Leonid Ryvkin

Publications and Preprints

Scientific publications

On Dirac structures admitting a variational approach, accepted in Mathematics and Mechanics of Complex Systems, 2022 with Oscar Cosserat, Camille Laurent-Gengoux, Alexei Kotov and Vladimir Salnikov, 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: Reduction of L-infinity-algebras of observables on multisymplectic manifolds, 2022, with Casey Blacker and Antonio Miti, arXiv:2206.03137

Other

New Article: 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.
Linear orbits of alternating forms on real vector spaces, 2016, arXiv:1609.02184.
A multisymplectic manifold not covered by Darboux charts, 2016, arXiv:1608.07424.

Events and Activities

2023

In July 2023, I will give 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 will give 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.

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".

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)

Click here or scroll down for more riddles.

More riddles and excercises

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).

Click here or scroll down for more riddles.

Even More riddles and excercises

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.

Contact

Leonid Ryvkin
Leonid@ryvkin.eu

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