International Programmes and Advanced Schools

Topological Methods in Mathematical Physics

74th School of Mathematics «Guido Stampacchia» and International Workshop, Majorana Foundation and Centre for Scientific Culture, September 2022

In 2022 I organised and directed the 74th School of Mathematics «Guido Stampacchia» and International Workshop on Topological Methods in Mathematical Physics at the Majorana Foundation and Centre for Scientific Culture in Erice (Sicily). The meeting received substantial financial support from the Department of Mathematics and Applications of the University of Milano-Bicocca (UniMiB), the Rector’s Office of UniMiB, and the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INFN). The conference hosted 38 contributions from experts coming from 12 different countries worldwide. All the contributions and the recorded talks were collected in the new form of electronic conference proceedings available on GEOTOP-A Events.

Launch of the Association for Mathematical Research (AMR)

A new world organization for the promotion of mathematical research and scholarship

As founding member of The Association for Mathematical Research (AMR), I contributed to the launch (in November, 2021) of this new, non-profit, volunteer-based organisation, to support mathematical research and scholarship worldwide. This is done through a broad spectrum of initiatives and services to the mathematical community. AMR stems from the free enterprise of mathematicians working in higher education institutions all over the world, with the aim to become a focal point for mathematical activities worldwide.


BJUT & Bicocca “Science-Silk Road” international meeting on Applications of Geometry and Topology to Topics of Modern Physics

BJUT & Bicocca on-line meeting

In January 2021 Xin Liu and I organised and chaired a 2-day meeting as an international joint venture between Beijing University of Technology (BJUT) and the University of Milano-Bicocca (UniMiB) to promote current research and collaboration between teams of the two universities. The meeting was entirely held in streaming. Speakers included Hao Guan (BJUT), Xinfei Li (Guangxi U. Science & Technology), Xin Liu (BJUT), Matteo Foresti (UniMiB), Alice Roitberg (UniMiB), Taliya Sahihi (UniMiB), Simone Zuccher (U. Verona), and myself.


First program on Knotted Fields in China

BJUT School, International Conference and Workshop on Knotted Fields

In September 2019 I chaired and organised with Xin Liu and Wenyu Wang (BJUT) an international advanced school on Knotted Fields. The School was held at the Beijing University of Technology (BJUT), and was part of a series of international events that included a conference in Beijing and a satellite workshop in Xi’an. Lecturers included Carlo Barenghi (U. Newcastle, UK), Mark Dennis (U. Birmingham, UK), Louis Kauffman (U. Illinois at Chicago, USA), Rob Scharaein (Hypnagogic, Canada), De Witt Sumners (Florida State U., USA), Paul Sutcliffe (U. Durham, UK) and myself. Lectures and conference contributions were broadcast live in China, and were attended in streaming by several thousands students from all over the Country.


From Algebraic Geometry to Geometric Topology – crossroads on applications

SIAM AG19 MiniSymposium on Algebraic Geometry and Geometric Topology, University of Bern, July 2019

In 2019 I organised with Jose-Carlos Gomez-Larrañaga (CIMAT, Mexico) and De Witt Sumners (FSU, USA) a mini-symposium on applications of Algebraic Geometry and Geometric Topology to mathematical sciences, covering topics that ranged from physics, to biology, from dynamical systems to topological data analysis. The meeting was held at the Mathematics Department of the University of Bern as a satellite event of the SIAM AG19 international conference held in Spain.


First graduate course on Topological Fluid Dynamics in China

The first Graduate Course on Topological Fluid Dynamics held in China sponsored by BJUT, September 2018

The first graduate course on Topological Fluid Dynamics was organised by myself in China, as a Guest Professor of Beijing University of Technology (BJUT). The course was sponsored by the Institute of Theoretical Physics and held at BJUT. It was attended by 40 students, some of whom came from as far afield as Shangai and Hong Kong. The lectures covered fundamental aspects and some recent progress, and lectures have been recorded and made available on various platforms (see the lecture series here).


GEOTOP-A : a global web-seminar series dedicated to the applications of geometry and topology

Launch of a new international web-seminar series denominated GEOTOP-A dedicated to the applications of Geometry and Topology, July 2018

A new international web-seminar series denominated GEOTOP-A, dedicated to the applications of Geometry and Topology, is launched in July 2018 thanks to the organisational efforts of Jose-Carlos Gomez-Larrañaga (CIMAT, Mexico), De Witt Sumners (Florida State U., USA), and myself. The seminars are broadcast world-wide (through the BlueJeans © platform) with the aim to provide and freely disseminate updated information on current research topics focused on modern applications of geometry and topology to mathematical sciences. Seminars can be attended in streaming (at 10 am Mexico City, 4 pm London, 12 pm Beijing time). They are then archived and made freely accessible for future reference on a dedicated channel. This initiative is intended to provide – free of charge – an international scientific platform to serve the pure interests of the international mathematics community at large (especially young researchers).

The current seminar series can be inspected here.

Proposals for topics and unsolicited contributions are welcome through the Inquiries web-page; interested researchers are invited to subscribe to the seminar mailing list by entering their email address with subject line subscribe.


Helicity, Structures and Singularity in Fluid and Plasma Dynamics

IUTAM Symposium on Helicity, Structures and Singularity in Fluid and Plasma Dynamics, Istituto Veneto di Scienze, Lettere ed Arti, April 2016

In 2016 I organised and directed the IUTAM Symposium on Helicity, Structures and Singularity in Fluid and Plasma Dynamics held at the Istituto Veneto di Scienze, Lettere ed Arti in Venice. The conference was organised also as a tribute to the achievements of Professor H.K. Moffatt, FRS (U. Cambridge University). The conference saw the participation of more than 100 experts from 20 different countries, and received financial support from the University of Milano-Bicocca (UniMiB), the Department of Mathematics and Applications of UniMiB, IUTAM and the International Center for Theoretical Physics (ICTP) of Trieste. The International Scientific Committee included Philip Boyland (U. Florida, USA), Jens Eggers (U. Bristol, UK), Marie Farge (ENS Paris, France), Yasuhide Fukumoto (Kyushu U., Japan), Tim Pedley FRS (U. Cambridge, UK), Michael Proctor FRS (U. Cambridge, UK), Katepalli Sreenivasan (New York U., USA), and myself.


Knots and Applications

Intensive research programme on Knots and Applications, “Ennio De Giorgi” Mathematical Research Center (CRM), May-July 2011

In 2011 I organised a 3-month intensive research programme on Knots and Applications at the Ennio De Giorgi Mathematical Research Center of the Scuola Normale Superiore in Pisa. The programme included a two-week long pedagogical school, hosting 10 internationally renown lecturers, 9 two-day workshops led by experts on different emerging fields, and an international conference, that I organised and directed, held under the auspices of the European Science Foundation, the European Mathematical Society, and INdAM (Italian National Institute for Higher Mathematics). The whole programme hosted more than 150 specialists from all over the world. For this I benefited from the active collaboration of several, long-time friends and colleagues, members of the the international scientific committee: Louis Kauffman (U. Chicago), Kenneth Millett (U. California at Santa Barbara), Carlo Petronio (U. Pisa), Dale Rolfsen (U. Vancouver) and De Witt Sumners (Florida State U.).

Advanced School, Workshops and Conference

Topological Fluid Mechanics

CIME Summer School on Topological Fluid Mechanics, June 2001

In 2001 I organised a CIME Summer School on Topological Fluid Mechanics.under the auspices of INdAM (Italian National Institute for Higher Mathematics), and UMI (Italian Mathematical Union). Mitch Berger, Louis Kauffman, Boris Khesin, Keith Moffatt, De Witt Sumners and many other senior participants contributed with lectures. The school was held in Cetraro (Italy), on the rugged coastline of the Mediterranean sea.


Geometry and Topology of Fluid Flows

Intensive research programme on Geometry and Topology of Fluid Flows, Isaac Newton Institute for Mathematical Sciences (INIMS), September-December, 2000

In the year 2000, UNESCO Year of Mathematics, I organised in collaboration with Hassan Aref, Tutsomu Kambe and Richard Pelz a 4-month intensive research programme on Geometry and Topology of Fluid Flows. The programme was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge (UK), and hosted several major events, including a NATO Advanced Study Institute workshop, a satellite workshop on singularities at MIR@W (Warwick U.) and a Royal Society Discussion Meeting in London, with additional daily seminars and thematic workshops. Themes ranged from to knot theory to topological dynamics, geometric mechanics, dynamical systems theory and emergent singularities in fluid flows.