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Just a brief update to the previous post. Gerhard Paseman and I have now set up a web site for the Short Communication Satellite (SCS) for the virtual International Congress of Mathematicians (ICM), which will be an experimental independent online satellite event in which short communications on topics relevant to one or two of the sections of the ICM can be submitted, reviewed by peers, and (if appropriate for the SCS event) displayed in a virtual “poster room” during the Congress on July 6-14 (which, by the way, has recently released its schedule and list of speakers). Our plan is to open the registration for this event on April 5, and start taking submissions on April 20; we are also currently accepting any expressions of interest in helping out with the event, for instance by serving as a reviewer. For more information about the event, please see the overview page, the guidelines page, and the FAQ page of the web site. As viewers will see, the web site is still somewhat under construction, but will be updated as we move closer to the actual Congress.

The comments section of this post would be a suitable place to ask further questions about this event, or give any additional feedback.

UPDATE: for readers who have difficulty accessing the links above, here are backup copies of the overview page and guidelines page.

*[As with previous posts regarding ICM satellite events, I am authoring this post as an individual, and not in my capacity as chair of the ICM Structure Committee, which does not have any advisory or supervisory role over ICM satellite events – T.]*

One of the traditional features of the International Congress of Mathematicians are the “short communications”, organized by the local organizing committee (as opposed to the International Mathematical Union), which allows participants at the congress to present either a poster or a short talk (typically 15 minutes or so) during the congress. For instance, here are the titles of the short communications and posters from the 2018 ICM, and here are the short communications and posters from the 2014 ICM. While not as high profile as other events of the ICM such as the plenary lectures, sectional lectures, or prize lectures, the short communications and posters can offer a chance for academics from a quite diverse range of institutions worldwide (and even a few independent mathematicians) be able to present their work to a mathematical audience.

There has been some volunteer effort to try to replicate some form of this event for the upcoming virtual ICM this July as a semi-official “satellite” event of the virtual ICM; it would technically not be part of the core ICM program, but I expect it would be recognized by the IMU as an independently organized satellite. Due to lack of time, funding, and technical expertise, we will not be able to offer any video, audio, or physical hosting for such an event, but we believe that a modest virtual event is possible involving submission of either a PDF “poster” or a PDF “slide deck”, together with other metadata such as author, title, abstract, and external links (e.g., to an externally hosted video presentation of the poster or slides), with some reviewing to ensure a certain minimum level of quality of approved submissions (we are thinking about setting guidelines similar to those required for a submission to the arXiv), and some ability to offer feedback on each submission. (For instance, we are thinking of hosting the event on a MediaWiki, with each communication being given a separate page which can attract discussion and responses to queries from the author(s).) We are also thinking of grouping the poster or slides according to the 20 sections of the 2022 ICM. We would then promote these communications during the virtual ICM, for instance on this blog or on the unofficial ICM Discord. Perhaps some of the other proposed online experiments for virtual events discussed in this previous post could also be implemented experimentally on this satellite event to demonstrate proof-of-concept. (If the event turns out to be successful, one could hope that it could serve as a pilot project for a longer-term and better funded platform for virtual short communications to accompany other conferences, but for now we would like to focus just on the virtual ICM satellite event.)

As one of our first actions, we would like to survey the level of interest in such an event, both among potential submitters of posters or slides, and also potential volunteers to help organize the event (in particular we may need some assistance in manually reviewing submissions, though we do plan to enlist peer reviewers by requiring submitters to rate and comment on other submissions in the same section). We have therefore created a form to (very unscientifically) gauge this level in order to decide on the scale of this project (or whether to attempt it at all). All readers of this blog are welcome to offer feedback through that form, or as a comment to this blog.

EDIT (Mar 29): a formal announcement will be made soon, but you can view a draft of the announcement here.

*[Note: while I happen to be the chair of the ICM Structure Committee, I am authoring this blog post as an individual, and not as a representative of that committee or of the IMU, as they do not have jurisdiction over satellite conferences. -T.]*

The International Mathematical Union (IMU) has just released some updates on the status of the 2022 International Congress of Mathematicians (ICM), which was discussed in this previous post:

- The General Assembly will take place in person in Helsinki, Finland, on July 3-4.
- The IMU award ceremony will be held in the same location on July 5.
- The ICM will take place virtually (with free participation) during the hours 9:00-18:00 CEST of July 6-14, with talks either live or pre-recorded according to speaker preference.

Due to the limited time and resources available, the core ICM program will be kept to the bare essentials; the lectures will be streamed but without opportunity for questions or other audience feedback. However, the IMU encourages grassroots efforts to supplement the core program with additional satellite activities, both “traditional” and “non-traditional”. Examples of such satellite activities include:

- “Traditional” satellite conferences, held in person at a time near the ICM. Several such satellite events had already been scheduled, and are now satellite events for the virtual ICM:
- 34th International Conference on Formal Power Series & Algebraic Combinatorics (July 18-22, India)
- Probability and Mathematical Physics (June 28-July 5, Finland)
- Geometric Representation Theory (June 27-July 2, Japan)
- Effective Methods in Algebraic Geometry (June 20-24, Poland)
- Recent Advances in Classical Algebraic Geometry (June 28-July 7, Poland)
- Operator Algebras, Dynamics and Groups (July 1-4, Denmark) [Note: several ICM speakers from Section 8 will present their lecture here.]
- Differential Geometry and its Applications (July 17-23, Czech Republic)
- Seminar Sophus Lie (June 12-19, Norway)
- 27th International Conference on Difference Equations and Applications (July 18-22, France)

- “Watch parties” or “mirror conferences” hosted by institutions and departments around the world.
- “Sectional overlay conferences”, in which ICM speakers from a specific section (or pair of sections) are invited to present their ICM talk in person in front of a live audience from that section. Some overlay conferences will be held concurrently with the ICM; others are planned to be held shortly beforehand, and the talks then supplied to the ICM as prerecorded talks. Of course, ICM speakers would not be obligated to attend these conferences (and several of these meetings may also schedule additional events not associated to the ICM). Currently we have the following such conferences:
- An ICM sectional workshop in number theory and algebraic geometry, ETH Zürich, July 11th–14th 2022, covering Sections 3 and 4 of the program.
- Geometry and Topology ICM sectional workshop, University of Copenhagen, July 6-14 2022, covering Sections 5 and 6 of the program.
- Representations and Characters: Revisiting the Works of Harish Chandra and André Weil, National University of Singapore, Jul 1-15, covering Section 7 of the program.
- Dynamics in Jerusalem, Hebrew University, July 6-8, covering Section 9 of the program.
- The aforementioned Probability and Mathematical Physics meeting in Finland on June 28-July 5 will also overlay Sections 11 and 12 of the program.
- Applied mathematics ICM overlay/satellite meeting, Imperial College London, July 8-12 2022, covering Sections 15 and 18 of the program.

- Regional satellite events, which would be similar to sectional overlay conferences but focused on a single geographical region rather than a section. Efforts are underway to set up such events in Australia, Boston, Bonn, Japan, and possibly Vietnam.
- Q&A sessions or online chats. A Discord channel has been set up (administered by Martin Hairer, Kevin Buzzard, and myself) to (unofficially) discuss the ICM lectures as they are being given; input is welcome on how best to utilize this channel.
- An online short communications satellite for the virtual ICM.
- The London Mathematical Society has kindly agreed to host the ICM public lectures (as well as the LMS lecture) as a virtual satellite event; details will be announced as they become available.
- Other creative examples of “non-traditional satellite events”. (For instance, one idea would be to create a wiki-type web site for the ICM in which speakers could supply introductory videos, slides, and other material for their talks; the IMU unfortunately does not have the logistical and technical capability to run this themselves, but one could imagine some third party being able to set this up instead.)

A more updated list of these events can be found here.

I will also mention the second Azat Miftakov Days, which are unaffiliated with the ICM but held concurrently with the beginning of the congress (and the prize ceremony).

Strictly speaking, satellite events are not officially part of the Congress, and not directly subject to IMU oversight; they also receive no funding or support from the IMU, other than sharing of basic logistical information, and recognition of the satellite conferences on the ICM web site. Thus this (very exceptional and *sui generis*) congress will differ in format from previous congresses, in that many of the features of the congress that traditionally were managed by the local organizing committee will be outsourced this one time to the broader mathematical community in a highly decentralized fashion.

In order to coordinate the various grassroots efforts to establish such satellite events, Alexei Borodin, Martin Hairer, and myself have set up a satellite coordination group to share information and advice on these events. (It should be noted that while Alexei, Martin and myself serve on either the structure committee or the program committee of the ICM, we are acting here as individuals rather than as official representatives of the IMU.) Anyone who is interested in organizing, hosting, or supporting such an event is welcome to ask to join the group (though I should say that most of the discussion concerns boring logistical issues). Readers are also welcome to discuss broader issues concerning satellites, or the congress as a whole, in the comments to this post. I will also use this space to announce details of satellite events as they become available (most are currently still only in the early stages of planning).

Jan Grebik, Rachel Greenfeld, Vaclav Rozhon and I have just uploaded to the arXiv our preprint “Measurable tilings by abelian group actions“. This paper is related to an earlier paper of Rachel Greenfeld and myself concerning tilings of lattices , but now we consider the more general situation of tiling a measure space by a tile shifted by a finite subset of shifts of an abelian group that acts in a measure-preserving (or at least quasi-measure-preserving) fashion on . For instance, could be a torus , could be a positive measure subset of that torus, and could be the group , acting on by translation.

If is a finite subset of with the property that the translates , of partition up to null sets, we write , and refer to this as a measurable tiling of by (with tiling set ). For instance, if is the torus , we can create a measurable tiling with and . Our main results are the following:

- By modifying arguments from previous papers (including the one with Greenfeld mentioned above), we can establish the following “dilation lemma”: a measurable tiling automatically implies further measurable tilings , whenever is an integer coprime to all primes up to the cardinality of .
- By averaging the above dilation lemma, we can also establish a “structure theorem” that decomposes the indicator function of into components, each of which are invariant with respect to a certain shift in . We can establish this theorem in the case of measure-preserving actions on probability spaces via the ergodic theorem, but one can also generalize to other settings by using the device of “measurable medial means” (which relates to the concept of a universally measurable set).
- By applying this structure theorem, we can show that all measurable tilings of the one-dimensional torus are
*rational*, in the sense that lies in a coset of the rationals . This answers a recent conjecture of Conley, Grebik, and Pikhurko; we also give an alternate proof of this conjecture using some previous results of Lagarias and Wang. - For tilings of higher-dimensional tori, the tiling need not be rational. However, we can show that we can “slide” the tiling to be rational by giving each translate of a “velocity” , and for every time , the translates still form a partition of modulo null sets, and at time the tiling becomes rational. In particular, if a set can tile a torus in an irrational fashion, then it must also be able to tile the torus in a rational fashion.
- In the two-dimensional case one can arrange matters so that all the velocities are parallel. If we furthermore assume that the tile is connected, we can also show that the union of all the translates with a common velocity form a -invariant subset of the torus.
- Finally, we show that tilings of a finitely generated discrete group , with a finite group, cannot be constructed in a “local” fashion (we formalize this probabilistically using the notion of a “factor of iid process”) unless the tile is contained in a single coset of . (Nonabelian local tilings, for instance of the sphere by rotations, are of interest due to connections with the Banach-Tarski paradox; see the aforementioned paper of Conley, Grebik, and Pikhurko. Unfortunately, our methods seem to break down completely in the nonabelian case.)

In this post I would like to collect a list of resources that are available to mathematicians displaced by conflict. Here are some general resources:

- The IIE Scholar Rescue Fund
- Scholars at Risk
- The New University in Exile Consortium programs for scholars
- (Europe) European fund for displaced scientists (a joint ALLEA-Breakthrough Prize Foundation partnership)
- (Brazil) The Sao Paulo Research Foundation has an initiative for Researchers at Risk.
- (Canada) Joint CRM-ISM initiative in support of mathematicians in distress
- (Canada) WES gateway program to assess educational credentials for displaced individuals
- (France) The French PAUSE program (National program for the urgent aid and reception of scientists and artists in exile)
- PAUSE has a special call for Ukrainian researchers at risk.

- (Germany) The Humboldt Foundation’s Philipp Schwartz initiative
- Special measures for the current crisis include postponing the deadline for applications to March 18 for Ukrainian scholars, and arrangements for current recipients from Russia who are threatened due to their critical attitude to the war to receive fellowship extensions.

- (UK) Cara – a lifeline to academics at risk
- (UK) Universities of Sanctuary network
- (UK) The Isaac Newton Institute for the Mathematical Sciences has a Solidarity list for researchers in the Mathematical Sciences, as well as a Solidarity for Mathematicians programme for displaced mathematicians.
- (UK) The University of Oxford Mathematical Institute has outreach sessions for Refugees and Asylum and Sanctuary Seekers to acclimate them to the academic environment in the UK.
- (USA) Harvard University’s Scholars at Risk (distinct from the preceding program of the same name)

There are also resources specific to the current crisis:

- Science for Ukraine
- See this web page for some background information on this initiative.

- Jobs for Ukraine
- Help for Displaced Ukrainian Mathematicians
- (Europe) The member universities of the Guild of European Research-Intensive Universities have a number of support measures for researchers, academics, and students affected by the war in Ukraine.
- (Europe) The European Research Centres on Mathematics (ERCOM) committee of the EMS has a number of offers of assistance to mathematicians who are refugees of the current war.
- (Europe) The EU agency EURAXESS has an initiative ERA4Ukraine that collects various support initatives for Ukrainian researchers.
- (North America) Opportunities in North America for Ukrainian Mathematicians
- (Austria) Austrian Academy of Sciences JESH academic mobility program – call for applications from Ukrainian researchers
- (Austria) FWF Austrian Science Fund has the Crisis Support for Researchers from Ukraine program.
- (Belgium) The KU Leuven program for researchers from the global South has relaxed its eligibility requirements for Ukrainian refugees.
- (Belgium) The Université libre de Bruxelles has implemented emergency procedures to welcome Ukrainian students who have fled or plan to flee Ukraine because of the war. Contact: helpukraine@ulb.be
- (Canada) A statement from the presidents of Canada’s federal research granting agencies to support Ukrainian research trainees (Additional contact: Lior Silberman lior@math.ubc.ca)
- (Canada) PIMS Mathematical Scientist Support Fund Program
- (Canada) NSERC Special Response Fund for Trainees (Ukraine)
- (Czechia) Announcement from the Czech Academy of Sciences (see also their “Help for Ukraine” page)
- (Czechia) Announcement from the Czech Science Foundation
- (Czechia) NF Neuron grant for Ukrainian scientists to study in the Czech republic
- (Finland) Call for grants for Ukrainian researchers in Finland
- (Finland) The University of Helsinki offers free courses at its Open University for citizens of Ukraine.
- (Germany) Opportunities in Germany for mathematicians from Ukraine (administered by the German Mathematical Society (DMV))
- (Germany) Support and assistance for Ukrainian students and scientists (administered by the German Academic Exchange Service (DAAD))
- (Germany) Funding for Refugee Scholars and Scientists from Ukraine by the Volkswagen Foundation (Additional contact: Delio Mugnolo delio.mugnolo@fernuni-hagen.de)
- (Germany) The Deutsch-Ukrainische Akademische Gesellschaft page on support for students and researchers from Ukraine
- (Germany) University of Muenster statement on Ukraine
- (Germany) Berlin Mathematics Research Center MATH+ Support for mathematicians for Ukraine
- (Luxembourg) The Luxembourg National Research Fund offers Temporary FNR support for Researchers who have fled the war in Ukraine.
- (Hungary) There are some resources available at the Renyi Institute in Hungary. Contact: Andras Stipsicz stipsicz.andras@renyi.hu
- (Poland) Science for Ukraine Action at AMU PAN (Polish Young Academy – Polish Academy of Sciences) Visits of Ukrainian scientists to the Polish Academy of Sciences
- This effort is also being supported by the National Academy of Sciences in the US via the Safe Passage Fund; more details here.

- (Poland) The National Science Center has a special program for researchers from Ukraine.
- (Sweden) The Swedish Foundation for Strategic Research has individual grants for Ukrainian scientists.
- (Sweden) The Royal Swedish Academy of Sciences announces scholarships for Ukrainian scientists to perform research in Sweden.
- (Taiwan) Taiwan is offering scholarships for Ukrainian students and scholars.
- (USA) The National Academy of Sciences has a page for resources supporting Ukraine’s scientists, engineers, and health care workers.
- (USA) The American Mathematical Society has a page on resources for displaced mathematicians.

Finally, there are a number of institutes and departments who are willing to extend visiting or adjunct positions to such displaced mathematicians:

- (Australia) The Sydney Mathematical Research Institute has launched a Visitor Program for Displaced Mathematical Scientists from Ukraine.
- (Austria) The Erwin Schrodinger Institute has a Special Research Fellowship for Ukrainian Scientists.
- (Brazil) IMPA offers a program in support of mathematicians affected by war or persecution.
- (Canada) Augusto Gerolin‘s research group at the University of Ottawa has PhD and postdoctoral positions available; Ukrainian students are highly encouraged to apply.
- (Denmark) AUFF-Ukraine research fellowships at AIAS, Aarhus University
- (Germany) MathCoRe at the Otto von Guericke University of Magdeburg supports visiting scientists affected by the current conflict. (Contact information contained in the link.)
- (Germany) Oberwolfach has a statement on Solidarity with Ukraine – support for Ukrainian scientists
- (Germany) Friedrich Alexander University (FAU) at Erlangen-Nuremberg has a page on assistance to Ukraine.
- (Israel) Tel Aviv University has launched an emergency fellowship fund for Ukrainian graduate students.
- (Israel) The Weizmann Institute of Science has a program to support visiting students and postdocs and encourages applications from Ukraine.
- (Israel) The Technion opened a specific budget to host undergraduate and graduate students, post-docs, and faculty from Ukraine. Contacts: Ms. Ortal Arazi Minyan ortala@int.technion.ac.il (for students) and Ms. Lisa Aisman lisa@technion.ac.il (for postdocs/faculty)
- (Israel) The Hebrew University of Jerusalem opened an emergency aid for researchers and students from Ukraine. The invitation is for a period of up to four months.
- (Israel) Ben Gurion University has a program for students and researchers affected by the war. Contact: oiaa@bgu.ac.il
- (Italy) Politecnico de Milano welcomes Ukrainian students and researchers.
- (Luxembourg) The University of Luxembourg offers support initiatives for displaced researchers and students from Ukraine.
- (Netherlands) Utrecht University has a page containing Support from the Mathematical Institute for students, lecturers and researchers from Ukrainian universities.
- (Poland) The Polish Academy of Sciences offers help to Ukrainian mathematicians, including accommodation and employment. Contact: mail.amu.pan@gmail.com
- (Poland) The Institute of Mathematics of the Polish Academy of Sciences (IMPAN) in particular offers such help to Ukrainian mathematicians. Contact: Piotr Achinger pachinger@impan.pl
- (Poland) The CS/math department of the University of Warsaw (MIMUW) also offers help. Contact: Piotr Achinger pachinger@impan.pl
- (Spain) A visiting position at the Universidad Carlos III de Madrid, aimed at Ukrainian nationals
- (USA) My home department at UCLA, in cooperation with IPAM, is likely to have a position available for such mathematicians. Contact: Dimitri Shylakhtenko shlyakht@math.ucla.edu
- (USA) An announcement from Columbia University
- (USA) The mathematics department at Indiana University, Bloomington has several positions. Contact: Kevin Pilgrim pilgrim@iu.edu
- (USA) The mathematics department at Michigan State University may have up to two positions for mathematics faculty who are displaced by the Ukrainian crisis. Applicants are encouraged to contact a faculty member at MSU who will support their nomination.
- (USA) The mathematics department at Johns Hopkins University has 2-3 one-year visiting positions for next year, and is willing to waive some of the required documents for such applications for displaced persons. Contacts: David Savitt savitt@jhu.edu and Emily Riehl eriehl@jhu.edu.
- (USA) MIT could accept a few Ukrainian/Russian mathematicians as visitors. Contact: Pavel Etingof etingof@math.mit.edu
- (USA) Georgia Tech has a program for displaced students.

If readers have other such resources to contribute (or to update the ones already listed), please do so in the comments and I will modify the above lists as appropriate.

As with the previous post, any purely political comment not focused on such resources will be considered off-topic and thus subject to deletion.

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