Neural ODE in the space of diffeomorphisms.
In case of control-linear Neural ODEs, a sub-Riemannian structure emerges. We show how the Lie Algebra Strong Approximating Property (see [Agrachev & Sarychev 2020,2022]) guarantees that, given two M-tuples of pairwise distinct points (M>1), we can steer one to the other. Moreover, this condition implies that we can approximate on compact sets any diffeomorphism isotopic to the identity using flows induced by the controlled dynamics. This ensures that ''sub-Riemannian'' ResNets are expressive.
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| 26/09/25 | Seminario | 10:30 | 11:30 | 1101 D'Antoni | Alfio Borzì | Institut für Mathematik, Universität Würzburg | Optimal Control and Machine Learning:
The Pontryagin Maximum Principle for Training Convolutional Neural Networks
batch sequential quadratic Hamiltonian (bSQH) algorithm for training convolutional neural networks with L2 and L0-based regularization is presented. This methodology is based on a discrete-time Pontryagin maximum principle.
It uses forward and backward sweeps together with the layerwise approximate maximization of an augmented Hamiltonian function, where the augmentation parameter is chosen adaptively.
The loss-reduction and convergence properties of the bSQH algorithm are analysed theoretically and validated numerically. Results of numerical experiments in the context of image classification with a sparsity enforcing L0-based regularizer demonstrate the effectiveness of the proposed method in full-batch and mini-batch modes.
This is joint work with Sebastian Hofmann. |
| 25/09/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Rotem Assouline | Institut de Mathématiques de Jussieu – Paris Rive Gauche | Seminario di Sistemi Dinamici & Analisi
Curvature-Dimension for Autonomous Lagrangians
In this talk, we will demonstrate how the celebrated connection between Ricci curvature, optimal transport, and geometric inequalities such as the Brunn-Minkowski inequality, extends to the setting of general Lagrangians on weighted manifolds. As applications, we will state a generalization of the horocyclic Brunn-Minkowski inequality to complex hyperbolic space of arbitrary dimension, and a new Brunn-Minkowski inequality for contact magnetic geodesics on odd-dimensional spheres. The main technical tool is a generalization of Klartag's needle decomposition technique to the Lagrangian setting.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
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| 24/09/25 | Seminario | 17:15 | 18:15 | 1201 Dal Passo | Stefan Hollands | University of Leipzig | Operator Algebras Seminar
Channel divergences and complexity in algebraic QFT
Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
TBA |
| 24/09/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Christopher Raymond | University of Hamburg | Operator Algebras Seminar
Inverse Hamiltonian reduction in VOA representation theory
Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Recent interest in vertex operator algebra theory has focused on examples whose representation theory describes conformal field theories with logarithmic divergences in their correlation functions (logCFTs). These VOAs admit non-semisimple representations that play a key role in the CFT, and additionally often feature infinitely many simple representations. A large class of examples of such VOAs are W-algebras associated to affine VOAs at fractional admissible level. However, representations for these VOAs are notoriously difficult to construct in a general way. One approach to solving this problem is known as inverse quantum hamiltonian reduction (IQHR). The aim of this talk will be to introduce the ideas behind IQHR in some accessible examples, and then discuss generalisations. |
| 19/09/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Johannes Rau | Universidad de Los Andes, Bogotà | Geometry Seminar
Counting rational curves over any field
An important problem in enumerative geometry is counting rational curves that interpolate a configuration of points on an algebraic surface. Over the complex numbers, the answer does not depend on the configuration of points and is called the Gromov-Witten invariant. In contrast, over the real numbers, this invariance fails. To recover it, Welschinger invented an “sign” rule that gives rise to Welschinger invariants. Recently, Kass, Levine, Solomon, and Wickelgren constructed an invariant over an (almost) arbitrary field. The small “inconvenience” is that these latter invariants are no longer numbers, but quadratic forms. In a current work with Erwan Brugallé and Kirsten Wickelgren, we establish direct relationships between these different types of invariants. In my talk, I want to give an introduction to this topic.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures |
| 16/07/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Simone Del Vecchio | University of Bari | Operator Algebras Seminar
On the Ryll-Nardzewski Theorem for Quantum Stochastic Processes
In Classical Probability, a sequence of random variables is said to be exchangeable if its joint distributions are invariant under all finite permutations. Ryll-Nardzeski’s Theorem establishes that exchangeability is the same as spreadability, the a priori weaker symmetry where all subsequences of the given sequence have the same joint distributions.
In the non-commutative setting, it is known that the two symmetries no longer coincide for general quantum stochastic processes. We show that under very natural hypothesis there is an extension of the Ryll-Nardzewski Theorem in the noncommutative setting which covers a wide variety of models. Furthermore we obtain an extended De Finetti’s Theorem for various models including processes based on the CAR algebra and on the infinite noncommutative torus.
This talk is based on joint work in progress with Valeriano Aiello and Stefano Rossi.
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| 09/07/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Wojciech Dybalski | University in Poznań | Operator Algebras Seminar
Exact Schwinger functions for a class of bounded interactions in d≥ 2
We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function V such that V± := lim w → ±∞ V(w) exist. We find a field renormalization such that all the n-point connected Schwinger functions for n ≠ 2 exist non-perturbatively in the UV limit. They coincide with the tree-level one-particle irreducible Schwinger functions of the erf(ϕ/ √ 2) interaction with a coupling constant (V+ - V-)/2. By a slight modification of our construction we can change this coupling constant to (V+ - V-)/2., where V± := lim w → 0± V(w). Thereby, non-Gaussianity of these latter theories is governed by a discontinuity of V at zero. |
| 02/07/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Arthur M. Jaffe | Harvard University | Operator Algebras Seminar
Higher-Order Fourier Analysis and Quantum Complexity
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