Research Groups

GEOMETRY, ALGEBRA AND THEIR APPLICATIONS
ACTIVITY DESCRIPTION

The research group deals with various topics in algebra and geometry ranging from algebraic, (hyper)complex and differential geometry to commutative, homological and combinatorial algebra, alongside methods for studying graph and image reconstruction problems and more specific methods of algebraic and enumerative combinatorics or of a properly computational algebraic nature. The unification of methods and the unified vision of the various themes characterize the participation of the various members of the group in different types of projects and work, and are an essential feature in the development of the research themes.

Current research mainly focuses in the areas of

  • Algebraic geometry
  • Commutative and combinatorial algebra
  • Algebraic, complex and hypercomplex analysis
  • Differential geometry and geometric analysis
  • Geometric and combinatorial theory of groups and semigroups
  • Algebraic theory of automata and formal languages
  • Study of graphs using algebraic and combinatorial techniques
  • Geometric and discrete tomography
  • Homological algebra and representation theory

Satellite site: https://www.geometry-algebra.polimi.it

COMPONENTS OF THE GROUP
Upcoming events

  • jun 29 mon 2026

    jul 03 fri 2026

    		WorkShop
    Commutative algebra and algebraic geometry in milan
    06/29/2026 - 07/03/2026
    logo matematica
    • WORKSHOP
    • CAAG26
    • organizers
      A. Constantinescu, A. D'Alì, P. Lella, A. Sammartano
    • The conference will be focused on the interplay between topics in commutative algebra, such as syzygies and singularities, and topics in algebraic geometry, such as moduli spaces and rationality problems. Speakers Ayah Almousa (University of Kentucky) Benjamin Briggs (Imperial College London) David Eisenbud (UC Berkeley) Eleonore Faber (University of Graz) Gavril Farkas (Humboldt-Universität zu Berlin) Michele Graffeo (SISSA Trieste) Eloísa Grifo (University of Nebraska-Lincoln) Srikanth Iyengar (University of Utah) Joachim Jelisiejew (University of Warsaw) Patricia Klein (Texas A&M University) Margherita Lelli-Chiesa (Università degli Studi Roma Tre) Alex Massarenti (Università degli Studi di Ferrara) Irena Peeva (Cornell University) Claudia Polini (University of Notre Dame) Elisa Postinghel (Università degli Studi di Trento) Claudiu Raicu (University of Notre Dame) Ritvik Ramkumar (University of Notre Dame) Francesco Russo (Università degli Studi di Catania) Alexandra Seceleanu (University of Nebraska-Lincoln) Bernd Ulrich (Purdue University) Keller VandeBogert (University of Kentucky) Matteo Varbaro (Università degli Studi di Genova
    • Monday, 29 June 2026 - Friday, 3 July 2026
      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

  • aug 31 mon 2026

    sep 03 thu 2026

    		WorkShop
    Late summer conference in geometric analysis
    08/31/2026 - 09/03/2026
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    • WORKSHOP
    • organizers
      Luca Benatti, Mattia Fogagnolo, Alessandra Pluda, Marco Pozzetta, Alberto Roncoroni.
    • This event brings together an international group of specialists to discuss cutting-edge topics in Geometric Analysis, such as minimal surfaces, isoperimetric problems, Lorentzian geometry, general relativity, geometric evolution equations, and geometric problems in the calculus of variations. Our goal is to turn recent progress into meaningful exchanges, giving participants fresh insights and new techniques to use in their own research on open problems.
    • Monday, 31 August 2026 - Thursday, 3 September 2026
      Università degli Studi di Padova
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • oct 01 thu 2026

    		MOX Colloquia
    Rainer Helmig, Porous Media Free-Flow Coupling - From REV to Pore Scale and Back,  10-01-2026, 14:30
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    MOX

    • MOX Colloquia
    • Rainer Helmig
    • Professor Emeritus, University of Stuttgart
    • Porous Media Free-Flow Coupling - From REV to Pore Scale and Back
    • Thursday, 1 October 2026 at 14:30
    • Sala Consiglio, Edificio 14, Politecnico di Milano
    • Abstract
      Flow and transport processes in domains composed of a porous medium and an adjacent free-flow region appear in a wide range of industrial, bio-medical and environmental applications. Industrial applications range from flow in fuel cells to drying processes; possible bio-medical applications include the interplay of distribution processes in blood vessels and in the surrounding tissue. Applications in environmental systems include infiltration of overland flow during rainfall, groundwater contamination due to infiltrating pollutants and evaporation from soil.

      One of the key challenges for coupled free flow and porous-medium flow arises from the fact that the overall effective behaviour depends strongly on interface processes that occur on small spatial scales (pore scale), although the overall system of interest is often too large to resolve these processes explicitly in detail. REV-scale models are usually not able to capture all the relevant physical processes for such coupled systems. For the accurate description of interface phenomena, it is therefore necessary to develop model concepts that combine information gained through pore-scale and REV-scale models.

      The first part of the lecture includes the following items:
      -an explanation of relevant processes of mass, momentum and energy transfer at the interface between a free-flow and a porous-media system;
      -a presentation of conceptual models for coupled single-phase free flow and two-phase porous-medium flow with a detailed description of the models in the free flow and in the porous medium for the pore and REV scale;
      -comparison studies to show the advantages and disadvantages in relation to classical approaches; the coupling concepts are discussed on the basis of different technical or environmental issues.

      In the second part of the lecture I would very much like to discuss the results on the basis of various detailed use cases. These include e.g. aspects of soil evaporation, heat storage in porous media, self-cooling of turbines or the salinization of soils.


      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
    • Rainer Helmig

      Rainer Helmig

      Rainer Helmig is Professor Emeritus of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart, Germany. He gained his doctoral degree from the University of Hannover in 1993 and a the Habilitation degree from the University of Stuttgart in 1997. In 1995, he was awarded the renowned "Dresdner Grundwasserforschungspreis" for his doctoral thesis. From 1997 to 2000, he held a professorship at the Technical University of Braunschweig. He was co-founder and, from 2009 to 2011, President of "InterPore"; from 2007 to 2015, he was spokesman of the International Research Training Group "NUPUS - Nonlinearities and upscaling in porous media", and from 2018 to 2023 he was spokesman of the Collaborative Research Centre 1313 “Interface-Driven Multi-Field Processes in Porous Media: Flow, Transport and Deformation”. From 2007 to 2018, he was a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is member of Academy of Sciences, Academia Europaea, Heidelberg and acatech. In 2020, he was granted the AGU Fellowship of the American Geophysical Union. In 2022 he got the Honorary Degree of Doctor of Engineering at the Heriot-Watt University. He was awarded the Kimberly-Clark Distinguished Lectureship 2025 and in 2025 he was granted the SIAM Geosciences Career Prize.

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

  • nov 02 mon 2026

    nov 06 fri 2026

    		WorkShop
    Model reduction and surrogate modeling 2026
    11/02/2026 - 11/06/2026
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    • WORKSHOP
    • MORe2026
    • organizers
      Andrea Manzoni (Chair), Nicolò Botteghi, Luca Dede', Nicola Farenga, Nicola Rares Franco, Andrea Manzoni, Simona Perotto, Piermario Vitullo, Paolo Zunino (Organizing Committee)
    • This 5-day conference will bring together the international community of computational scientists, engineers, mathematicians, and domain experts from industry, the national laboratories and academia to address the topic of model reduction and surrogate modeling for high-dimensional complex systems.
    • Monday, 2 November 2026 - Friday, 6 November 2026
      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

  • nov 09 mon 2026

    nov 13 fri 2026

    		WorkShop
    Two workshops on mathematics for sustainability
    11/09/2026 - 11/13/2026
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    • WORKSHOP
    • M4E-M4H
      Two workshops on mathematics for sustainability
    • organizers
      M4H - Scientific Committee: Luca Dedè (SC chair), Pasquale Ciarletta, Francesca Ieva, Laura Maria Sangalli, Paolo Zunino; M4H - Organizing Committee: Francesco Regazzoni (OC chair), Francesca Bonizzoni, Ivan Fumagalli, Stefano Pagani, Andrea Signori; M4E - Scientific Committee: Simona Perotto (SC chair), Alessio Fumagalli, Andrea Manzoni, Daniele Marazzina, Edie Miglio, Simone Vantini, Marco Verani; M4E - Organizing Committee: Anna Scotti (OC chair), Michele Azzone, Michele Botti, Gabriele Ciaramella, Carlo De Falco, Ilario Mazzieri, Alessandra Menafoglio
    • The second edition of the initiative “Mathematics for Sustainability” will take place in November 2026, as part of the activities of the Department of Excellence, Department of Mathematics, Politecnico di Milano. The initiative is organized into two workshops: Mathematics for Planet Earth (M4E), November 9-11, 2026 Mathematics for our Health (M4H), November 11-13, 2026 Both events will be held at Politecnico di Milano (Leonardo Campus, Aula Rogers). Mathematics for Planet Earth aims to highlight the fundamental role of mathematics in understanding the challenges related to our planet. Presentations will cover several areas, including climate change, resource management, and conservation. Participants will have the opportunity to learn about state-of-the-art mathematical methodologies for understanding and preserving our planet. Mathematics for our Health brings together experts at the intersection of mathematics, data science, and medical research to explore innovative models for improving healthcare. The workshop will focus on how mathematical, computational, statistical, and machine learning techniques can support the development of precision medicine, optimize healthcare resource allocation, and improve the analysis and management of multimodal patient data. Further information is available on the events' webpages: https://www.mate.polimi.it/events/M4H26/ https://www.mate.polimi.it/events/M4E26/
    • Monday, 9 November 2026 - Friday, 13 November 2026
      Politecnico di Milano, Milan, Italy
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jul 05 mon 2027

    jul 09 fri 2027

    		WorkShop
    International conference on spectral and high-order methods
    07/05/2027 - 07/09/2027
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    • WORKSHOP
    • ICOSAHOM2027
    • organizers
      P.F. Antonietti, N. Parolini, M. Verani (Conference Chairs), C. Canuto, A. Quarteroni (Honorary Chairs), L. Beirao da Veiga, F. Bonizzoni, L. Dede’, I. Fumagalli, P. Gervasio, C. Marcati, L. Mascotto, I. Mazzieri, S. Perotto, G. Sangalli
    • Since 1989, the International Conference on Spectral and High-Order Methods (ICOSAHOM) has served as a leading international forum for researchers and practitioners working on the theoretical, computational, and applied aspects of high-order and spectral methods for solving differential equations. The 2027 edition of ICOSAHOM will be proudly hosted by Politecnico di Milano, bringing together experts from around the world to share the latest advances and foster new collaborations in this vibrant field. ICOSAHOM 2027 is a satellite meeting of the 11th International Congress on Industrial and Applied Mathematics (ICIAM), The Hague, The Netherlands, 12-16 July 2027.
    • Monday, 5 July 2027 - Friday, 9 July 2027
      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