Courses 23/24

Courses 2023-24
SSD Name of the course Professor Semester Language Credits
MAT/05
(BA)		 Stability and instability in dynamical systems Giuliani Fall English 5
SECS-S/01
(BA)		 Advanced statistical learning for complex data Ieva Fall English 5
MAT/08
(BA)		 Mathematical and numerical foundations of scientific machine learning Pagani, Miglio Fall English 5
MAT/05, MAT/07
(SC)		 Spectral and scattering theory in quantum mechanics Borrelli, Fermi Spring English 5
MAT/08
(SC)		 Advanced numerical methods for predictive digital twins Fresca, Zunino Spring English 5
MAT/05
(SC)		 Mathematical Aspects of Fluid Mechanics Giorgini Fall English 5
MAT/06
(SC)		 An introduction to the Malliavin calculus Zanella Fall English/Italiano 5
  Advanced mathematical methods in engineering I Correggi Spring/Fall   5
  Advanced mathematical methods in engineering II Correggi Spring/Fall   5
Today's events
Upcoming events

  • may 21 wed 2025

    		Seminar
    Per Moosavi, Anisotropic quantum Hall droplets challenge the plasma analogy,  05-21-2025, 14:00 precise
    logo matematica
    • Seminar
    • Per Moosavi
    • Stockholm University
    • Anisotropic quantum Hall droplets challenge the plasma analogy
    • Wednesday, 21 May 2025 at 14:00 right
    • Aula Seminari III piano, Bd. 14, Campus Leonardo
    • Abstract
      I will present recent work on integer quantum Hall droplets with anisotropic trapping potentials. Using semiclassical methods, we obtain the one-particle energy spectrum and wave functions in the lowest Landau level by deriving and solving a transport equation inspired by standard WKB theory. This shows that energy eigenstates are localized on equipotentials of the trap, generalizing the rotational-symmetric case for isotropic potentials. From these microscopic first-principle considerations, we show that many-body correlations along the droplet's edge are long-ranged, in agreement with low-energy edge modes described by a free chiral conformal field theory in terms of the canonical angle variable of the potential. Comparing our results with the widely used plasma analogy, we show that the latter is unreliable at predicting edge properties of quantum Hall states. This discrepancy arises from a difference in geometries between quantum Hall droplets and plasmas (Coulomb gases): The former are incompressible liquids subject to area-preserving deformations, while the latter are governed by electrostatics and thus involve conformal maps. Consequently, the plasma analogy generally fails at the edge of anisotropic droplets.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 21 wed 2025

    		Seminar
    Francisco Jose Cruz-Zamorano, Holomorphic function spaces and the geometry of image domains,  05-21-2025, 17:00 precise
    logo matematica
    • Seminar
    • Francisco Jose Cruz-Zamorano
    • Universidad de Sevilla, Spain
    • Holomorphic function spaces and the geometry of image domains
    • Wednesday, 21 May 2025 at 17:00 right
    • On-line (il link verrà reso disponibile il giorno stesso del seminario)
    • Abstract
      This talk surveys the problem of characterizing the \(X-\)domains: planar domains \(\Omega\subset\mathbb C\) such that every holomorphic map \(f:\mathbb D\to\mathbb C\) belongs to a given holomorphic function space \(X\) on the unit disk \(\mathbb D\). Classical contributions include characterizations for \(X\) being the Bloch space (Seidel, Walsh, 1942), the space of analytic functions of bounded mean oscillation BMOA (Hayman, Pommerenke, 1978), and the Smirnov class (Ahern, Cohn, 1983).

      The case of Hardy spaces \(H^p\) has remained particularly active. Hansen (1970) introduced the Hardy number of a domain \(\Omega\subset\mathbb C\), defined as the supremum of all \(p>0\) such that \(\operatorname{Hol}(\mathbb D,\Omega)\). Subsequent work, notably by Essén (1981) and Kim and Sugawa (2011), established connections between the Hardy number of a domain and harmonic measure. More relations between the Hardy number of a domain and other potential-theoretic quantities have been encountered recently. The Hardy number of domains with special geometric properties has also been explored, including star-like domains (Hansen, 1971), comb domains (Karafyllia, 2021), and Koenigs domains (Contreras, Cruz-Zamorano, Kourou, Rodr'iguez-Piazza, 2024).

      Karafyllia (2023), building on a previous work with Karamanlis, extended this problem to (weighted) Bergman spaces, introducing the Bergman number of a domain. We will also discuss a close relationship between the Hardy number and the Bergman number of a planar domain, covering recent ideas on this topic obtained in collaboration with Betsakos.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 22 thu 2025

    		Seminar
    Carlo Nitsch, Improving a Spectral Inequality by Payne,  05-22-2025, 15:15
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    • Seminar
    • Carlo Nitsch
    • Università degli Studi di Napoli - Federico II
    • Improving a Spectral Inequality by Payne
    • Thursday, 22 May 2025 at 15:15
    • Aula B.4.4
    • Abstract
      A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne’s original estimate—which is not sharp—can in fact be improved. Our result provides a refined spectral bound and opens the way to further investigations into quantitative enhancements of classical inequalities in spectral theory.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 23 fri 2025

    		Seminar
    Madalin Guta, Local asymptotic normality in quantum statistics,  05-23-2025, 10:15
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    • Seminar
    • Madalin Guta
    • University of Nottingham
    • Local asymptotic normality in quantum statistics
    • Friday, 23 May 2025 at 10:15
    • Aula seminari MOX, VI piano, Dipartimento di Matematica del Politecnico di Milano
    • Abstract
      Local asymptotic normality is a key concept in mathematical statistics, which underlies the asymptotic achievability of the Cramer-Rao bound and the asymptotic normality of optimal estimators.

      In this presentation, I will review some of the current progress in extending this concept to the field of quantum statistics. In quantum estimation, one is given “quantum data” in the form of a quantum system prepared in a state that depends on an unknown parameter, and would like to estimate the parameter based on “classical data” obtained by measuring the system. This raises the problem of finding optimal measurements which extract maximum amount of information about the parameter.

      Quantum local asymptotic normality (QLAN) shows that in the limit of large “sample size”, certain quantum statistical models can be approximated by simpler Gaussian models where the unknown parameter is encoded linearly in the mean of the canonical variables. This simplification provides a procedures for constructing optimal estimators with normally distributed errors. I will discuss two settings in which QLAN holds: ensembles of identical, independent systems, and quantum Markov chains.

      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.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 23 fri 2025

    		Seminar
    Cristina Trombetti, Some free boundary problems in thermal insulation,  05-23-2025, 11:30 precise
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    • Seminar
    • Cristina Trombetti
    • Università degli Studi di Napoli Federico II
    • Some free boundary problems in thermal insulation
    • Friday, 23 May 2025 at 11:30 right
    • Aula B.5.4, quinto piano, ed. 14 "La Nave", Politecnico di Milano
    • Abstract
      Free boundary problems in partial differential equations (PDEs) are a class of mathematical problems in which both the solution to the PDE and the domain on which it is defined must be determined simultaneously, as the region is not known in advance. These problems arise in many physical and engineering contexts, such as fluid dynamics, solid mechanics, and heat conduction. In this talk, we will focus on certain free boundary problems related to thermal insulation, where either the boundary itself must be found, or the presence of an insulating material requires determining its optimal placement in order to minimize heat loss or maximize energy efficiency.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 26 mon 2025

    may 30 fri 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : mathematics of condensed matter systems
    05/26/2025 - 05/30/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 29 thu 2025

    		Seminar
    Vittorino Pata, Weak Solutions of Linear Differential Equations in Hilbert Spaces,  05-29-2025, 15:15
    logo matematica
    • Seminar
    • Vittorino Pata
    • Politecnico di Milano
    • Weak Solutions of Linear Differential Equations in Hilbert Spaces
    • Thursday, 29 May 2025 at 15:15
    • Aula Seminari - III Piano
    • Abstract
      We address the well-posedness of weak solutions for a general linear evolution problem on a separable Hilbert space. For this classical problem there is a well-known challenge of obtaining a priori estimates, as a constructed weak solution may not be regular enough to be utilized as a test function. This issue presents an obstacle for obtaining uniqueness and continuous dependence of solutions.
      When formal energy estimates ara available, we provide a general notion of weak solution and, through a straightforward observation, obtain that arbitrary weak solutions have additional time regularity and obey an a priori estimate. This yields weak well-posedness. Our result rests upon a central hypothesis asserting the existence of a "good" Galerkin basis for the construction of a weak solution. A posteriori, a strongly continuous semigroup may be obtained for weak solutions, and by uniqueness, weak and semigroup solutions are equivalent.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 03 tue 2025

    jun 06 fri 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : recent advances in operator theory and applications
    06/03/2025 - 06/06/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 09 mon 2025

    		MOX Seminar
    Lucas Bouck, Thin Sheets of Liquid Crystal Elastomers: Modeling, Approximation, and Computation,  06-09-2025, 11:30
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    MOX
    MOX Numeth

    • MOX Seminar
    • Lucas Bouck
    • Carnegie Mellon University
    • Thin Sheets of Liquid Crystal Elastomers: Modeling, Approximation, and Computation
    • Monday, 9 June 2025 at 11:30
    • Aula seminari MOX, VI piano
    • Abstract
      Liquid crystal elastomers (LCEs) are materials where a nematic liquid crystal is coupled 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 LCEs are natural candidates for soft robotics applications. Starting from the classical 3D trace energy formula of Bladon, Warner and Terentjev (1994), we derive a 2D plate theory as the asymptotic limit of the 3D energy using the tools of Gamma-convergence. The resulting bending problem consists of minimizing an energy that is a function of the curvatures of the parameterized surface, subject to a metric constraint. This metric constraint is the leading order behavior that drives large deformations of LCEs. Numerically, we solve this metric constraint by numerical minimization of a formally derived stretching energy with the bending energy serving as a regularization for the discrete problem. We prove that minimizers of the discrete energy converge to zero energy states of the stretching energy in the spirit of Gamma convergence. We solve the discrete minimization problem via an energy stable gradient flow scheme. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of nonisometric origami, both within and beyond theory. The plate theory derivation is joint work with P. Plucinsky and D. Padilla-Garza and the computational work is joint with R.H. Nochetto and S. Yang.

      Contatto:
      marco.verani@polimi.it

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 12 thu 2025

    jun 13 fri 2025

    		WorkShop
    Financial education – why, what works, what doesn't and for whom
    06/12/2025 - 06/13/2025
    logo matematica
    • WORKSHOP
    • EDUFIN25
    • organizers
      Emilio Barucci
    • The objective of the conference is twofold: the first is to analyse the importance of financial literacy in supporting financial well-being, financial inclusion, financial market development and enabling a wider economic prosperity; the second is to review concrete experiences, comparing what worked and what didn't and for whom. The aim is to have an international conference on best practices in financial education with a multidisciplinary scientific approach involving academia and policy-makers.
    • Thursday, 12 June 2025 - Friday, 13 June 2025
      Politecnico di Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 12 thu 2025

    		Seminar
    Alberto Bressan, Modeling Traffic Flow,  06-12-2025, 15:30
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    • Seminar
    • Alberto Bressan
    • Penn State University
    • Modeling Traffic Flow
    • Thursday, 12 June 2025 at 15:30
    • aula U5-3014 del Dip. di Matematica e Applicazioni, Università Bicocca
    • Abstract
      The talk will survey various models of traffic flow, with particular focus on new mathematical problems arising from some of these models. A large literature is currently available on particle models, describing the position of every car in terms of a large number of ODEs, and macroscopic models, where the traffic density is determined by a PDE.
      Vehicular traffic can also be analyzed from the point of view of decision theory. Indeed, daily traffic patterns arise as the outcome of the decisions of a large number of drivers, who choose their departure time and route to destination in an ``optimal" way. Some recent work and open problems will be discussed.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 23 mon 2025

    jun 27 fri 2025

    		WorkShop
    29th international conference on domain decomposition methods
    06/23/2025 - 06/27/2025
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    • WORKSHOP
    • DD29
    • organizers
      Paola F. Antonietti, Lourenco Beirao da Veiga, Silvia Bertoluzza, Michele Botti, Claudio Canuto, Gabriele Ciaramella, Paola Gervasio, Luca Pavarino, Alfio Quarteroni, Simone Scacchi, Christian Vergara
    • The purpose of the meeting is to discuss recent developments in various aspects of domain decomposition methods, bringing together mathematicians, computational scientists, and engineers working on numerical analysis, scientific computing, high-performance computing, machine learning, and computational science with industrial and societal applications. This event is part of the activities of the Department of Exellence 2023-27.
    • Monday, 23 June 2025 - Friday, 27 June 2025
      Politecnico di Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 30 mon 2025

    jul 04 fri 2025

    		WorkShop
    Differential geometry @ l'aquila 2025
    06/30/2025 - 07/04/2025
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    • WORKSHOP
    • organizers
      Lucio Bedulli, Luciano Mari, Giuseppe Pipoli, Mario Santilli, Alberto Roncoroni, Luigi Vezzoni
    • The aim of the workshop is to focus on different recent advances in differential geometry and its applications, with particular emphasis on riemannian, metric and global differential geometry, theory of submanifolds and geometric flows.
    • Monday, 30 June 2025 - Friday, 4 July 2025
      Università degli Studi dell'Aquila
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jul 01 tue 2025

    		Seminar
    Florian Fischer, Optimal Poincaré-Hardy inequalities on graphs,  07-01-2025, 14:15
    logo matematica
    • Seminar
    • Florian Fischer
    • University of Bonn
    • Optimal Poincaré-Hardy inequalities on graphs
    • Tuesday, 1 July 2025 at 14:15
    • Aula Seminari III Piano
    • Abstract
      We review a method to obtain optimal Poincaré-Hardy inequalities on the hyperbolic spaces by Berchio, Ganguly and Grillo. Then we show how to transfer the basic idea to the discrete setting. This yields optimal Poincaré-Hardy-type inequalities on model graphs which include fast enough growing trees and anti-trees. Moreover, this method yields optimal weights which are larger outside of a ball than the optimal weights constructed via the Fitzsimmons ratio of the square root of the minimal positive Green's function. Joint work with Christian Rose.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jul 07 mon 2025

    jul 11 fri 2025

    		WorkShop
    New perspectives in nonlocal and nonlinear pde
    07/07/2025 - 07/11/2025
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    • WORKSHOP
    • organizers
      José Antonio Carrillo (Univ. of Oxford), Antonio Esposito (Univ. dell'Aquila), Filomena Feo (Univ. "Parthenope"), Giuseppe Savarè (Univ. Bocconi), Bruno Volzone (Politecnico di Milano)
    • The goal of this workshop is to gather researchers working in the field of Partial Differential Equations with expertise in nonlocal and nonlinear equations. Among others, one of the simplest mathematical ways to describe many real-world problems is to start from a set of interacting particles, resulting in nonlocal and nonlinear PDEs in the many-particle limit. Despite the past progress in this field, recent discoveries in biology, plasma physics, and data science, among others, shed the lights on new challenges involving nonlocal structures, such as networks or graphs, and highly nonlinear and singular aggregation-diffusion equations. During the workshop we will focus on various mathematical issues in this direction, for instance: micro-macro description of diffusion process, evolutions on graphs, fluxes with nonlinear mobility, fourth-order aggregation-diffusion equations, etc. This workshop is partially funded by the Advanced Grant Nonlocal-CPD: "Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization" of the European Research Council Executive Agency (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 883363).
    • Monday, 7 July 2025 - Friday, 11 July 2025
      Anacapri
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jul 15 tue 2025

    jul 16 wed 2025

    		WorkShop
    Workshop 2025 - digimath il ruolo delle tecnologie digitali a supporto della didattica della matematica: esperienze di buone pratiche a livello universitario
    07/15/2025 - 07/16/2025
    logo matematica
    • WORKSHOP
    • DIGiMATH
    • organizers
      COMITATO SCIENTIFICO Domenico Brunetto Monica Conti Michele G. Fiorentino Annamaria Miranda COMITATO ORGANIZZATORE Caterina Bassi Domenico Brunetto Monica Conti Helena Dell'Anna
    • Il gruppo UMI DIGiMATH lavora per favorire lo sviluppo della cultura digitale per l'innovazione dei processi di insegnamento e apprendimento della matematica a livello universitario. Lo scopo del workshop è quello di confrontare e discutere le esperienze già in atto nelle università italiane di pratiche e ricerche sull’uso delle tecnologie digitali nella didattica della matematica e promuovere lo sviluppo di collaborazioni tra ricercatori in didattica della matematica e in altre aree della matematica per la definizione di pratiche e ricerche congiunte. I temi di discussione includono quelli già individuati da DIGiMATH e quelli emersi dal precedente Workshop - difficoltà, progettazione, valutazione, individualizzazione/personalizzazione - declinati lungo i tre contesti di transizione scuola/università, corsi di base di matematica, formazione insegnanti (iniziale e in continuo). Lo stile della giornata sarà improntato a favorire la discussione e la collaborazione tra i partecipanti, pertanto sarà dato ampio spazio al confronto e all’elaborazione delle idee. Inoltre, a chiusura del workshop ci sarà una sessione di brainstorming di programmazione di future attività di DIGiMATH.
    • Tuesday, 15 July 2025 - Wednesday, 16 July 2025
      Aula Laboratorio FDS
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • sep 08 mon 2025

    sep 11 thu 2025

    		WorkShop
    Perspectives in geometric analysis
    09/08/2025 - 09/11/2025
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    • WORKSHOP
    • PGA25
    • organizers
      Giovanni Catino, Dario D. Monticelli, Alberto Roncoroni
    • The aim of the workshop is to focus on different recent advances in geometric analysis and its applications.
    • Monday, 8 September 2025 - Thursday, 11 September 2025
      Aula Consiglio - 7th floor
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • sep 18 thu 2025

    		MOX Colloquia
    Malgorzata Peszynska, Multi-* mathematics and simulations of coupled processes the Arctic,  09-18-2025, 14:00
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    MOX

    • MOX Colloquia
    • Malgorzata Peszynska
    • Department of Mathematics, Oregon State University
    • Multi-* mathematics and simulations of coupled processes the Arctic
    • Thursday, 18 September 2025 at 14:00
    • Sala Consiglio, Edificio 14, Politecnico di Milano
    • Abstract
      We present our joint work with many collaborators on multi-physics and multiple scales, with focus on processes in  the Arctic, a vast and complex environment of great current interest, with physical models sharing some (but not all) features with high alpine environments and other cold regions.  Our interest is in robust, accurate and conservative computational schemes for the multi-physics: thermal, flow and mechanical deformation (TpHM) in the snow, ice and soils responding to the forcings from the environment for which the data is sparse. The models account for multiple phases and components and present challenges due to the presence of free boundary e.g. of freezing/thawing/sublimation, strong dependence of constitutive parameters on the micro-physics of TpHM, disparate time scales, and micro- and macro heterogeneity. We show how to build constitutive relationships for Darcy scale models from the first principles at the interface- and pore-scale by a combination of mathematically rigorous theory, practical computational upscaling, and surrogate data science tools. We illustrate with simulations of practical scenarios.

      Contatto:
      alessio.fumagalli@polimi.it
    • Malgorzata Peszynska

      Malgorzata Peszynska

      Malgorzata Peszynska received her Ph.D. in Mathematics from University of Augsburg, and M.S. and Habilitation from Warsaw University of Technology. She held academic positions at Polish Academy Of Sciences, Warsaw University of Technology, Purdue University, and The University of Texas at Austin. She has been at Oregon State since 2003 as a full professor since 2012. In 2019-21 she served as a Program Director at the NSF DMS (National Science Foundation, Division of Mathematical Sciences). She is a 2024 University Distinguished Professor, 2022-24 Joel Davis Faculty Scholar, AAAS Honorary Fellow; 2021 SIAM Geosciences Career Prize recipient; 2017 Kosciuszko Foundation College of Eminent Scientists, and holder of OSU Mathematics Graduate mentoring award (2016), Joel Davis Excellence award (2016). She is a 2009-10 Fulbright Research Fellow, as well as Mortar Board professor (2004). She believes in "paying it forward" : M. Peszynska also held leadership and service positions at SIAM (Society for Industrial and Applied Mathematics) including President of SIAM Pacific Northwest Section (2018-20) and SIAM Geosciences (2009-10) and AWM (Association for Women in Mathematics), is serving on editorial boards for 4+ journals, and on the Executive Board of Pacific Math Alliance. She directed several postdocs, doctoral, masters and undergraduate students; see MP people. Her research is in broadly defined applied and computational mathematics modeling of real life phenomena, with foundations in analysis and other core mathematics, and with interdisciplinary applications and collaborations in geosciences (hydrology and oceanography), engineering, and material science.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • oct 09 thu 2025

    		MOX Colloquia
    Mark Girolami, Statistical Finite Element Methods,  10-09-2025, 14:00
    logo matematica
    MOX
    MOX Numeth

    • MOX Colloquia
    • Mark Girolami
    • University of Cambridge
    • Statistical Finite Element Methods
    • Thursday, 9 October 2025 at 14:00
    • Aula Consiglio - VII piano
    • Abstract
      The finite element method (FEM) is one of the great triumphs of applied mathematics, numerical analysis and software development. Recent developments in sensor and signalling technologies enable the phenomenological study of complex natural and physical systems. The connection between sensor data and FEM has been restricted to solving inverse problems placing unwarranted faith in the fidelity of the mathematical description of the system under study. If one concedes mis-specification between generative reality and the FEM then a framework to systematically characterise this uncertainty is required. This talk will present a statistical construction of the FEM which systematically blends mathematical description with data observations by endowing the Hilbert space of FEM solutions with the additional structure of a Probability Measure.
    • Mark Girolami

      Mark Girolami

      Mark Girolami is the Sir Kirby Laing Professor of Civil Engineering within the Department of Engineering at the University of Cambridge where he also holds the Royal Academy of Engineering Research Chair in Data Centric Engineering. Prior to joining the University of Cambridge Professor Girolami held the Chair of Statistics in the Department of Mathematics at Imperial College London. He is the Chief Scientist of the Alan Turing Institute, which is the UK national institute for Data Science and AI. Professor Girolami is an elected fellow of the Royal Academy of Engineering and the Royal Society of Edinburgh, he was an EPSRC Advanced Research Fellow (2007-2012), an EPSRC Established Career Research Fellow (2012-2018), a recipient of a Royal Society Wolfson Research Merit Award, and in 2023 was awarded the Guy Medal in Silver by the Royal Statistical Society. He delivered the IMS Medallion Lecture at the Joint Statistical Meeting 2017, and the Bernoulli Society Forum Lecture at the European Meeting of Statisticians 2017.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • oct 16 thu 2025

    		MOX Colloquia
    Colin Cotter, Compatible finite elements for numerical weather prediction,  10-16-2025, 14:00
    logo matematica
    MOX

    • MOX Colloquia
    • Colin Cotter
    • Imperial College
    • Compatible finite elements for numerical weather prediction
    • Thursday, 16 October 2025 at 14:00
    • Sala Consiglio, Dipartimento di Matematica, Politecnico di Milano
    • Abstract
      I will discuss the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's “C-grid” finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this talk I focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz decomposition, which has been used to exclude the possibility of several types of spurious oscillations from linear equations of geophysical flow. This means that compatible finite element spaces provide a useful framework for building dynamical cores. In this talk I will introduce the main concepts of compatible finite element spaces, and discuss their wave propagation properties. I will then cover a selection of the following topics (depending on recent advances, and interests of the audience): practical application to numerical weather prediction and ocean models, structure preserving methods, and scalable iterative solver techniques.
    • Colin Cotter

      Colin Cotter

      Colin Cotter is Professor of Computational Mathematics at Imperial College, researching numerical analysis and scientific computing focusses on the design, analysis and implementation of numerical methods and data assimilation algorithms for weather forecasting, ocean modelling and climate simulation. His work on compatible finite element methods underpins the next generation Met Office forecast modelling system. He has co-authored over 100 journal publications, and co-authored a book with Sebastian Reich on data assimilation published by Cambridge University Press. He has served on the editorial board of three journals. He was awarded a PhD in Mathematics at Imperial in 2004 under the supervision of Sebastian Reich, and subsequently held positions in the departments of Earth Science and Engineering and Aeronautics before rejoining the department of Mathematics in 2014, where he is is currently the head of Applied Mathematics in the Department of Mathematics at Imperia, and is co-Director of the UCL/Imperial EPSRC Centre for Doctoral Training in Collaborative Computational Modelling at the Interface.

    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568