18 Gennaio, 2023 17:00

Sezione di Geometria, Algebra e loro applicazioni

Spectral analysis of Kohn Laplacian on spherical manifolds

Yunus Zeytuncu, University of Michigan-Dearborn

On line

abstract

abstract

In this talk, we discuss the spectral analysis of Kohn Laplacian on spheres and the quotients of spheres. In particular, we obtain an analog of Weyl’s law for the Kohn Laplacian on lens spaces. We also show that two 3-dimensional lens spaces with fundamental groups of equal prime order are isospectral with respect to the Kohn Laplacian if and only if they are CR isometric.

16 Gennaio, 2023 11:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

The Hilbert scheme of a pair of linear spaces

Ritvik Ramkumar, Cornell University

Aula Seminari III piano

abstract

abstract

The Grassmannian is a smooth moduli space with very rich geometry that parameterizes simple varieties, namely, linear spaces. One can study a natural generalization, the component of a Hilbert scheme that parameterizes a pair of linear spaces in P^n. In this talk, I will describe the geometry of this component and show that they are smooth Mori dream spaces. Along the way, we will obtain a complete classification of the degenerations of a pair of linear spaces.

12 Gennaio, 2023 15:00

MOX Seminar

Uncertainty Quantification for spatially-extended neurobiological networks

Daniele Avitabile, VU-Amsterdam

Aula Saleri VI piano - Dipartimento di Matematica

abstract

abstract

This talk presents a framework for forward uncertainty quantification problems in spatially-extended neurobiological networks. We will consider networks in which the cortex is represented as a continuum domain, and local neuronal activity evolves according to an integro-differential equation, collecting inputs nonlocally, from the whole cortex. These models are sometimes referred to as neural field equations.
Large-scale brain simulations of such models are currently performed heuristically, and the numerical analysis of these problems is largely unexplored. In the first part of the talk I will summarise recent developments for the rigorous numerical analysis of projection schemes [1] for deterministic neural fields, which sets the foundation for developing Finite-Element and Spectral schemes for large-scale problems.
The second part of the talk will discuss the case of systems in the presence of uncertainties modelled with random data, in particular: random synaptic connections, external stimuli, neuronal firing rates, and initial conditions (and any combination thereof). Such problems give rise to random solutions, whose mean, variance, or other quantities of interest have to be estimated using numerical simulations. This so-called forward uncertainty quantification problem is challenging because it couples spatially nonlocal, nonlinear problems to large-dimensional random data.
I will present a family of schemes that couple a spatial projector for the spatial discretisation, to stochastic collocation for the random data. We will analyse the time-dependent problem with random data and the schemes from a functional analytic viewpoint, and show that the proposed methods can achieve spectral accuracy, provided the random data is sufficiently regular.
Acknowledgements. This talk presents joint work with Francesca Cavallini (VU Amsterdam), Svetlana Dubinkina (VU Amsterdam), and Gabriel Lord (Radboud University).
References
[1] Avitabile D, Projection methods for Neural Field Equations arXiv e-prints,
arXiv:2112.03244 doi.org/10.48550/arXiv.2112.03244

Contatto: simona.perotto@polimi.it

11 Gennaio, 2023 11:00

Sezione di Finanza Quantitativa

Sentiment risk premia in the cross-section of global equity

Massimo Guidolin, Università Bocconi

Aula Seminari III piano - polimi-it.zoom.us/j/96365275017?pwd=cFMrc1VtbUh5K2VXQ2dLY2hzR3gxQT09

abstract

abstract

This paper applies a recently developed sentiment proxy to the construction of a new risk factor and provides a comprehensive understanding of its role in sentiment-augmented asset pricing models. We find that news and social media search-based indicators are significantly related to excess returns of international equity indices. Adding sentiment factors to both classical and more recent linear factor pricing models leads to a significant increase in their performance. When it is estimated using the Fama-MacBeth procedure, our sentiment-adjusted pricing model implies positive (negative) estimates of the risk premium for positive (negative) sentiment factors. We further differentiate between developed and emerging markets and uncover different patterns of return reversals / persistence in the long-term. Our results contribute to the explanation of global cross-sectional average excess returns and are robust to augmenting the model with fundamental factors, momentum, idiosyncratic volatility, skewness, kurtosis, and the returns on international currencies. When compared to competing definitions of sentiment factors popular in the literature, our novel sentiment risk variable turns out to be superior in terms of predictive power.

21 Dicembre, 2022 17:00

Sezione di Geometria, Algebra e loro applicazioni

Basic Clifford q-Calculus

Swanhild Bernstein, TU Bergakademie Freiberg

On line

This paper applies a recently developed sentiment proxy to the construction of a new risk factor and provides a comprehensive understanding of its role in sentiment-augmented asset pricing models. We find that news and social media search-based indicators are significantly related to excess returns of international equity indices. Adding sentiment factors to both classical and more recent linear factor pricing models leads to a significant increase in their performance. When it is estimated using the Fama-MacBeth procedure, our sentiment-adjusted pricing model implies positive (negative) estimates of the risk premium for positive (negative) sentiment factors. We further differentiate between developed and emerging markets and uncover different patterns of return reversals / persistence in the long-term. Our results contribute to the explanation of global cross-sectional average excess returns and are robust to augmenting the model with fundamental factors, momentum, idiosyncratic volatility, skewness, kurtosis, and the returns on international currencies. When compared to competing definitions of sentiment factors popular in the literature, our novel sentiment risk variable turns out to be superior in terms of predictive power.

15 Dicembre, 2022 17:00

Seminario Matematico e Fisico di Milano

Diagrammi geometrici e teoria dello spazio dall'antichità all'età moderna

Vincenzo De Risi, CNRS Université de Paris; Max Planck Institute

Sala di Rappresentanza del Dip. di Matematica, via C. Saldini 50

abstract

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Il seminario prende in considerazione il ragionamento diagrammatico in geometria elementare e le sue origini nella pratica matematica greca. Si discutono alcuni limiti ed alcune potenzialità di questo approccio ala geometria. Si mostra che il ruolo delle inferenze diagrammatiche diminuì nel corso della storia della geometria moderna anche prima di arrivare alla matematica astratta del diciannovesimo secolo. Le ragioni dell'abbandono delle pratiche diagrammatiche sembra legato alla trasformazione della geometria da una scienza delle figure in una scienza dello spazio. Si mostra allora che tale trasformazione ha preceduto e reso possibile la nascita della matematica astratta e di un ideale dimostrativo non-diagrammatico.

15 Dicembre, 2022 15:15

Sezione di Analisi

Chemotaxis model for tumour growth

Andrea Signori, Politecnico di Milano

Aula Seminari III Piano

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We discuss analytic results for a new diffuse interface model describing the evolution of a tumour mass under the effects of a chemical substance (e.g., a nutrient). The process is described by utilising an order parameter representing the local proportion of tumour cells, and a variable describing the concentration of the chemical. The order parameter is assumed to satisfy a suitable form of the Cahn–Hilliard equation with mass source and logarithmic potential of Flory–Huggins type, whereas the chemical concentration satisfies a reaction-diffusion equation where the cross-diffusion term has the same expression as in the celebrated
Keller–Segel model. Weak well-posedness, regularity, and continuous dependence results are presented.
This is a joint work with E. Rocca (University of Pavia) and G. Schimperna (University of Pavia).

14 Dicembre, 2022 15:00

Seminari FDS

Rappresentazioni e problem-solving

Chiara Andrà, Rosa Iaderosa, Università del Piemonte Orientale, Rally Matematico Transalpino

Aula seminari VI piano

abstract

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Il seminario si propone di analizzare rappresentazioni esterne spontanee o indotte messe in atto da studenti durante la risoluzione di problemi. Le rappresentazioni esterne possono fare da ponte per l’elaborazione di una strategia risolutiva. A volte si trovano schemi personali che riflettono il processo di pensiero utilizzato. Spesso esse sostituiscono anche un’esplicitazione verbale del processo risolutivo, o comunque coesistono con questa in un intreccio tra registro verbale e iconico, o grafico-simbolico. Durante il seminario saranno analizzate le risposte degli studenti con lo scopo di fornire indicazioni didattiche durante attività di problem-solving.

13 Dicembre, 2022 10:15

Sezione di Fisica Matematica

An information-theoretic approach to thermodynamical systems at the equilibrium

Arnaldo Spalvieri, Politecnico di Milano

Aula Seminari III Piano, Dipartimento di Matematica, Politecnico di Milano

Il seminario si propone di analizzare rappresentazioni esterne spontanee o indotte messe in atto da studenti durante la risoluzione di problemi. Le rappresentazioni esterne possono fare da ponte per l’elaborazione di una strategia risolutiva. A volte si trovano schemi personali che riflettono il processo di pensiero utilizzato. Spesso esse sostituiscono anche un’esplicitazione verbale del processo risolutivo, o comunque coesistono con questa in un intreccio tra registro verbale e iconico, o grafico-simbolico. Durante il seminario saranno analizzate le risposte degli studenti con lo scopo di fornire indicazioni didattiche durante attività di problem-solving.

12 Dicembre, 2022 15:30

MOX Seminar

Inverse Design for Nanoscale Heat Transport

Giuseppe Romano, Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology (MIT), Cambridge, MA,

On-line

abstract

abstract

How to identify the geometry of a nanostructure given the desired effective thermal conductivity tensor? While several topology optimization methods have been developed for macroscale scenarios, they can’t be readily applied to nanoscale devices. In fact, when the feature size of the material becomes comparable with the particles’ mean-free path, flux becomes nondiffusive, and a momentum-resolved model is needed. On the other side, standard material interpolation methods, such as SIMP, are mostly applied to averaged quantities, such as the local thermal conductivity. In this talk, I will discuss our recent attempt at solving this issue [1], based on a novel method, termed the “Transmission Interpolation Method” (TIM). Instead of working with locally resolved variables, TIM acts on the interfacial phonon flux and links it to the material distribution. The talk will show the application of this approach to two examples: Tuning the effective thermal conductivity tensor of a nanostructure and maximizing phonon size effects. The talk will conclude with a demo and remarks for future developments.
[1] Giuseppe Romano and Steven G Johnson, Structural and Multidisciplinary Optimization 65, 297 (2022)

Contatto: giulia.pozzi@polimi.it