Leonid Ryvkin

Publications and Preprints

Scientific publications

Reduction of L-infinity-algebras of observables on multisymplectic manifolds, 2024, with Casey Blacker and Antonio Miti, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), also available at arXiv:2206.03137
On Dirac structures admitting a variational approach, Mathematics and Mechanics of Complex Systems, 2023 with Oscar Cosserat, Camille Laurent-Gengoux, Alexei Kotov and Vladimir Salnikov, availabvle at: arXiv:2109.00313
The holonomy of a singular leaf, with Camille Laurent-Gengoux, 2021, Selecta Mathematica, also available on the arXiv:1912.05286.
The L-infinity-algebra of a symplectic manifold, with Bas Janssens and Cornelia Vizman, 2021, the Pacific Journal of Mathematics, available on the arXiv:2012.03836.
The neighbourhood of a singular leaf, with Camille Laurent-Gengoux, 2021, Journal de l'École polytechnique.
On the extension problem for weak moment maps, with Leyli Mammadova, 2021, Homology, Homotopy and Applications, also available on the arXiv:2001.00264.
Multisymplectic actions of compact Lie groups on spheres, with Antonio Michele Miti, 2020, Journal of Symplectic Geometry.
An invitation to multisymplectic geometry, with Tilmann Wurzbacher, Journal of Geometry and Physics, 2019. Also on the arXiv.
Conserved quantities on multisymplectic manifolds, with Tilmann Wurzbacher and Marco Zambon, Journal of the Australian Mathematical Society, 2019. Also on the arXiv.
Observables and Symmetries of n-Plectic Manifolds , BestMasters. Springer Spektrum Verlag, Wiesbaden, 2016.
Existence and unicity of co-moments in multisymplectic geometry. with Tilmann Wurzbacher, Journal of Differential Geometry and Applications, 2015. Also on the arXiv.

Preprints

New paper: Multisymplectic observable reduction using constraint triples, with Antonio Miti, arXiv:2506.00234.
Darboux type theorems in multisymplectic geometry, arXiv:2503.03672.
Density-valued symplectic forms from a multisymplectic viewpoint, with Laura Leski, arXiv:2502.02224.
Universal central extension of the Lie algebra of exact divergence-free vector fields, 2024, with Bas Janssens and Cornelia Vizman, arXiv:2409.05182
Poisson bundles over unordered configurations, 2024, with Alessandra Frabetti and Olga Kravchenko, arXiv:2407.15287
Differentiating Lie infinity groupoids -- Part I, 2023, with Du Li, Arne Wessel and Chenchang Zhu arXiv:2309.00901

Other

I wrote a little overview article on which formal languages can be recognized by various types of unique hard attention transformer encoder. It can be found here arXiv:2506.03370
I helped in the creation of a jspsych plugin and in the data collection for the article Iconicity in Large Language Models, authored by Anna Marklová, Jiří Milička, Ľudmila Lacková Bennet, Libuše Kormaníková and myself.
Camille Laurent-Gengoux, Ruben Louis and I wrote Lecture notes for the summer school "Poisson geometry CRM Barcelona 2022" booklet series, which can be found here: arXiv:2407.14932
I wrote a short note containing a nice solution to a problem/riddle suggested by Tanya Kovanova. It can be found under arXiv:2306.11655.
Alfonso Garmendia and I contributed a short article on how we organise an international online seminar during the Pandemic in the EMS Magazine.
Normal forms and conserved quantities in multisymplectic geometry. Dissertation at the Ruhr-University, Bochum, 2018.

Events and Activities

2025

In the week of October 27. - 31. 2025, I am organizing the workshop Who is afraid of infinite dimensions? at the University of Lyon 1.
In the week of August 3. - 8. 2025, I am one of the organizers of the conference Around singularities in Poisson geometry happening at the BIRS center in Hangzhou, China.
From July 17. to 18. 2025, Karandeep Singh and I organize a little workshop called 'Higher structures and singular foliations' in Würzburg. Registration and further infos are available under this link.
From May 26th to 29th 2025, I gave a minicourse over zoom at the University of Jilin.
On May 21, 2025, I give a talk at the seminar Seminario di Algebra et Geometria in Rome.
On May 7, 2025, I give a talk at the seminar Cohomology in algebra, geometry, physics and statistics in Prague.
On April 23, 2025, I give a talk at the Higher Differential Geometry Seminar at the MPI Bonn.
On March 19, 2025, I give a talk at the Trans-Carpathian Seminar on Geometry and Physics.
On February 4, 2025, I gave a talk at the topology seminar in Göttingen.

2024

On December 13, 2024, I give a talk at the Deformation quantization and geometry seminar in Würzburg.
On November 26, 2024, I give a talk at the Geometry and Analysis seminar in Paderborn.
On November 11, 2024, I gave a talk at the online seminar Geometry and Applications. Modern Mathematical Approaches.
On October 24, 2024 at 16:00 my Habilitation defense will take place in Lyon.
From September 23 to 26, 2024 I am coorganizing with Giuseppe Dito, Alessandra Frabetti and Tilmann Wurzbacher the Journées Phyique-Mathématique in Lyon, I am also giving a talk there.
In September 2024, I gave a talk at the conference Non Commutative Geometry and Higher Structures in Thessaloniki, Greece.
On August 07, 2024, I gave a talk at the Higher Differential Geometry Seminar at the MPI Bonn.
On July 23, 2024, I gave a talk at the Geometry seminar of the Max-Planck institute in Leipzig.
On June 20. 2024, I gave a talk at the Geometry Seminar in Metz.
On June 14. 2024, I gave a talk at the Analysis seminar of the university of Potsdam.
On June 3rd, 2024, I gave a talk in the mini-worhshop on singular foliations in Göttingen.
In May 2024, with Antonio Miti we give a minicourse at the Workshop on Symmetry & Reduction in Poisson & Related Geometries in Salerno.
On 10. May 2024, I will give a talk at the University of Barcelona.
On March 06. 2024, I gave a gong-talk (5 minutes) at the 59th Seminar Sophus Lie in Würzburg.
On March 01. 2024, I gave a talk at the Geometry Workshop in Timisoara.
On January 16. 2024, I gave a talk at the Topology seminar in Bochum.
On January 10. Casey Blacker, Antonio Miti and I organized a Mini-workshop on multisymplectic geometry in Lyon.

2023

On Decmber 01. 2023 with Alessandra Frabetti and Giuseppe Dito, I organized the Journée Physique-mathématique here in Lyon.
On November 08. 2023, I gave a talk in the seminaire Pizza at the ICJ in Lyon.
From October 31. to November 3. 2023, I organized the second installement of the Atelier on Higher structures in Differential Geometry in Lyon, this time with Mini-Courses by Christian Blohmann and Madeleine Jotz.
In September 2023, I gave a talk at the Developments in Modern Mathematics: a WiMGo conference in Goettingen.
In August 2023, I gave a talk at the the thematical physics seminar in Würzburg.
In July 2023, I gave a talk at Dg-manifolds in Geometry and Physics in Paris. It is part of the IHP trimester on Higher structures in geometry and mathematical physics.
In June 2023, I gave a talk at Analyse des EDP, géométrie et physique in Toulouse. The conference is held in honor of Prof. Frédéric Hélein for his 60th birthday.
In June 2023, I co-organized a workshop on Singular foliations and dg-manifolds with Camille Laurent-Gengoux at the IHP in Paris.

2022

From 07. to 09. December 2022, I organized the Atelier on higher structures in differential geometry in Lyon.
On the 12. October 2022, I gave a short talk at the meeting of the PSPM group at the Institut Camille Jordan in Lyon.
On the 10. October 2022, I spoke in the virtual SFARS seminar.
On the 30. September 2022, I gave a talk at the mathematical physics seminar at the Institut Camille Jordan in Lyon.
In August 2022, I gave a talk at the thematic programme on Higher Structures and Field Theory at the ESI in Vienna. A youtube-recording of the talk can be accessed here.
On June 09. 2022, I gave a talk at the conference on Noncommutative Geometry and Higher Structures in Scalea, Italy.
On March 15. 2022, I gave a talk at the Göttingen-Würzburg Geometry day.
From Februaray 28. 2022 to March 04. 2022, Jérémy Mougel, Thomas Schick and I are organizing a winter school on Foliations, Pseudodifferential operators and groupoids.
In February 2022, I gave an introductory lecture on Foliations, Lie groupoids and Lie algebroids in Göttingen.

2021

In November 2021, I gave a talk at the Oberseminar in Halle.
In October 2021, I gave a talk at the Rencontre Poisson in La Rochelle.
In September 2021, I gave a talk in the Mathematical Physics seminar at the University of Lyon.
In September 2021, I taught a minicourse on differential geometry (in French) at the école d'été de mécanique théorique in Quiberon.
In August 2021, I gave a talk at the A finite and infinite-dimensional meeting on Lie groupoids, Poisson geometry and integrability at the Pauli institute in Vienna. A video recording of the talk can be found here.
In July 2021, I spoke at the Young Researchers’ Virtual Multisymplectic Geometry Conference organized by Casey Blacker.
In May 2021, I gave a talk at the joint Geometry seminar in Göttingen.
In March and May 2021, I spoke in the virtual SFARS seminar.

2020

In December 2020, I gave a talk at the Kolloquium at the Mathematical Institute in Göttingen.
In November 2020, I gave a talk at the Higher structures seminar in my new home Göttingen.
In November 2020, I gave a talk at the Rencontre du GDR GDM in Paris.
In November 2020, I spoke in the virtual SFARS seminar.
In October 2020, Alfonso Garmendia and I organized an online workshop on Singular Foliations and Related Structures, that has now turned into a weekly seminar.
In September 2020, gave a talk at the thematic programme on Higher Structures and Field Theory at the ESI in Vienna. A youtube-recording of the talk can be accessed here.
In September 2020, I gave a talk at the Junior Global Poisson Workshop at the university of Geneva (on-line). A youtube-recording of the talk can be accessed here.
In September 2020, I gave a talk at the workshop on multisymplectic geometry at the KU Leuven (on-line).
In August 2020 I spoke at the first meeting of the GraNum project members.
In July 2020, I spoke at the Young Researchers’ Virtual Multisymplectic Geometry Workshop organized by Casey Blacker.
In June 2020, I gave a talk in the RTG seminar at the University of Duisburg-Essen.
In May 2020, I would have given a talk at the Rencontre Poisson in La Rochelle. (Postponed due to COVID-19)
In April 2020, I gave a talk at the Séminaire Théorie de Lie, Géométrie et Analyse in Metz.
In March 2020, Cornelia Vizman and I would have given a mini-course on our research at the geometry seminar at the University of Salerno. ( Postponed due to COVID-19)

2019

In December 2019, I gave a talk on singular foliations at the Journées Lensoises de Géométrie et Topologie.
In November 2019, I gave a talk on singular foliations in Timisoara, as a satellite seminar talk to the Workshop on Contact and Poisson geometry in Timișoara.
In September 2019, I gave a mini-talk (gong show) at the summer school on theoretical mechanics in Quiberon.
In June 2019, I gave a talk at the Rencontre du GDR GDM à La Rochelle.
In May 2019, I gave a talk on Singular foliations and Lie algebroids at the Seminar on Complex Geometry in Bochum and participated at the Conference on Higher Homotopy Algebras in Topology in Bonn and the Workshop on Singular Foliations in Leuven.
In April 2019, I gave a six-hour minicourse on multisymplectic geometry at the working group Mécanique et Géométrie at La Rochelle University.
In March 2019, I gave a talk on Darboux type theorems in multisymplectic geometry at the Séminaire Géométrie et Quantification at the Institut Henri Poincaré in Paris (in French).

2018 and before

In November 2018, I gave a talk about comoments in multisymplectic geometry in the Séminaire de géométrie et physique mathématique here in Paris, in French.
In September 2018, I gave a talk at the Atelier sur la géométrie multisymplectique et applications in Metz and at the conference on Homotopy algebras, deformation theory and quantization in Będlewo.
In August 2018, I participated at the gong show at the Conference on Higher algebra and mathematical physics with a 5-minute talk on Comoments in multisymplectic geometry.
I delivered seminar talks on Darboux theorems in multisymplectic geometry in Metz in November 2016, in Paris in March 2017 in Leuven in November 2017 and in Bochum in July 2018.
I gave a seminar about comoments and conserved quantities in multisymplectic geometry in Bochum in May 2018.
In August 2016 at the conference on Graded geometry and applications to physics in Sheffield, I gave a poster presentation on comoments in multisymplectic geometry.
I gave a seminar talk on comoments in multisymplectic geometry in Leuven in April 2016.

Puzzles and hunts

Scavenger Hunt

Alfonso Garmendia and I have created a scavenger hunt for the participants of the SFARS seminar, that we organize. It is still available here, the access code to start the hunt is "Request Mission".

Pen-and-Paper adventure

Josef Adamčík, Anna Marklová and I created an adventure for the Mausritter Pen-and-Paper role plaing game. It is called Chrismous Forever and can be downloaded here. The rules of the basic game are available here.

A few elementary riddles and excercises

I know some of the following from Benjamin Böhme, who in turn credits Wim Martens. If you know a source I should refer to for some of them, please let me know.

Subsets
Let \(n\in \mathbb N\) be a natural number. Consider an \(n+1\)-element subset \(A\) of \(\{1,...,2n\}\). Show that \(A\) contains two distinct numbers \(a,b \), such that \(a\) divides \(b\).
Checkerboard
Consider a checkerboard of \(n\times n\) fields. Some fields contain pieces, others don't. Now put pieces on every field that touches (through its edges) at least two fields already containing pieces. Repeat the process until no further pieces are added. What is the minimal number of pieces on the field at the beginning of the procedure, if every field contains a piece at the end? (And why?)

Hexagonal checkerboard How is the situation for a hexagonal board with sides of 6 fields, and hexagonal fields, if we need 3 neighbors of a field to already carry pieces for it to also get a piece? (communicated by Anne Marlen Prepeneit)
Coins
\(2n\) coins lie in a line on the table. Alice and Bob take turns in taking a coin away from the bounday of the row. Each coin is labelled with a value. In the end, after all coins are picked, the person who has taken coins with the larger value wins. In case of a draw Alice, who also takes the first turn, wins. Does someone have a winning strategy, if yes how does the strategy look?
Burning cords
You have two cords (or fuses), that each take exactly 60 seconds to burn. You don't know whether they burn down at a constant speed and whether they burn down in the same way. How can you use them to measure exactly 45 seconds?
Poisoned chocolate
Alice and Bob have an \(n\times m\) chocolate bar. The top left corner piece is poisoned. Starting with Alice, they take turns in picking a point in the chocolate bar and eating all chococolate pieces, that are right of this point and all that are below this point. They have to choose in a way that makes them eat at least one piece of chocolate. The person eating the poisoned piece loses. Does one of them have a winning strategy? If yes, who is it? Click here for an example game in which Bob loses.

Poisoned chocolate (addendum) Does the answer change if the chocolate is infinitely big? (communicated by: Anne Marlen Prepeneit)
Pirates
A group of a thousand pirates earns 1000 pieces of gold. They have a very complicated gold distribution procedure, your task will be to find out how the gold will be distributed. First of all, all gold pieces are identically large, individual gold pieces can not be split and the pirates are totally hierarchically ordered. Pirate 1 is more important than pirate 2, pirate 2 is more important than pirate 3 etc. Their distribution procedure works as follows:
1. The most important alive pirate proposes a distribution.
2. The alive pirates vote whether they accept this distribution, if more than half of them are against it, the most important alive pirate is killed and they restart the procedure. Otherwise, the proposed distribution is accepted and the gold is distributed.
All pirates behave perfectly rationally (other than choosing to be a pirate)m know that all other pirates also behave rationally and have the following preferences:
1. From two options a pirate would always choose the one, where she survives.
2. If she survives in both cases, she prefers the options where she gets more gold.
3. If there are two cases with survival and equal amount of gold, she chooses the one where more other pirates die.
So, how will the gold be distributed among the pirates and how many of them will survive?
An unknown square
We are interested in a square with (unknown) corners \(A,B,C,D\) and unknown side length \(a\). Assume, that for some point \(P\), we know the distance between \(A\) and \(P\), the distance between \(B\) and \(P\), and the distance between \(C\) and \(P\). Can we determine \(a\) from this data? (There is a beautiful solution using straightedge and compass).
Prisoners' hats
A group of 100 prisoners discovers that it will be executed (or freed) on the next day. They will have to stand in a row on a staircase, such that each prisoner sees all the prisoners in front of them but none behind them. Each prisoner will wear a hat, which is either black or white. From back to front, the henchman will ask each prisoner "What color is your hat?" If the answer is correct, then the prisoner is free, otherwise he/she is heheaded. All the remaining prisoners hear the question and answer and also hear whether the person leaves or is beheaded. Before the procedure, the prisoners have time to discuss and agree on a strategy. Assuming a reasonable level of solidarity among them, what should their strategy be and how many would be sure to survive? (communicated by: Anna Marklová)
Toasting coordination
A group of people are standing in a circle and want to toast (let their glasses of wine touch). It is considered impolite for the glasses to cross. Assuming that only 2 glasses are allowed to touch at a time (during one "round") and that the people don't change places and don't toast behind each others backs, how many rounds of toasting are necessary so everyone has toasted with everyone? (communicated by: Oscar Cosserat)
Prime Sudoku
Can you fill a Sudoku field with prime numbers, so all rows, columns and the 9 3x3-subfields contain a number at most once and sum up to prime numbers? (Additional question to which I do not know the answer: Can you fill it completely with distinct numbers). (proposed by Anna Marklová)
Semi-integer rectangles
Take a rectangle which is decomposed into smaller rectangles, which all have at least one integer side-length. Must the original rectangle also have an integer side length? (communicated by: Anne Marlen Prepeneit)
Monotony
In whatever order one puts the numbers \(1,...,n^2+1\), there will always be an \(n\)-element subsequence which is monotonous.