Prossimi seminari del Dipartimento di Matematica

Maggio
dal giorno
19/05/2025
al giorno
20/05/2025
Conference
Knots & Proteins
da lunedì 19 maggio 2025 a martedì 20 maggio 2025
Maggio
19
Lunedì
Mathematical formalization has attracted increasing attention in recent years, with Lean 4 emerging as one of the central tools in this area. This series of four seminars will introduce mathematical formalization, discuss its significance, and showcase recent examples of successful formalization projects. Two of the seminars will provide hands-on tutorials using the interactive theorem prover Lean 4. In the final seminar, we will examine how artificial intelligence and formalization interact, highlighting recent developments in autoformalization and automatic theorem proving.
The functional organization of primary motor cortex (M1) across the cortical sheet remains obscure. Aside from the crude and static somatotopic organization of M1, there is little evidence of spatially organized dynamic patterning across the motor cortical sheet. We have previously demonstrated that spatially organized propagating patterns of excitability along a rostro-caudal axis in non-human primates signal the initiation of movement but do not specify the details of the movement (Balasubramanian, Arce-McShane, Dekleva, Collinger, & Hatsopoulos, 2023). These propagating patterns of excitability were observed in the attenuation of low frequency beta oscillation (15-35 Hz) amplitude of the local field potential (LFP). We are now investigating patterns of high frequency components of the LFP (200-400 Hz referred to as high gamma) that propagate intermittently across M1 during reaching behaviors and have found that the propagation direction carries kinematic information (Liang, Balasubramanian, Papadourakis, & Hatsopoulos, 2023; unpublished data). Given that the high gamma signal serves as an accurate proxy for multi-unit activity (Ray & Maunsell, 2011), these results suggest that a spatially organized recruitment order of multi-unit activity provides behaviorally relevant information.
Maggio
19
Lunedì
Simona Paoli
Seminario di algebra e geometria, logica, teoria delle categorie
ore 14:00
presso Seminario I
The simplicial category \Delta plays an important role in category theory. One of the reasons is that there is a fully faithful nerve functor from the category Cat to the category of simplicial sets (that is functors from the opposite of \Delta to Set). Its essential image consists of simplicial sets satisfying additional conditions that the Segal maps are isomorphisms. This allows to think of a small category as a type of simplicial set, and this idea has been carried on in higher dimensions in defining appropriate notions of higher categories. This talk is about a modification of \Delta, introduced by J. Kock, called the fat delta. After explaining the motivation for our interest in fat delta, both from higher category theory and from type theory, we present a study of fat delta in terms of monad with arities. This leads to a nerve theorem for relative semicategories, as well as a description of fat delta as a hypermoment categories in the sense of Berger. This is joint work with Tom de Jong, Nicolai Kraus and Stiephen Pradal, arXiv.2503.10963v1.
Maggio
20
Martedì
Ludwig Schmid
Seminario di fisica matematica, interdisciplinare
ore 14:00
presso Aula Seminario VIII piano
Large-scale quantum computing requires fault-tolerant algorithms to counter hardware noise that would otherwise corrupt information. While the overhead of fault-tolerant quantum computation exceeds current hardware capabilities, optimizing these protocols is crucial for practical implementation. Clifford circuits are fundamental to these protocols, as many universal fault-tolerant quantum computing schemes, such as magic state distillation, utilize the Clifford gate set. Currently, Clifford circuits for fault-tolerant protocols are typically manually designed for specific error correction codes. Inspired by the well-established field of digital circuit design, this work approaches Clifford circuit synthesis using satisfiability-solving techniques. We show the NP-completeness of depth-optimal Clifford synthesis and illustrate how satisfiability solving can synthesize fault-tolerant state-preparation circuits for Calderbank-Shor-Steane codes. This entails both heralded repeat-until-success and deterministic state preparation protocols. The resulting Clifford circuit designs surpass existing constructions and enable state preparation circuits for previously under-explored quantum codes, demonstrating how classical circuit design techniques can advance fault-tolerant quantum computing.
Maggio
20
Martedì
Carlo Maria Scandolo
Seminario di fisica matematica
ore 15:00
presso Aula Seminario VIII piano
Quantum systems can and have been used to develop algorithms and communication protocols that outperform their classical counterparts. The advantages provided by quantum systems are studied within the framework of quantum resource theories, in which quantum states and operations are divided into free and resourceful. Many of these resource theories share an interesting property: an operation is free if and only if its image under an isomorphism known as the Choi isomorphism is a free state. We refer to resource theories exhibiting this property as Choi-defined resource theories. In this talk, I will present the mathematical framework used in quantum information and introduce quantum resource theories. Furthermore, I will define Choi-defined resource theories and demonstrate how and under what conditions one can construct them. Lastly, I will present some properties shared by all Choi-defined resource theories.
In this presentation I will provide a brief overview on the origin of Fractional Calculus and its current rigorous formulation. I will then discuss some physical motivations for the generalisation of this theory to the variable-order case. Then I will introduce a novel perspective on variable-order fractional calculus, its precise formulation in terms of the General Fractional Calculus framework, and I will discuss some of its implications considering the fractional relaxation equation as a case study. Lastly, I will discuss an application of the proposed formalism to the theory of viscoelasticity.
Maggio
21
Mercoledì
Cristiano Bocci
Seminario di algebra e geometria
ore 14:30
presso Seminario I
In this talk I will introduce the main topics about the new field of research called Neuroalgebraic Geometry. In particular I will focus on the definitions, results (and conjectures) contained in the papers - J. Kileel, M. Tranger, J. Bruna, On the Expressive Power of Deep Polynomial Neural Networks, (2019). - K. Kubjas, J. Li, M. Wiesmann, Geometry of polynomial neural networks, (2024). - G. L. Marchetti, V. Shahverdi, S. Mereta, M. Trager, K. Kohn, An Invitation to Neuroalgebraic Geometry, (2025). and I will talk also about my recent results on it and a list of suggested problems.
Maggio
21
Mercoledì
Maggio
22
Giovedì
Mathematical formalization has attracted increasing attention in recent years, with Lean 4 emerging as one of the central tools in this area. This series of four seminars will introduce mathematical formalization, discuss its significance, and showcase recent examples of successful formalization projects. Two of the seminars will provide hands-on tutorials using the interactive theorem prover Lean 4. In the final seminar, we will examine how artificial intelligence and formalization interact, highlighting recent developments in autoformalization and automatic theorem proving.
The Hochschild cohomology of a differential graded algebra or more generally of a differential graded category admits a natural map to the graded center of its derived category: the characteristic homomorphism. We interpret this map as an edge homomorphism in a spectral sequence, which allows to study the characteristic homomorphism systematically in many interesting examples from algebra, geometry, topology and physics. To illustrate this, we will discuss several concrete examples related to coherent sheaves on algebraic curves and cochains of classifying spaces of Lie groups. If time permits, I will also indicate a new extension of this framework to $A_\infty$-categories. Some of this is joint work with M. Szymik (Sheffield) other with A. Phimister (Leicester).
Maggio
26
Lunedì
In this talk I will study generalized automata (in the sense of Adámek-Trnková) in Joyal’s category of combinatorial species; as an important preliminary step, I will provide examples of coalgebras for the "derivative" endofunctor ∂ and for the ‘Euler homogeneity operator’ L∂ arising from the adjunction L⊣∂⊣R. The theory is connected with, and in fact provides nontrivial examples of, differential 2-rigs—a concept I recently introduced by treating combinatorial species in the same way that a generic (differential) semiring (R,d) relates to the (differential) semiring N[[X]] of power series with natural coefficients. Joyal himself has long regarded species as categorified formal power series. This perspective aligns with a fundamental category-theoretic insight: free objects in the category of rings naturally acquire a canonical differential structure. At the heart of this phenomenon lies the representability of the prestack of derivations by an object of Kähler differentials. These ideas categorify elegantly within the 2-category of differential 2-rigs, revealing that species possess a universal property as differential 2-rigs. The desire to study categories of ‘state machines’ valued in an ambient monoidal category (K,⊗) gives a pretext to further develop the abstract theory of differential 2-rigs, proving lifting theorems of a differential 2-rig structure from (R,∂) to the category of ∂-algebras on objects of R, and to categories of Mealy automata valued in (R,⊗), as well as various constructions inspired by differential algebra such as jet spaces and modules of differential operators. This talk covers the content of the paper Automata and Coalgebras in Categories of Species (Proceedings of CMCS24, Luxembourg), as well as parts of an ongoing project with Todd Trimble.
Maggio
27
Martedì
Mathematical formalization has attracted increasing attention in recent years, with Lean 4 emerging as one of the central tools in this area. This series of four seminars will introduce mathematical formalization, discuss its significance, and showcase recent examples of successful formalization projects. Two of the seminars will provide hands-on tutorials using the interactive theorem prover Lean 4. In the final seminar, we will examine how artificial intelligence and formalization interact, highlighting recent developments in autoformalization and automatic theorem proving.
Maggio
28
Mercoledì
Mathematical formalization has attracted increasing attention in recent years, with Lean 4 emerging as one of the central tools in this area. This series of four seminars will introduce mathematical formalization, discuss its significance, and showcase recent examples of successful formalization projects. Two of the seminars will provide hands-on tutorials using the interactive theorem prover Lean 4. In the final seminar, we will examine how artificial intelligence and formalization interact, highlighting recent developments in autoformalization and automatic theorem proving.
Maggio
dal giorno
29/05/2025
al giorno
30/05/2025
Conference
da giovedì 29 maggio 2025 a venerdì 30 maggio 2025
Maggio
30
Venerdì
TBA
Maggio
30
Venerdì
For n greater or equal than 1 we show that the length 1 nested Hilbert scheme of the total space Xn of the line bundle OP1(-n), parameterizing pairs of nested 0-cycles in Xn, is a quiver variety associated with a suitable quiver with relations. This generalizes previous work about nested Hilbert schemes on C2 in one direction, and about the Hilbert schemes of points of Xn in another direction.
Giugno
03
Martedì
This teaching unit will introduce students to the Bayesian statistical framework for performing inference in high-dimensional inverse problems related to imaging sciences. We will start from basic concepts on probabilistic modelling, Bayesian decision theory, and Monte Carlo integration for Bayesian computation, and progress quickly to modern Bayesian imaging approaches. We will pay special attention to strategies based on stochastic diffusion processes and to Bayesian imaging models that combine elements derived from machine learning with elements derived from the physics of the considered imaging problem. The key ideas and techniques will be illustrated on imaging problems where we will conduct challenges inferences such as uncertainty quantification, hypothesis testing, model self-calibration, and model selection without ground truth.
This teaching unit introduces a computational "toolbox" for learning priors in the context of solving Bayesian inverse problems in imaging. The tools covered include methods for learning optimal discretizations of total-variation related regularization terms, explicit diffusion models based on products of 1D Gaussian mixture models, and the application of the maximum entropy principle for learning generative priors.
Giugno
04
Mercoledì
Two-dimensional barcodes (such as QR and Datamatrix) are widely used in warehouse logistics and high-speed production pipelines to automate product tracking. However, to handle various size packages, it happens frequently that small and high-resolution barcodes are challenging to decode. Conventional solutions address such challenges by utilizing expensive hardware (e.g. CPU, FPGA, ASIC) or powerful lighting sources, increasing the costs of the system. This study introduces a multi-step, scalable, and adaptive super-resolution (SR) method that focuses primarily on the areas where barcodes are present and minimizes the computational burden on the uniform regions of the background. Our approach achieves superior image quality by dynamically determining the required refinement steps for each region of the image analyzed. Experiments demonstrate that our method outperforms the state-of-the-art SR models on barcode images, reaching higher PSNR and decoding rates while reducing the latency.
Giugno
05
Giovedì
Maciej Zworski
Seminario di analisi matematica, fisica matematica
ore 15:00
presso Aula Arzelà
This question has been much discussed in physics and one suggestion is that the long time persistence of classical/quantum correspondence is due to interaction of a small, observed system with a larger environment. Lindblad or GKSL evolution is one of the standard models for describing such interactions. In that context the question of the length of time of classical/quantum agreement was recently revisited in physics by Hernández-Ranard-Riedel. In my talk I will introduce the concept of Lindblad evolution and present results showing that the evolution of a quantum observable remains close to the classical Fokker-Planck evolution in the Hilbert-Schmidt norm for times vastly exceeding the Ehrenfest time (the limit of such an agreement when there is no interaction with a larger system). The time scale is the same as in two recent papers by Hernández-Ranard-Riedel but the statement and methods are different. The talk is based on joint work with J Galkowski and numerical results obtained jointly with Z Huang. I will also comment on recent progress on trace class estimates by Z Li and on the hypoelliptic case by H Smith.
Giugno
05
Giovedì
Matteo Roffilli (Bioretics)
Seminario di analisi numerica
ore 16:30
presso Complesso Belmeloro Aula G
Vision Transformers (ViT) are very powerful deep architectures capable of recognizing and using very subtle statistical patterns, often invisible to humans. Nice but... to achieve these performances they require having large databases, well maintained and representative of the domain of interest, perhaps even i.i.d.. This usually only happens in paper-academic contexts or technological superpowers. But fortunately (for you) in this seminar we will show how it is possible to profitably use ViTs in real low-budget industrial contexts where the raw material (i.e. data) is few, dirty and often ugly.
We rigorously analyse fully-trained neural networks of arbitrary depth in the Bayesian optimal setting in the so-called proportional scaling regime where the number of training samples and width of the input and all inner layers diverge proportionally. We prove an information-theoretic equivalence between the Bayesian deep neural network model trained from data generated by a teacher with matching architecture, and a simpler model of optimal inference in a generalized linear model. This equivalence enables us to compute the optimal generalization error for deep neural networks in this regime. We thus prove the "deep Gaussian equivalence principle" conjectured in Cui et al. (2023) (arXiv:2302.00375). Our result highlights that in order to escape this "trivialisation" of deep neural networks (in the sense of reduction to a linear model) happening in the strongly overparametrized proportional regime, models trained from much more data have to be considered.
Giugno
06
Venerdì
Giugno
09
Lunedì
We will introduce the basic concepts of (deterministic) regularisation theory and discuss model- and data-driven regularisations. We will discover how these concepts can be utilised to optimally sample data in magnetic resonance imaging and single-pixel camera applications, or to construct decoders for trained encoders in deep learning without additional training of the decoder.
Giugno
09
Lunedì
Note: this is the first part of a two-part seminar. AI is progressing at a remarkable speed, but we still don’t have a clear understanding of basic concepts in cognition (e.g. learning, understanding, abstraction, awareness, intelligence, etc). I shall argue that research focused on understanding how learning machines such as LLMs or deep neural networks do what they do, sidesteps the key issue by defining these concepts from the outset. For example, statistical learning is based on a classification of problems (supervised/unsupervised, classification, regression etc.) and addresses the resulting optimisation problem (maximisation of the likelihood, minimisation of errors, etc). Learning entails first of all detecting what makes sense to be learned 1) from very few samples, and 2) without a priori knowing why that date makes sense. This requires a quantitative notion of relevance that can distinguish data that makes sense from meaningless noise. I will first introduce and discuss the notion of relevance. Next I will claim that learning differs from understanding, where the latter implies integrating data that make sense into a pre-existing representation. The properties of this representation should be abstract, i.e. independent of the data, precisely because they need to represent data of a widely different domain. This is what enables higher cognitive functions that we do all the time, like drawing analogies and relating data learned independently from widely different domains. Such a representation should be flexible and continuously adaptable if more data or more resources are made available. I will show that such an abstract representation can be defined as the fixed point of a renormalisation group transformation, and it coincides with a model that can be defined from the principle of maximal relevance. I will provide empirical evidence that the representations of simple neural networks approach this universal model as the network is trained on a broader and broader domain of data. Overall, the aim of the seminar is to support the idea that an approach to central issues in cognition is also possible studying very simple models and does not necessarily require understanding large machine learning models.
Note: this is the second part of a two-part seminar. AI is progressing at a remarkable speed, but we still don’t have a clear understanding of basic concepts in cognition (e.g. learning, understanding, abstraction, awareness, intelligence, etc). I shall argue that research focused on understanding how learning machines such as LLMs or deep neural networks do what they do, sidesteps the key issue by defining these concepts from the outset. For example, statistical learning is based on a classification of problems (supervised/unsupervised, classification, regression etc.) and addresses the resulting optimisation problem (maximisation of the likelihood, minimisation of errors, etc). Learning entails first of all detecting what makes sense to be learned 1) from very few samples, and 2) without a priori knowing why that date makes sense. This requires a quantitative notion of relevance that can distinguish data that makes sense from meaningless noise. I will first introduce and discuss the notion of relevance. Next I will claim that learning differs from understanding, where the latter implies integrating data that make sense into a pre-existing representation. The properties of this representation should be abstract, i.e. independent of the data, precisely because they need to represent data of a widely different domain. This is what enables higher cognitive functions that we do all the time, like drawing analogies and relating data learned independently from widely different domains. Such a representation should be flexible and continuously adaptable if more data or more resources are made available. I will show that such an abstract representation can be defined as the fixed point of a renormalisation group transformation, and it coincides with a model that can be defined from the principle of maximal relevance. I will provide empirical evidence that the representations of simple neural networks approach this universal model as the network is trained on a broader and broader domain of data. Overall, the aim of the seminar is to support the idea that an approach to central issues in cognition is also possible studying very simple models and does not necessarily require understanding large machine learning models.
Giugno
09
Lunedì
This seminar will cover some concepts and recent advances in the emerging field of self-supervised learning methods for solving imaging inverse problems with deep neural networks. Self-supervised learning is a fundamental tool deploying deep learning solutions in scientific and medical imaging applications where obtaining a large dataset of ground-truth images is very expensive or impossible. The seminar will present different self-supervised methods, discuss their theoretical underpinnings and present practical self-supervised imaging applications. Finally, I will discuss my experience developing and collaborating on open-source software for science (https://deepinv.github.io/), and some of the lessons learned along the way.
Giugno
09
Lunedì
Julián Tachella (CNRS, ENS de Lyon Laboratoire de physique)
Seminario di analisi numerica
ore 16:30
presso Aula 31 - Dipartimento Scienze Econoniche - Piazza Scaravilli 1
This seminar will cover some concepts and recent advances in the emerging field of self-supervised learning methods for solving imaging inverse problems with deep neural networks. Self-supervised learning is a fundamental tool deploying deep learning solutions in scientific and medical imaging applications where obtaining a large dataset of ground-truth images is very expensive or impossible. The seminar will present different self-supervised methods, discuss their theoretical underpinnings and present practical self-supervised imaging applications. Finally, I will discuss my experience developing and collaborating on open-source software for science (https://deepinv.github.io/), and some of the lessons learned along the way.
Giugno
10
Martedì
Ricardo H. Nochetto
nell'ambito della serie: SCUBE
Seminario di analisi matematica, analisi numerica, interdisciplinare
ore 15:00
presso Aula Vitali
seminario on line •
Modeling, analysis and computation are three pillars of computational science. We discuss them within the context of liquid crystal networks (LCNs). These materials couple a nematic liquid crystal with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. Thin bodies of LCNs are natural candidates for soft robotics applications. We start from the classical 3D trace energy formula and derive a reduced 2D membrane energy as the formal asymptotic limit of vanishing thickness, including both stretching and bending energies, and characterize the zero energy deformations. We design a sound numerical method and discuss its Gamma convergence. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of nonisometric origami within and beyond theory. This work is joint with L. Bouck, G. Benavides, and S. Yang.
Giugno
11
Mercoledì
Micaela Verucchi and Giorgia Franchini (Hipert Lab - Unimore)
Seminario di analisi numerica
ore 16:30
presso Aula 31 - Dipartimento di Scienze Economiche - P.zza Scaravilli 1
The Indy Autonomous Challenge and the Abu Dhabi Autonomous Racing League represent two of the world’s most groundbreaking competitions in autonomous racing. Nearly ten teams from across the globe compete for multimillion-dollar prizes, showcasing autonomous vehicles capable of racing at ever-increasing speeds. The events feature both head-to-head and multi-vehicle scenarios—with three or more cars simultaneously on the track—pushing the boundaries of artificial intelligence and engineering. Unimore Racing, representing the University of Modena and Reggio Emilia (UNIMORE), has consistently ranked among the top three teams in each competition. Notably, they secured second place in a head-to-head race in Indianapolis, reaching speeds exceeding 290 kph, and claimed victory in Las Vegas during the first four-team autonomous race in history. This ongoing success highlights Unimore Racing’s expertise and the continued evolution of autonomous driving technologies.
Giugno
13
Venerdì
Ilja Gogic
Seminario di analisi matematica
ore 14:00
presso Seminario II
The most basic class of derivations on C*-algebras consists of the inner derivations—those expressible as commutators with elements from the multiplier algebra. A fundamental question in the theory of C*-algebras is to determine which algebras admit only inner derivations. Landmark results by Sakai, Kadison, and Sproston established this property for all von Neumann algebras, simple C*-algebras, and homogeneous C*-algebras. In the separable setting, the problem was completely resolved in 1979 by Akemann, Elliott, Pedersen, and Tomiyama, who showed that a separable C*-algebra has only inner derivations if and only if it is a direct sum of a C*-algebra with continuous trace and a C*-algebra with discrete primitive spectrum. However, the non-separable case remains largely unsettled—even for 2-subhomogeneous algebras. In 1978, Pedersen posed a unifying question, inspired by the work of Sakai and Kadison: given a C*-algebra, does its local multiplier algebra—defined as the C*-direct limit of the multiplier algebras of its essential closed ideals—admit only inner derivations? In this talk, we revisit the classical innerness problem for derivations on C*-algebras, highlighting both recent developments and emerging perspectives.
Giugno
dal giorno
16/06/2025
al giorno
18/06/2025
Conference
Three Days in Sub-Riemmanian Geometry
da lunedì 16 giugno 2025 a mercoledì 18 giugno 2025
Giugno
dal giorno
16/06/2025
al giorno
18/06/2025
Conference
Three Days in Sub-Riemannian Geometry
da lunedì 16 giugno 2025 a mercoledì 18 giugno 2025
Giugno
dal giorno
16/06/2025
al giorno
18/06/2025
Conference
Three Days in Sub-Riemmanian Geometry
da lunedì 16 giugno 2025 a mercoledì 18 giugno 2025
Category theory was initially developed to address some structural questions in algebraic topology. Shortly after it was extended to algebraic geometry, logic, universal algebra, and more recently, theoretical computer science. Each of these subjects was heavily influenced by category theory, and in turn, the development of category theory was prominently shaped by the strucures and problems arising in these fields. In the past few years there has been a growing interest in applying categorical techniques to fields such as probability, statistics and information theory, to study their structures and to find patterns in their techniques. Perhaps surprisingly, it turns out that these fields present a rich and principled structure when addressed categorically, with functors and universal properties arising everywhere. However, most of the time, new category theory is needed to study these subjects, as they are quite far from the algebra and geometry for which category theory was initially developed. Two of the current most prolific environments to study probability categorically are Markov categories and dagger categories. In this talk we will give an introduction to both, show their similarities, differences and connections, and use them to prove some core theorems of probability.
Giugno
18
Mercoledì
Giuseppina Guatteri
nell'ambito della serie: STOCHASTICS AND APPLICATIONS - 2025
Seminario di probabilità
ore 11:00
presso - Aula Da Stabilire -
seminario on line •
Giugno
19
Giovedì
Valentina Ros
TBA
Seminario di fisica matematica
ore 11:00
presso - Aula Da Stabilire -
TBA
Giugno
19
Giovedì
Giulio Galise, Sapienza Università di Roma
ore 16:00
presso - Aula Da Stabilire -
seminario on line • collegamento al meeting
Giugno
23
Lunedì
Eric Anschuetz
Seminario di fisica matematica, interdisciplinare
ore 11:00
presso Aula Bombelli
We show a surprising relation between quantum learning theory and algorithmic hardness. We demonstrate that finding the ground state of certain sparse disordered quantum systems is average-case hard for "Lipschitz" quantum algorithms if there exists an efficient, local learning algorithm---such as the classical shadows algorithm---for estimating the energy of a state of the system. A corollary of our result is that both $O(\log(n))$-depth variational quantum algorithms and $O(\log(n))$-time Lindbladian dynamics fail to find the near-ground state of these systems, matching known bounds for classical disordered systems. To achieve this, we prove that there exists a topological property of certain quantum systems that we call the quantum overlap gap property (QOGP). We then show that systems which exhibit this topological property in their low-energy space exhibit a form of average-case algorithmic hardness. We prove that the QOGP is satisfied for a sparsified variant of the quantum $p$-spin model, giving the first known average-case hardness-of-approximation result for quantum algorithms in finding the ground state of a non-stoquastic, noncommuting quantum system. Conversely, we show that the Sachdev--Ye--Kitaev (SYK) model does not exhibit the QOGP, consistent with previous evidence that the model is rapidly mixing at low temperatures.
Giugno
23
Lunedì
Valentina Disarlo
TBA
ore 14:00
presso Seminario II
Giugno
dal giorno
25/06/2025
al giorno
27/06/2025
Conference
da mercoledì 25 giugno 2025 a venerdì 27 giugno 2025
We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N-$dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\geq 3$, we sharpen it to $\boldsymbol{\omega}(r) \approx \exp (-c| \ln r|^{\frac1N})$; for $p>\max\{2,N\}$, we derive an unexpected H\"older modulus. This is a joint work with Ugo Gianazza and Naian Liao.
Giugno
27
Venerdì
Gianluca Paolini
Seminario di algebra e geometria, interdisciplinare, logica
ore 14:00
presso Seminario II
An uncountable $\aleph_1$-free group can not admit a Polish group topology but an uncountable $\aleph_1$-free abelian group can, as witnessed e.g. by the Baer-Specker group $\mathbb{Z}^\omega$, in fact, more strongly, $\mathbb{Z}^\omega$ is separable. In this paper we investigate $\aleph_1$-free abelian non-Archimedean Polish groups. We prove two main results. The first is that there are continuum many separable (and so torsionless, and so $\aleph_1$-free) abelian non-Archimedean Polish groups which are not topologically isomorphic to product groups and are pairwise not continuous homomorphic images of each other. The second is that the following four properties are complete co-analytic subsets of the space of closed abelian subgroups of $S_\infty$: separability, torsionlessness, $\aleph_1$-freenees and $\mathbb{Z}$-homogeneity.
Giugno
30
Lunedì
In this talk we will introduce uberhomology, a combinatorially defined homology theory for simplicial complexes. After proving some of its properties, we’ll show how this invariant is related to dominating sets and to the Mayer-Vietoris spectral sequence. We will conclude with some open questions and problems. All results are joint work with L. Caputi and D. Celoria.
Luglio
07
Lunedì
Andrew Waldron
Seminario di algebra e geometria, fisica matematica
ore 09:00
presso - Aula Da Stabilire -
In this talk we prove that the renormalized Yang-Mills energy on six dimensional Poincaré-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the corresponding anomaly boundary integrand in the seven dimensional renormalized Yang-Mills energy. Our methods rely on a generalization of the Chang-Qing-Yang method for computing renormalized volumes of Poincaré-Einstein manifolds, as well as known scattering theory results for Schrödinger operators with short range potentials.
Settembre
dal giorno
01/09/2025
al giorno
05/09/2025
Conference
da lunedì 01 settembre 2025 a venerdì 05 settembre 2025
Summer School sponsored by the CIME Foundation Local expenses for speakers are paid by CIME Trave expenses for speakers to be reimbursed using the funds of the ERC project DAT
Settembre
08
Lunedì
Mateusz Rzepecki
TBA
Seminario di logica
ore 14:00
presso Seminario II
TBA