PhD program on Mathematical Models and Methods in Engineering - Dipartimento di Matematica

General information

The Department of Mathematics of the Politecnico di Milano is hosting a PhD program in Mathematical Models and Methods in Engineering, aiming at training high level researchers in advanced areas of Pure and Applied Mathematics. The teaching activities include a broad range of possibilities designed for the PhD program. As a successful approach to practical applications depends on a deep understanding of real-world phenomena and knowledge of mathematical tools for their description and design, both modelling, methodological and theoretical aspects are included. Courses are offered in various areas of mathematics, and may vary every year.

Geometrindi e Matematindi (Luigi Serafini 2002)

Numerical simulation of blood flow in the heart
(courtesy of Prof. Alfio Quarteroni)

Objectives

The development of advanced technologies in Science and Engineering brings an increasing demand of advanced mathematical theories and methods, which in turn fosters the demand for education and training of skilled mathematicians in pure and applied research. The main scope of the Ph.D. course “Mathematical Models and Methods in Engineering” is to train high-level researchers in various fields of pure and applied mathematics.

Professional Opportunities

Expected professional placements for Ph.D. doctorates are: academic research in Italian or International Universities and Research Institutions, R & D divisions of private companies, study and research centers of public Agencies, financial and insurance Institutions.

Today's events

apr 16 tue 2024

Seminar
Jérémy Faupin & Sébastien Breteaux, Number of bound states for fractional Schrödinger operators, 04-16-2024, 14:15 precise
- Seminar
- Jérémy Faupin & Sébastien Breteaux
- Institut Élie Cartan de Lorraine - Université de Metz
- Number of bound states for fractional Schrödinger operators
- Tuesday, 16 April 2024 at 14:15 right
- Sala Consiglio, VII piano
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 16 tue 2024

Seminar
Barbara Guardabascio, Climate and environmental attention: a news-based composite indicator, 04-16-2024, 16:30 precise
- Seminar
- Barbara Guardabascio
- Università Perugia
- Climate and environmental attention: a news-based composite indicator
- Tuesday, 16 April 2024 at 16:30 right
- Politecnico di Milano Aula IV (accanto aula Rogers)
- Abstract
  
  The way people perceive the risks associated with climate change is influenced by scientific research, social awareness, and by media representation Boykoff [2011]. The effects of perception of climate risk extend beyond Environmental concerns and permeate decision-making processes in both economic and social policy.
  We believe that a composite index to measure climate attention, if well-constructed and robust, can provide valuable insights for policymakers and serve as a leading indicator in macroeconomic and financial analysis [Luxon, 2019]. The composite indicator proposed in this article is based on a novel methodology that evaluates the semantic relevance, and not the favorability, of selected keywords, each of them provided with a semantic score, based both on the number of appearances and on the interconnectedness with other words in the text corpus.
  Finally, the Benefit of the Doubt (BoD) aggregation strategy is adopted that takes advantage of a time-varying optimal weighting scheme. The index is compared to alternative approaches.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 16 tue 2024

Seminar
Viola Schiaffonati, L'etica dell'intelligenza artificiale fra vecchi problemi e nuove sfide, 04-16-2024, 17:30
- Seminar
- Viola Schiaffonati
- Politecnico di Milano
- L'etica dell'intelligenza artificiale fra vecchi problemi e nuove sfide
- Tuesday, 16 April 2024 at 17:30
- Aula Rogers e in collegamento webex su tiny.cc/mathseminars
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

Upcoming events

apr 17 wed 2024

Seminar
Eric Schippers, Conformal invariants and quadratic differentials, 04-17-2024, 17:00 precise
- Seminar
- Eric Schippers
- University of Manitoba, Winnipeg, Canada
- Conformal invariants and quadratic differentials
- Wednesday, 17 April 2024 at 17:00 right
- On-line (il link verrà reso disponibile il giorno stesso del seminario)
- Abstract
  
  A general principle in complex function theory is that functionals on classes of conformal maps are associated to quadratic differentials. Various theorems and techniques illustrate this principle. For example, the variational theory of M. Schiffer shows that extremal mappings map onto the image domain minus trajectories of a quadratic differential. In this talk, we associate functionals on bounded univalent functions to quadratic differentials with singularities. This functional is conformally invariant, monotonic, and bounded. Examples of particular inequalities (new and old) are given, arising from various choices of the quadratic differential.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 18 thu 2024

Seminar
Alessio D'Alì, Symmetry counts: an introduction to equivariant Hilbert and Ehrhart series, 04-18-2024, 13:00 precise
- Seminar
- Alessio D'Alì
- Politecnico di Milano
- Symmetry counts: an introduction to equivariant Hilbert and Ehrhart series
- Thursday, 18 April 2024 at 13:00 right
- Aula seminari III piano
- Abstract
  
  The Ehrhart series of a lattice polytope P is a combinatorial gadget that counts the number of lattice points of P and of its dilations. The Hilbert series of a simplicial complex S counts how many monomials supported on faces of S exist in each possible degree.
  The aim of this talk is to introduce equivariant versions of such constructions, where we are not just interested in counting but we also want to record how the action of a finite group affects such collections of lattice points or monomials.
  Inspired by previous results by Betke-McMullen, Stembridge, Stapledon and Adams-Reiner, we will investigate which extra combinatorial features of the group action give rise to "nice" rational expressions of the equivariant Hilbert and Ehrhart series, and how the two are sometimes related.
  This is joint work with Emanuele Delucchi (SUPSI and Pisa).
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 18 thu 2024

Seminar
François Delarue, Mean field control and games. Some prospects, 04-18-2024, 14:00
- Seminar
- François Delarue
- Université Côte d'Azur
- Mean field control and games. Some prospects
- Thursday, 18 April 2024 at 14:00
- aula U5 RATIO-3014 Dip di Matematica e Applicazioni - Università Milano - Bicocca
- Abstract
  
  I will first give a brief overview of the notion of mean-field control and games. In particular, I will focus on the Eulerian formulation, through the notion of master equation, which is a nonlinear PDE on the space of probability measures. This PDE is notoriously difficult to solve, at least in a classical sense, except in cases presenting a form of convexity or monotonicity in the argument of the measure. I will then present two problems outside the convex/monotonic framework: (i) non-convex mean-field control problems and their particle approximation, (ii) mean-field games subject to certain non-standard forms of common noise.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 18 thu 2024

Seminar
Elena Danesi, Strichartz estimates for the Dirac equation on compact manifolds without boundary, 04-18-2024, 15:00
- Seminar
- Elena Danesi
- Università di Padova
- Strichartz estimates for the Dirac equation on compact manifolds without boundary
- Thursday, 18 April 2024 at 15:00
- Aula seminari - III piano
- Abstract
  
  The Dirac equation on Rn can be listed within the class of dispersive equations, together with, e.g., the wave and Klein-Gordon equations. In the years a lot of tools have been developed in order to quantify the dispersion of a system. Among these one finds the Strichartz estimates, that are a priori estimates of the solutions in mixed Lebesgue spaces. For the flat case Rn they are known, as they are derived from the ones that hold for the wave and Klein-Gordon equations. However, when passing to a curved spacetime domain, very few results are present in the literature. In this talk I will firstly introduce the Dirac equation on curved domains. Then, I will discuss the validity of this kind of estimates in the case of Dirac equations on compact Riemannian manifolds without boundary. This is based on a joint work with Federico Cacciafesta (Università di Padova) and Long Meng (CERMICS-École des ponts ParisTech).
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 19 fri 2024

Seminar
Jérémy Faupin & Sébastien Breteaux, Number of bound states for fractional Schrödinger operators, 04-19-2024, 10:30 precise
- Seminar
- Jérémy Faupin & Sébastien Breteaux
- Institut Élie Cartan de Lorraine - Université de Metz
- Number of bound states for fractional Schrödinger operators
- Friday, 19 April 2024 at 10:30 right
- Sala Consiglio, VII piano
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 22 mon 2024

Seminar
Andrea Calignano, Emergence of Macroscopic Models from the BCS Theory of Superconductivity, 04-22-2024, 11:00
- Seminar
- Andrea Calignano
- Politecnico di Milano
- Emergence of Macroscopic Models from the BCS Theory of Superconductivity
- Monday, 22 April 2024 at 11:00
- Aula Seminari F. Saleri - VI piano
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 22 mon 2024

Seminar
Maxim Smirnov, Derived categories of G\P, 04-22-2024, 15:30 precise
- Seminar
- Maxim Smirnov
- Universität Augsburg
- Derived categories of G\P
- Monday, 22 April 2024 at 15:30 right
- Aula seminari III piano
- Abstract
  
  Starting from the pioneering works of Beilinson and Kapranov, derived categories of coherent sheaves on homogeneous varieties G/P have attracted a lot of attention over the last decades. We’ll begin by an introduction into this area and then discuss more recent developments related to Lefschetz exceptional collections, quantum cohomology and homological mirror symmetry.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

apr 23 tue 2024

Seminar
Filippo de Feo, SDEs on Hilbert Spaces: Slow-fast Systems of SPDEs, Stochastic Optimal Control with Delays and Applications to Economics and Finance, 04-23-2024, 10:00

Seminar
Filippo de Feo
Politecnico di Milano
SDEs on Hilbert Spaces: Slow-fast Systems of SPDEs, Stochastic Optimal Control with Delays and Applications to Economics and Finance
Tuesday, 23 April 2024 at 10:00
Sala Consiglio - VII piano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

may 02 thu 2024

Seminar
Federico Cornalba, Numerical and analytical aspects for stochastic equations from Fluctuating Hydrodynamics, 05-02-2024, 11:00
- Seminar
- Federico Cornalba
- University of Bath
- Numerical and analytical aspects for stochastic equations from Fluctuating Hydrodynamics
- Thursday, 2 May 2024 at 11:00
- Aula seminari - III piano. Zoom link: polimi-it.zoom.us/j/91570308862?pwd=Qy9pQy9JdEViVTJValAzN2tGbng3QT09
- Abstract
  
  Large-scale systems of interacting particles are ubiquitous, with applications ranging from thermal advection phenomena to gradient descent algorithms in machine learning. While the mean-field-limit (MFL) perspective allows to efficiently characterize the ‘average’ evolution of many such particles systems (usually via PDEs), it does not incorporate a macroscopic description of the particles’ intrinsic fluctuations. The theory of Fluctuating Hydrodynamics addresses this aspect by instead describing the particle systems via stochastic PDEs which enrich the underlying MFL dynamics.
  For a weakly interacting multi-species system, we will discuss the interplay between MFL dynamics and associated stochastic PDE, and show that numerical discretizations of the latter can approximate the particles’ fluctuations in an accurate and efficient way.
  Based on joint works with Julian Fischer (IST Austria), Jonas Ingmanns (IST Austria), Claudia Raithel (TU Dresden).
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 06 mon 2024

may 08 wed 2024

WorkShop
Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 18th edition
05/06/2024 - 05/08/2024
- WORKSHOP
- TAIR
  Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 18th edition
- organizers
  Paolo Dulio - Politecnico Milano, Paolo Finotelli – Université de Caen Normandie, Andrea Frosini - Universita' Firenze, Silvia Pagani - Universita' Cattolica,
- The aim of the Meeting is to share interdisciplinary aspects between the experimental and the mathematical research concerning image reconstruction, with a special focus on tomography and neuroscience
- Monday, 6 May 2024 - Wednesday, 8 May 2024
  Mathematics Department - 7th floor
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 06 mon 2024

may 10 fri 2024

WorkShop
The geometry of hilbert schemes of points
05/06/2024 - 05/10/2024
- WORKSHOP
- GHiSP
  The geometry of hilbert schemes of points
- organizers
  Michele Graffeo (SISSA), Paolo Lella (Polimi), Sergej Monavari (EPFL), Andrea T. Ricolfi (SISSA), Alessio Sammartano (Polimi)
- The Hilbert scheme is a classically studied moduli space, which parametrises closed subschemes with prescribed Hilbert polynomial in an ambient projective scheme. These moduli spaces where initially introduced by Grothendieck, but turned out to have a prominent rôle in many modern areas outside the realm of Algebraic Geometry: Mathematical Physics, Combinatorics, Theoretical Physics (just to mention some recent examples). Generalisations of the Hilbert scheme have a wide range of applications as well, such as nested Hilbert schemes (parametrising flags of closed subschemes), moduli spaces of framed sheaves and Quot schemes (parametrising quotient sheaves). The easiest example one can consider is the Hilbert scheme of points, which parametrises closed zero-dimensional subschemes of fixed length. Already in this case, the geometry of the moduli space is rich and intriguing, as it is in general considerably pathological. For instance, if the dimension of the ambient variety is 3, the Hilbert scheme of points is in general reducible, and for dimension larger than 4 its singularities can be as bad as possible. Hilbert schemes (and their generalisation) played an important role in the development of modern Enumerative Geometry. In fact, for a large and interesting class of cases, the Hilbert scheme of points is not smooth but carries a virtual fundamental class. Donaldson-Thomas theory deals precisely with the (virtual) invariants one can compute on the Hilbert schemes with respect to its virtual structure. Donaldson-Thomas theory is very rich and admits several layers of refinements, for example: cohomological, K-theoretical, elliptic, categorical, motivic and is predicted to match Gromov-Witten invariants. SPEAKERS Alessandra Bernardi, Gergely Bérczi, Nadir Fasola, Anthony Iarrobino, Joachim Jelisiejew, Tomasz Mandziuk, Cristina Manolache, Alina Marian, Rosa Maria Miro-Roig, Andrei Negut, Ritvik Ramkumar, Ilaria Rossinelli, Reinier F. Schmiermann, Roy Skjelnes
- Monday, 6 May 2024 - Friday, 10 May 2024
  BellaVista Relax Hotel, Levico Terme (TN), Italy
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 07 tue 2024

Seminar
Annalisa Panati, Fisica a teatro: lo strano caso di Wolfgang Pauli, 05-07-2024, 17:30
- Seminar
- Annalisa Panati
- Università di Tolone
- Fisica a teatro: lo strano caso di Wolfgang Pauli
- Tuesday, 7 May 2024 at 17:30
- Aula Rogers e in collegamento webex su tiny.cc/mathseminars
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 09 thu 2024

may 11 sat 2024

WorkShop
Quantum probability control and engineering
05/09/2024 - 05/11/2024
- WORKSHOP
- QPCE
  Quantum probability control and engineering
- organizers
  Franco Fagnola, Ameur Dhari, Federico Girotti, Matteo Gregoratti
- Scuola su QUANTUM PROBABILITY CONTROL AND ENGINEERING (3 minicorsi, 3 seminari)
- Thursday, 9 May 2024 - Saturday, 11 May 2024
  Sala riunioni VII piano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 24 fri 2024

Seminar
Francesco Vaccaro, Modelling of memristive devices for Bio-Inspired computing, 05-24-2024, 11:00
- Seminar
- Francesco Vaccaro
- Politecnico di Milano
- Modelling of memristive devices for Bio-Inspired computing
- Friday, 24 May 2024 at 11:00
- Aula Seminari F. Saleri - VI piano
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 29 wed 2024

Seminar
Paolo Cremonesi, La magia dei Computer Quantistici, 05-29-2024, 17:30
- Seminar
- Paolo Cremonesi
- Politecnico di Milano
- La magia dei Computer Quantistici
- Wednesday, 29 May 2024 at 17:30
- Aula T12 e in collegamento webex su tiny.cc/mathseminars
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 05 wed 2024

jun 07 fri 2024

WorkShop
Perspectives in pdes, global and functional analysis
06/05/2024 - 06/07/2024
- WORKSHOP
- Perspectives in pdes, global and functional analysis
- organizers
  Matteo Bonforte (Universidad Autónoma de Madrid, Spain) Matteo Muratori (Politecnico di Milano, Italy) Fabio Punzo (Politecnico di Milano, Italy) Alberto Setti (Università degli Studi dell'Insubria, Italy)
- This workshop aims at bringing together world experts from Analysis and Geometry, with a particular accent on the broad field of Partial Differential Equations and their applications. In particular, the main topics addressed lie at the interface between Global Analysis, Functional Analysis, Geometric Analysis and Differential Geometry. The meeting is held on the special occasion given by the 60th birthday of Gabriele Grillo, Professor of Mathematical Analysis at Politecnico di Milano since 2009.
- Wednesday, 5 June 2024 - Friday, 7 June 2024
  Università degli Studi dell'Insubria - Sede di Sant'Abbondio a Como
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 19 wed 2024

jun 21 fri 2024

WorkShop
Kickoff workshop of the erc synergy grant ''nemesis: new generation methods for numerical simulations''
06/19/2024 - 06/21/2024
- WORKSHOP
- NEMESIS Kickoff Workshop
  Kickoff workshop of the erc synergy grant ''nemesis: new generation methods for numerical simulations''
- organizers
  Paola F. Antonietti (Politecnico di Milano), Lourenco Beirao da Veiga (Università degli Studi di Milano-Bicocca), Daniele A. Di Pietro (Université de Montpellier), Jerome Droniou (CNRS)
- The ERC NEMESIS project has been funded in the 2023 Synergy call for a duration of six years. Its goal is to lay the groundwork for a novel generation of numerical simulators by tackling key difficulties of PDE problems of the 21st century: -Incomplete differential operators in Hilbert complexes; -The efficient solution of the discrete problems relating to the latter; -The presence of nonlinear and hybrid-dimensional multi-physics, encountered in applications such as geological flows or magneto-hydrodynamics. The NEMESIS project aims at overcoming the above difficulties, therefore boosting the prediction capabilities of numerical simulators in engineering and applied sciences. A key point will be the use of polytopal meshes and the higher-level point of view provided by polytopal constructions. This kick-off workshop will gather a community of mathematicians and engineers working in the broad field of the project, to foster exchanges and promote long-term collaborations.
- Wednesday, 19 June 2024 - Friday, 21 June 2024
  Montpellier (FR)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 02 tue 2024

MOX Seminar
Patrick Vega, An adaptive superconvergent mixed finite element method based on local residual minimization, 07-02-2024, 14:00
- MOX Seminar
- Patrick Vega
- Universidad de Santiago de Chile
- An adaptive superconvergent mixed finite element method based on local residual minimization
- Tuesday, 2 July 2024 at 14:00
- Aula Saleri
- Abstract
  
  We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal variable with an adaptive finite element method via residual minimization. Such a residual minimization procedure is performed on a local postprocessing scheme, commonly used in the context of mixed finite element methods. Given the local nature of that approach, the underlying saddle point problems associated with residual minimizations can be solved with minimal computational effort. We propose and study a posteriori error estimators, including the built-in residual representative associated with residual minimization schemes; and an improved estimator that adds, on the one hand, a residual term quantifying the mismatch between discrete fluxes and, on the other hand, the interelement jumps of the postprocessed solution. We present numerical experiments in two dimensions using Brezzi-Douglas-Marini elements as input for our methodology. The experiments perfectly fit our key theoretical findings and suggest that our estimates are sharp.
  
  Contatto:
  michele.botti@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 04 thu 2024

jul 05 fri 2024

WorkShop
Hpcsim - frontiers of high-performance computing in modeling and simulation
07/04/2024 - 07/05/2024
- WORKSHOP
- HPCSIM2024
  Hpcsim - frontiers of high-performance computing in modeling and simulation
- organizers
  Luca Formaggia, Paolo Cremonesi, Carlo de Falco, Ivan Fumagalli, Ilario Mazzieri, Nicola Parolini (Politecnico di Milano), Carlo Janna, Andrea Franceschini (Università di Padova), Nicolò Spiezia (M3E)
- HPCSIM aims to explore recent methodologies to accelerate simulation software on massively parallel platforms and provide researchers and practitioners with a survey on the potential of HPC in real-world applications. Registration at https://www.mate.polimi.it/events/HPCSIM24/"
- Thursday, 4 July 2024 - Friday, 5 July 2024
  Politecnico di Milano, Leonardo Campus - Aula Rogers
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
sep 09 mon 2024

sep 11 wed 2024

WorkShop
13th symposium on conformal and probabilistic prediction with applications
09/09/2024 - 09/11/2024
- WORKSHOP
- COPA 2024
  13th symposium on conformal and probabilistic prediction with applications
- organizers
  Simone Vantini (General Chair); Matteo Fontana (Programme Chair); Alfredo Gimenez Zapiola, Teresa Bortolotti, Khuong An Nguyen (Organizing Chairs); Francesca Ieva (Stakeholder Relation Chair)
- Conformal prediction (CP) is a modern machine and statistical learning method that allows to develop valid predictions under weak probabilistic assumptions. CP can be used to form set predictions, using any underlying point predictor, and for very general target variables, allowing the error levels to be controlled by the user. Therefore, CP has been widely used to develop robust forms of probabilistic prediction methodologies, and applied to many practical real life challenges. The aim of this symposium is to serve as a forum for the presentation of new and ongoing work and the exchange of ideas between researchers on any aspect of conformal and probabilistic prediction, including their application to interesting problems in any field.
- Monday, 9 September 2024 - Wednesday, 11 September 2024
  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
sep 19 thu 2024

MOX Colloquia
Jay Gopalakrishnan, From scalar to tensor finite elements, 09-19-2024, 14:00
- MOX Colloquia
- Jay Gopalakrishnan
- Portland State University
- From scalar to tensor finite elements
- Thursday, 19 September 2024 at 14:00
- Aula Consiglio VII piano - Dipartimento di Matematica
- Abstract
  
  In the history of finite elements, the earliest Lagrange finite elements, consisted of scalar-valued functions. To approximate fluxes, vector-valued finite elements with continuous normal (n) components across element interfaces, or n-continuous elements, were developed later. The finite element toolkit was then supplemented by t-continuous vector-valued Nedelec elements with continuous tangential (t) components, now routinely used for Maxwell equations. Although these elements were developed separately, today we understand them together as fitting into a cochain subcomplex of a de Rham complex of Sobolev spaces.
  Other tensor-valued finite elements are now being viewed with increasing interest and they form the main subject of this talk. The earliest of these consists of matrix-valued functions whose normal-normal (nn) component varies continuously across element interfaces: these are the nn-continuous matrix fields of the Hellan-Herrmann-Johnson element. More recently, nt-continuous matrix-valued finite elements were developed to approximate viscous stress in incompressible flows: they have continuous shear, or normal-tangential (nt) components. To add to this picture, matrix-valued elements with continuous tangential-tangential (tt) components, called Regge elements, are finding increasing utility: they are key to approximating the metric tensor of Riemannian manifolds. This talk delves into the details of these developments.
  How does one connect these disparate developments with nn-, nt-, and tt-continuous matrix finite elements? This does not appear to be as easy as the previous synthesis of vector-valued elements by the de Rham complex. The spaces in de Rham complexes are connected by fundamental first-order differential operators (grad, curl, and div in three dimensions), all derived from a single definition of the exterior derivative. In contrast, what is natural for the above-mentioned tensor finite elements are other second-order differential operators. We conclude grazing the frontiers of our understanding on potentially unifying connections.
  
  This initiative is part of the “Ph.D. 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 Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
  
  Contatti:
  paola.antonietti@polimi.it
  gabriele.ciaramella@polimi.it
  ilario.mazzieri@polimi.it
- Jay Gopalakrishnan
  Jay Gopalakrishnan is a computational mathematician whose research centers around improving accuracy and efficiency of finite element methods for partial differential equations. He co-invented two classes of numerical methods, now known as the discontinuous Petrov Galerkin (DPG) methods, and the hybridizable discontinuous Galerkin (HDG) methods. He has co-authored over ninety publications, has served in the editorial boards of seven journals, including service as one of the managing editors. He earned his PhD in 1999 under the supervision of James Bramble and Joseph Pasciak He then worked at Bell Labs, Medtronic Inc, University of Minnesota, and was a mathematics professor at University of Florida for over a decade. He currently holds an endowed chair at Portland State University in Oregon, where he is engaged in a variety of regional activities to bolster scientific computation.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 17 thu 2024

MOX Colloquia
Marc G. Genton, Exascale Geostatistics for Environmental Data Science, 10-17-2024, 14:00
- MOX Colloquia
- Marc G. Genton
- King Abdullah University of Science and Technology (KAUST), Saudi Arabia
- Exascale Geostatistics for Environmental Data Science
- Thursday, 17 October 2024 at 14:00
- Aula Consiglio VII piano - Dipartimento di Matematica
- Abstract
  
  Environmental data science relies on some fundamental problems such as: 1) Spatial Gaussian likelihood inference; 2) Spatial kriging; 3) Gaussian random field simulations; 4) Multivariate Gaussian probabilities; and 5) Robust inference for spatial data. These problems develop into very challenging tasks when the number of spatial locations grows large. Moreover, they are the cornerstone of more sophisticated procedures involving non-Gaussian distributions, multivariate random fields, or space-time processes. Parallel computing becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications. In this talk, I will explain how high-performance computing can provide solutions to the aforementioned problems using tile-based linear algebra, tile low-rank approximations, as well as multi- and mixed-precision computational statistics. I will introduce ExaGeoStat, and its R version ExaGeoStatR, a powerful software that can perform exascale (10^18 flops/s) geostatistics by exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, i.e., supercomputers. I will then describe how ExaGeoStat can be used to design competitions on spatial statistics for large datasets and to benchmark new methods developed by statisticians and data scientists for large-scale environmental data science.
  
  Contatti: laura.sangalli@polimi.it
- Marc G. Genton
  Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 21 thu 2024

MOX Colloquia
Klaus-Robert Müller, Machine Learning and AI for the Sciences: toward understanding, 11-21-2024, 14:00
- MOX Colloquia
- Klaus-Robert Müller
- Technische Universität Berlin
- Machine Learning and AI for the Sciences: toward understanding
- Thursday, 21 November 2024 at 14:00
- Aula Consiglio VII piano
- Abstract
  
  In recent years, machine learning (ML) and artificial intelligence (AI) methods have begun to play a more and more enabling role in the sciences and in industry. In particular, the advent of large and/or complex data corpora has given rise to new technological challenges and possibilities. In his talk, Müller will touch upon the topic of ML applications in the sciences, in particular in chemistry and physics. He will also discuss possibilities for extracting information from machine learning models to further our understanding by explaining nonlinear ML models. Finally, Müller will briefly discuss perspectives and limitations.
- Klaus-Robert Müller
  Klaus-Robert Müller has been a professor of computer science at Technische Universität Berlin since 2006; at the same time he is directing rsp. co-directing the Berlin Machine Learning Center and the Berlin Big Data Center and most recently BIFOLD . He studied physics in Karlsruhe from 1984 to 1989 and obtained his Ph.D. degree in computer science at Technische Universität Karlsruhe in 1992. After completing a postdoctoral position at GMD FIRST in Berlin, he was a research fellow at the University of Tokyo from 1994 to 1995. In 1995, he founded the Intelligent Data Analysis group at GMD-FIRST (later Fraunhofer FIRST) and directed it until 2008. From 1999 to 2006, he was a professor at the University of Potsdam. From 2012 he has been Distinguished Professor at Korea University in Seoul. In 2020/2021 he spent his sabbatical at Google Brain as a Principal Scientist. Among others, he was awarded the Olympus Prize for Pattern Recognition (1999), the SEL Alcatel Communication Award (2006), the Science Prize of Berlin by the Governing Mayor of Berlin (2014), the Vodafone Innovations Award (2017), Hector Science Award (2024), Pattern Recognition Best Paper award (2020), Digital Signal Processing Best Paper award (2022). In 2012, he was elected member of the German National Academy of Sciences-Leopoldina, in 2017 of the Berlin Brandenburg Academy of Sciences, in 2021 of the German National Academy of Science and Engineering and also in 2017 external scientific member of the Max Planck Society. From 2019 on he became an ISI Highly Cited researcher in the cross-disciplinary area. His research interests are intelligent data analysis and Machine Learning in the sciences (Neuroscience (specifically Brain-Computer Interfaces, Physics, Chemistry) and in industry.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568