Ultrafilters and Ultraproducts Across Mathematics, and Related Topics
Pisa _ June 6/11 _ 2022

UltraMath 2022

UltraMath 2022 /
Scientific Committee

Vitaly Bergelson (Ohio State University, USA)
Andreas Blass (University of Michigan, USA)
Mauro Di Nasso (Università di Pisa, Italia)
Renling Jin (College of Charleston, USA)

UltraMath 2022

UltraMath 2022 /
Organizing Committee

Mauro Di Nasso (Università di Pisa, Italia) – chair
Lorenzo Luperi Baglini (Università di Milano, Italia)

Local organizers: Rosario Mennuni, Moreno Pierobon, Mariaclara Ragosta.

EMAIL: ultramath2022@cs.dm.unipi.it

After two years of postponement, this 2022 edition will be held with the physical presence of lecturers and participants. All participants will be able to exchange information on their research, and also socialize in a welcoming environment.
We will make every effort to ensure that this is done safely and, to this end, we will follow the safety protocols established by the University of Pisa.

Please check this web site for updates.

UltraMath 2022 / Supported by

Ph: Davide Chionna. Click here to download a high quality version of this picture.

UltraMath 2022 /

The international Conference “ULTRAMATH 2022” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts.

Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems.
Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics.
This is the second edition of “UltraMath”, after the one held in Pisa in 2008. [link]
The previous edition of “UltraMath” originated a volume that was published in the Contemporary Mathematics Series of the AMS. [link]

The covered topics include (but are not limited to):

  • Additive and Combinatorial Number Theory.
  • Combinatorics and Ramsey Theory.
  • Algebra and Geometry.
  • General Topology.
  • Measure Theory.
  • Ergodic Theory and Dynamics.
  • Functional Analysis and Metric Spaces.
  • Nonstandard Analysis and Model Theory.
  • Generalized Spaces and Differential Equations.
  • Set Theory.

Greater prominence will be given to those results that satisfy (most of) the following conditions:

  • The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician.
  • The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results.
  • The results connect different areas of mathematics.
  • The results reveal new facets of known important topics.

The ULTRAMATH2022 conference promotes gender equality.


Registrations are now closed (please contact ultramath2022@cs.dm.unipi.it).

call for papers

The call for papers is now closed.


The deadline for submitting grant applications has now expired.

Mailing list

If you want to be included in our mailing list, please send us an email to ultramath2022@cs.dm.unipi.it.

conference poster

You can download the ULTRAMATH 2022 poster from this link.

supported by

P.R.I.N. “Mathematical Logic: models, sets, computability”
Università di Milano

P.R.A. Università di Pisa “Sistemi dinamici in logica, geometria, fisica matematica, e scienza delle costruzioni”.

under the auspices of

AILA (Associazione Italiana di Logica e Applicazioni)


On June 6-7-8, the conference site will be “Polo Congressuale Le Benedettine”: http://en.residence.unipi.it/home_en/
The second part of the program on June 10-11 will be held at “Aula Magna Pontecorvo”, Largo Bruno Pontecorvo 3, next to the Math Department.

Registration will start on Sunday, June 5, at 5 pm at “Polo Congressuale Le Benedettine”, followed by a welcome cocktail, starting 6 pm. Registration will continue in the morning of Monday, June 6.

There will be morning sessions and afternoon sessions on Monday June 6, Tuesday June 7, Wednesday June 8, and Friday June 10. The last session of talks is scheduled for the morning of Saturday June 11. There will be a closing cocktail on June 11, starting at about 13:00.
The whole day of Thursday June 9 is reserved for social activities.
The social dinner will be on Friday June 10, 20:00 at Ristorante la Pergoletta (three different menus will be available: meat, fish, veg).

Final list of invited speakers

  • Vieri Benci — Università di Pisa, Italia
  • Vitaly Bergelson — Ohio State University, USA
  • Natasha Dobrinen — University of Denver, USA
  • Cornelia Druţu — University of Oxford, UK
  • Neil Hindman — Howard University, USA
  • Michael Hrušák — Universidad Nacional Autónoma, México
  • Renling Jin — College of Charleston, USA
  • Imre Leader — University of Cambridge, UK
  • Steven Leth — University of Northern Colorado, USA
  • Martino Lupini — Newcastle University, UK
  • Joel Moreira — University of Warwick, UK
  • Florian Richter – EPFL, Switzerland
  • Sławomir Solecki — Cornell University, USA
  • Dona Strauss — University of Hull, UK

The invited speakers who will not be able to come to Pisa are:

Andreas Blass, Artem Chernikov, Isaac Goldbring, C. Ward Henson, Jaroslav Nešetřil, David A. Ross, Stevo Todorcevic, Luca Zamboni.

These speakers have the possibility to send a video of their talk (up to 45 minutes long), which will be linked here.

Andreas Blass: Ultrafilters containing intersections

Isaac Goldbring: A nonstandard proof of the spectral theorem for unbounded self-adjoint operators

David Ross: Asymptotic fixed points and theorems of Du Bois-Reymondand Hadamard

FINAL LIST OF CONTRIBUTED SPEAKERS: Agostini, Arruda, Bowen, Chevalier, Chodounsky, De, De Bondt, Eleftheriadis, Eskew, Garcia, Hosseini, Hubicka, Ivan, Japon, Juhasz, Patra, Konecny, Massas, Meir, Shaikh, Sobot, Spadaro.

The contributed speakers who will not be able to come to Pisa are: Kumduang, Lipparini, Saveliev, Shroff. These speakers have the possibility to send a video of their talk (up to 25 minutes long), which will be linked here.

Thodsaporn Kumduang: An application of linear formulas to the fundamental theorem of ultraproduct

Call for papers

The call for papers is now closed.

Participants are invited to submit abstracts. The submission deadline is Monday, March 21.
Decisions on acceptance will be communicated to the authors by Tuesday, April 5.
To submit an abstract, attach it to an email to the Congress address: ultramath2022@cs.dm.unipi.it specifying “Submission” in the subject.

Please follow these instructions:

  • Abstracts should be written in LaTeX (also plain text files are ok).
  • Please, avoid as much as possible the use of your own macros or external packages.
  • Abstracts must fit on at most one page when processed.
  • Clearly indicate your name, affiliation, and email address (in case of multiple authors, please indicate who will present the paper, and include names, affiliation, and email addresses of all authors).
  • Specify which one(s) of the main topics of the Conference best describes the subject of your abstract:
  1. Additive and Combinatorial Number Theory.
  2. Combinatorics and Ramsey Theory.
  3. Algebra and Geometry.
  4. General Topology.
  5. Measure Theory.
  6. Ergodic Theory and Dynamics.
  7. Functional Analysis and Metric Spaces.
  8. Nonstandard Analysis and Model Theory.
  9. Generalized Spaces and Differential Equations.
  10. Set Theory.


The deadline for submitting grant applications has now expired.

Graduate students, young researchers, and contributors from disadvantaged areas are invited to apply for financial support. Applications will be processed by the Scientific Committee, and the number and size of assigned grants will depend on the funds available. Please note that funds will be in any case limited.

Grants will provide support to cover, probably only in part, the expenses for travel and/or accommodation and/or food.

The deadline for grant applications is Monday March 21. Applicants will be notified by Tuesday April 5.

Submit your application by email to the Conference address: ultramath2022@cs.dm.unipi.it indicating “Financial support” in the subject. Please strictly follow these instructions:

  • Specify which of the following qualifications apply to you : (1) Graduate Student; (2) Young researcher; (3) Contributor from a disadvantaged area. (You may specify more than one.)
  • If you are a graduate student, ask your advisor to send us a recommendation letter by email.
  • If you are a young researcher, include a short CV, and attach the abstract of the talk that you are willing to contribute.
  • If you are from a disadvantaged area, include a short CV, specifying your current affiliation.
  • Indicate the minimum level of support that would be necessary for you to be able to attend ULTRAMATH 2022. (This means that without this you would not be able to participate.)
  • DO NOT send us any .doc attachment (nor any other proprietary format), but only use plain text or public formats (.txt, .tex., html, .pdf, .ps).
  • Provide any additional information that you think may help the Scientific Committee in their allocation of grants for ULTRAMATH.


Registration is now closed.



book of abstracts

You can download the book of abstracts here.

downloadable schedule

A downloadable version of the schedule of talks is available here.



Opera della Primaziale Pisana (The Leaning Tower), museum and tickets: www.opapisa.it.
Azienda Promozione Turismo Pisa (Tourist Office): www.turismo.pisa.it.


  • Lungo Arno

reaching pisa

Pisa International Airport “Galileo Galilei”
is conveniently located close to the city center (about 1.5 Km). For information about links and timetables, visit the airport web site: www.pisa-airport.com.

Florence Airport “Amerigo Vespucci” is located close to center of Florence, at a distance of about 85 Km from Pisa. There are bus connections to “Firenze Santa Maria Novella” railway station, from where frequent connections to “Pisa centrale” station are available. For more information, visit the airport web site: www.aeroporto.firenze.it.

When reserving your ticket, we suggest you to double check with your agency whether your flight actually lands in Pisa Airport or in Florence Airport (sometimes, tickets generically indicate Pisa/Florence airport).


The “Pisa centrale” railway station is located at walking distance from the center of town. There are direct trains from Rome, Florence, Milan, Genoa and many other cities to “Pisa centrale”. For information about timetables, visit the web site: www.trenitalia.com.


From Monday to Wednesday, the conference will be held at Polo Congressuale Le Benedettine, located in Piazza S. Paolo a Ripa D’Arno, 16, Pisa. On Friday and Saturday, the conference will be held in Aula Magna Pontecorvo, located in Largo Bruno Pontecorvo 3, next to the Math Department. Both sites are within walking distance of the center of Pisa.

The organization of UltraMath 2022 is not involved in reservations of hotels.