The UMD2026 conference aims to support Ukrainian mathematicians in exile while strengthening scientific ties between France and Ukraine. It provides a unique forum to exchange ideas and foster collaborations with — and within — the Ukrainian mathematical community in Europe. Bringing together early-career researchers and senior mathematicians, UMD2026 places special emphasis on mentoring young Ukrainian students based in Europe, particularly in the Paris Region.

The first edition of this conference will be held on June 4-5, 2026 at the Institut Henri Poincaré, in Paris, in the Amphithéâtre Yvonne Choquet-Bruhat.

This inaugural edition will embrace a broad scientific scope, reflecting the scientific expertise of Ukrainian mathematics, with a particular emphasis on partial differential equations (PDEs), stochastic differential equations (SDEs), operator algebras, and machine learning.

We intend this event to launch a biennial series bringing together Ukrainian and Western European mathematicians to present collaborative research, foster new partnerships, and further strengthen the integration of the Ukrainian mathematical community into the European research landscape. 

Register here

The conference program is available in the left-hand panel under “Program”. The first day will be mainly devoted to operator algebras, and the second day to PDEs and SDEs.

Nadiia Derevianko (TU Munich, Germany), 
The detection of singularities using neural networks and its application to the solution of PDEs.

Abstract: In the talk, we will present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities [1] .  In contrast to known research, our neural network approximant is a discontinuous function itself, and singularities of the neural network capture singularities of the function under consideration. To achieve these properties, we introduce a concept of  "unsafe" PAUs (Padé Activation Units):  an adaptive construction of rational activation functions as meromorphic functions with a single pole each, situated within the domain of investigation. Furthermore, we present a  novel backpropagation-free method for determining the weights and biases of the hidden  layer from the parameters of rational Laurent-Padé approximation [2]. We will illustrate the effectiveness of our method through numerical experiments, including the construction of extensions of the time-dependent solutions of nonlinear PDEs into the complex plane, and study the dynamics of their singularities.

1. Derevianko N., Kevrekidis I.G., Dietrich F., Neural network-based singularity detection and applications, Arxiv preprint (2025): arxiv.org/abs/2509.10110] 
2. Gonnet P., Güttel S., Trefethen L.N., Robust Padé approximation via SVD, SIAM Review, V. 55,  pp. 101-117, 2013. 

Svitlana Mayboroda (ETH Zurich, Switzerland)
The hidden structure of the disorder

Abstract: The geometry of the environment perceived by the human eye differs from the one that guides propagation of waves or formation of free boundaries. Already the relationship between the regularity of the coefficients of the equation, smoothness of the domain, and properties of the solutions is highly nontrivial. However, even more mysterious are effects which are not measurable in terms of regularity, such as disorder or mesoscopic phenomena. We will broadly concentrate on two subjects: localization of waves in disordered media and harmonic measure on rough sets. 

Sergey Neshveyev (University of Oslo, Norway)
TBA

Vasyl Ostrovskyi (Institute of Mathematics of National Academy of Science of Ukraine, Kyiv, Ukraine)
On quantum symmetries of graphs

Abstract: Let G, H be simple finite graphs with the same set of vertices. We first recall how to describe the corresponding non-local game of their isomorphism and quantum isomorphism and list some facts about quantum automorphisms of graph. For a graph G, let U_G be the related quantum graph. We study the game algebra C(Qut(U_G)) of quantum automorphism of U_G. We show that for the complete graph K_n, the algebra C(Qut(U_K_n)) is noncommutative already for all n ≥ 3, in contrast to C(Qut(K_n)) = C(S_n^+). Moreover, we prove that for any graph G with |V (G)| ≥ 3, the quantum graph U_G admits nonlocal symmetry, meaning that there exists a perfect quantum no-signaling correlation for the quantum automorphism game for U_G which is not local.

The talk is based on the joint research with Olha Ostrovska and Ludmila Turowska.

Andrey Pilipenko (University of Geneva, Switzerland, and Institute of Mathematics of National Academy of Science of Ukraine, Kyiv, Ukraine)

Analytic and stochastic description of Brownian motions on star graphs

Abstract: We provide a detailed description of all possible Feller processes on infinite star graphs with finite number of edges, processes that while away from the graph's center behave like a one-dimensional Brownian motion. The analytic part includes constructing generators, Markov semigroups, and resolvents. Additionally, we derive a representation of Brownian motion on a star graph as a measurable function of a finite set of one-dimensional Wiener processes and subordinators. The description can be seen as a continuation of the seminal paper [1] by Itô and McKean (devoted to Brownian motions on the half-line), recast from the perspective of the theory of multi-armed bandits.

(The work is based on a recent paper with Adam Bobrowski [2])

1. K. Itô and H. P. McKean Jr., Brownian motions on a half line, Illinois J. Math. 7 (1963), 181–231
   
2. A. Bobrowski, A. Pilipenko, Analytic and stochastic description of Brownian motions on stargraphs (arXiv 2025). 

Mykhailo Zarichnyi (University of Rzeszów, Poland, and Ivan Franko Lviv National University, Ukraine) 

The Scottish book: continuing tradition

Olena Atlasiuk (University of Helsinki, Finland, and Institute of Mathematics, National Academy of Science of Ukraine) 

On parameter-dependent inhomogeneous boundary-value problems in Sobolev spaces

Abstract: We study a wide class of linear inhomogeneous boundary-value problems of arbitrary order ODE whose solutions range over the Sobolev spaces. These boundary conditions may contain derivatives of the unknown vector function of integer and/or fractional orders that can exceed the order of the differential equation. For problems of this class, constructive necessary and sufficient conditions for the continuity of solutions with respect to a parameter from an abstract metric space have been found. We prove that the solutions to the considered problems can be approximated in the Sobolev space by solutions to some differential systems with polynomial coefficients and multipoint boundary conditions.

Anna Bahrii (Evry Paris-Saclay University)