31 Maggio, 2024 10:00

Sezione di Fisica Matematica

Self-adjoint extensions by a Krein-type resolvent formula

Andrea Posilicano, Università dell'Insubria

Sala Consiglio, VII piano

abstract

abstract

We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

31 Maggio, 2024 14:30

MOX Seminar

Isotonic subgroup selection and its role in clinical trials

Richard Samworth, Cambridge

B.51

abstract

abstract

Given a sample of covariate-response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a pre-determined threshold. This is particularly relevant in clinical trials and other applications in the life sciences, for instance where we might want to determine a subgroup that would benefit from a vaccine or treatment. We introduce a computationally-feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically-structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate guarantee with power that attains the minimax optimal rate up to poly-logarithmic factors. Extensions cover classification, isotonic quantile regression and heterogeneous treatment effect settings. Questa iniziativa è parte delle Ph.D. Lectures finanziate dal Dipartimento di Eccellenza, 2023-2027, Dipartimento di Milano, Politecnico di Milano. La Lezione è corredata da incontri con gli studenti di dottorato, per approfondimenti legati al tema di ricerca presentato nella lezione, ed alle ricerche specifiche dei singoli studenti. Contatto: laura.sangalli@polimi.it.

30 Maggio, 2024 10:00

Sezione di Fisica Matematica

Self-adjoint extensions by a Krein-type resolvent formula

Andrea Posilicano, Università dell'Insubria

Sala Consiglio, VII piano

abstract

abstract

We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

29 Maggio, 2024 17:30

Seminari di Cultura Matematica

La magia dei Computer Quantistici

Maurizio Ferrari Dacrema, Politecnico di Milano

Aula T12 e in collegamento webex su tiny.cc/mathseminars

We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

24 Maggio, 2024 11:00

Seminari di Cultura Matematica

Modelling of memristive devices for Bio-Inspired computing

Francesco Vaccaro, Politecnico di Milano

Aula Seminari F. Saleri - VI piano

We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

24 Maggio, 2024 10:00 in punto

Sezione di Fisica Matematica

Trace formulas for one-dimensional Schrödinger operators

Hynek Kovarik, Università di Brescia

Sala Consiglio, VII Piano

abstract

abstract

One-dimensional Schrödinger operators satisfy certain identity, called the trace formula, which relates the scattering and spectral data of the operator in question with integral means of the corresponding potential. In this mini-course we will give a sketch of the proof of this formula and discuss some of its applications.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

22 Maggio, 2024 11:00 in punto

Sezione di Fisica Matematica

Trace formulas for one-dimensional Schrödinger operators

Hynek Kovarik, Università di Brescia

Sala Consiglio, VII Piano

abstract

abstract

One-dimensional Schrödinger operators satisfy certain identity, called the trace formula, which relates the scattering and spectral data of the operator in question with integral means of the corresponding potential. In this mini-course we will give a sketch of the proof of this formula and discuss some of its applications.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

21 Maggio, 2024 15:00

MOX Seminar

Continuous-time multivariate analysis: the “transpose” of functional data analysis

Philip Tzvi Reiss, University of Haifa

aula Beltrami

abstract

abstract

The starting point for much of multivariate analysis (MVA) is an n × p data matrix whose n rows represent observations and whose p columns represent variables. Some multivariate data sets, however, may be best conceptualized not as n discrete p-variate observations, but as p curves or functions defined on a common time interval. Here we introduce a framework for extending techniques of multivariate analysis to such settings. The proposed continuous-time multivariate analysis (CTMVA) framework rests on the assumption that the curves can be represented as linear combinations of basis functions such as B-splines, as in the Ramsay-Silverman representation of functional data; but whereas functional data analysis extends MVA to the case of observations that are curves rather than vectors — heuristically, n × p data with p infinite — we are instead concerned with what happens when n is infinite. We present continuous-time extensions of the classical MVA methods of covariance and correlation estimation, principal component analysis, Fisher’s linear discriminant analysis, and k-means clustering. We show that CTMVA can improve on the performance of classical MVA, in particular for correlation estimation and clustering, and can be applied in some settings where classical MVA cannot, including variables observed at disparate time points. CTMVA is illustrated with a novel perspective on a well-known Canadian weather data set, and with applications to data sets involving international development, brain signals, and air quality. The proposed methods are implemented in the R package ctmva, available on CRAN. This is joint work with Biplab Paul, Erjia Cui and Noemi Foà.

20 Maggio, 2024 10:00 in punto

Sezione di Fisica Matematica

Trace formulas for one-dimensional Schrödinger operators

Hynek Kovarik, Università di Brescia

Sala Consiglio, VII Piano

abstract

abstract

One-dimensional Schrödinger operators satisfy certain identity, called the trace formula, which relates the scattering and spectral data of the operator in question with integral means of the corresponding potential. In this mini-course we will give a sketch of the proof of this formula and discuss some of its applications.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

16 Maggio, 2024 15:00

Sezione di Analisi

Well-posedness results for Kolmogorov equations with applications to mean-field control problems for multi-agent systems

Francesca Anceschi, Università Politecnica delle Marche

Aula Seminari - III Piano

abstract

abstract

In this talk, based on a joint project with G. Ascione, D. Castorina and F. Solombrino, we discuss some well-posedness results for Kolmogorov-Fokker-Planck equations with measurable coefficients in time and locally Holder continuous coefficients in space with possibly unbounded drift terms and their application to the study of particle systems of the second order whose prototypical agent is driven by a McKean-Vlasov SDE, or by a Vlasov-Fokker-Planck PDE.