[vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_separator type=”normal” border_style=””][vc_empty_space][vc_column_text]<\/p>\n
Laureates of the International Banach Prize – edition 2025<\/b><\/p>\n
[\/vc_column_text][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]MAIN PRIZE<\/strong>[\/vc_column_text][vc_column_text]Feliks R\u0105czka<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”714″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: <\/strong>\u201c\ud835\udc9f-modules on rigid analytic varieties\u201d The first group of results is concerned with invariants related to hyperplanes in Banach spaces (such as the minimal number of hyperplanes needed to cover given Banach space). Among the results obtained are calculations of these invariants for many wide classes of Banach spaces and found connections to important open problems in general topology and set theory.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n Further results include constructions of Banach spaces of continuous functions with special properties related to dimension theory and measure theory. The constructions provide counterexamples for known conjectures in functional analysis. The methods used combine techniques from various areas of mathematics such as operator algebras, measure theory, general topology, the use of additional axioms or the method of forcing.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The last part of the thesis concerns set-theoretic properties of the Calkin algebra and other related C*-algebras. The results focus on problems that are independent of usual axioms on set theory, including the existence of embeddings of certain C*-algebras into the Calkin algebra.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]MACIEJ KUCHARSKI<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”731″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_column_text]<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: \u201cNorm estimates for Riesz transforms\u201d Laureates of the International Banach Prize – edition 2024<\/b><\/p>\n [\/vc_column_text][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]MAIN PRIZE<\/strong>[\/vc_column_text][vc_column_text]DALIMIL PE\u0160A<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”646″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: <\/strong>\u201cFine properties of certain specific function spaces\u201d The focus of the dissertation of dr. Dalimil Pe\u0161a are function spaces, a subject that is approached from three distinct angles.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The\u00a0first part of\u00a0the\u00a0thesis is concerned with function spaces in\u00a0the\u00a0abstract. It studies the\u00a0so-called quasi-Banach function spaces, a\u00a0general class of\u00a0spaces that covers many examples occurring naturally in\u00a0many fields such as\u00a0harmonic analysis and operator theory. A\u00a0major contribution of the\u00a0thesis\u00a0is the\u00a0introduction of\u00a0the\u00a0so-called Wiener\u2013Luxemburg amalgam spaces, an abstract framework for constructing rearrangement-invariant amalgams, that is, spaces where the\u00a0conditions on\u00a0the\u00a0local and global behaviour can be\u00a0prescribed separately.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The\u00a0second part provides a\u00a0comprehensive treatment of\u00a0Lorentz\u2013Karamata spaces. This is a\u00a0fairly recent class of\u00a0function spaces that in\u00a0the\u00a0last two decades has found significant applications, especially for treating the\u00a0limiting cases of\u00a0interpolation or\u00a0Sobolev embeddings. The\u00a0thesis provides a\u00a0unified approach to\u00a0said spaces that is also more general than some of\u00a0the\u00a0previous attempts and solves several interesting open problems.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The\u00a0final part of the dissertation is dedicated to\u00a0applications of\u00a0the\u00a0function space theory. The\u00a0thesis establishes a\u00a0reduction principle for a\u00a0class of\u00a0kernel-type integral operators that is closely related to\u00a0optimal higher-order Sobolev embeddings, and also several variants of\u00a0strongly non-linear Gagliardo\u2013Nirenberg inequalities.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]KAROL DUDA<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”647″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: \u201cDynamics and computability in Geometric Group Theory\u201d The first part of the dissertation concerns computable aspects of amenability. Dr. Duda proves a computable version of Tarski’s Alternative Theorem. The proof is based on a new, computable version of Hall’s harem Theorem. There are several computable versions of this theorem in the dissertation. By applying one of these to non-amenable computable coarse spaces Dr. Duda obtains a computable version of the generalization of Whyte results concerning geometric Von Neumann conjecture.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The second part is devoted to the locally elliptic actions of groups on small cancellation complexes. Dr. Duda proves that there are no infinite torsion subgroups in groups defined by C(6), C(4)-T(4), or C(3)-T(6) small cancellation presentations. This result was specifically distinguished by the referees of the dissertation. It is an answer to the problem that has been open for many years. This follows from a more general result of the dissertation on the existence of fixed points for locally elliptic actions of groups on simply connected small cancellation complexes.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The methods used in the proof give other, stronger results in the case of C(3)-T(6) complexes. In particular, simply connected C(3)-T(6) complexes may be equipped with a CAT(0) metric. This implies the Tits Alternative for groups acting on simply connected C(3)-T(6) small cancellation complexes.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]JAKUB SKRZECZKOWSKI<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”648″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: <\/strong>\u201cSingular limits and rough behavior in evolutionary equations arising in physics and biology\u201d The dissertation addresses three important issues in the theory of partial differential equations inspired by biology and mathematical physics: models of fast chemical reactions responsible for the propagation of the electrical signal in synaptic connections in the brain, the degenerate Cahn-Hilliard equation occurring in materials sciences and models of cell-cell adhesion as well as variational analysis of two-phase functionals used to describe materials composed of two components of different hardness. One of the most important results of the thesis is the proof of the limit of the non-local degenerate Cahn-Hilliard equation to its local counterpart, which completes the program of deriving this equation initiated by Giacomin and Lebowitz in the 1990s. The results presented in the thesis were published in journals such as Communications on Pure and Applied Mathematics, Journal of Functional Analysis and Communications in Mathematical Physics.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][vc_column_text]<\/p>\n Laureates of the International Banach Prize – edition 2023<\/b><\/p>\n [\/vc_column_text][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]BLAS FERN\u00c1NDEZ<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”606″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: <\/strong>\u201cOn certain problems related with Terwilliger algebras and Distance-Balanced graphs\u201d, The dissertation by Dr. Fernandez is concerned with Terwilliger algebras, which are algebraic objects defined by the graph’s incidence matrix. They are studied mainly with algebraic tools, and one of the goals is their classification. The contribution by Dr. Fernandez relies on an interpretation of certain properties of Terwilliger algebras in terms of combinatorial properties, such as path counting in the graphs describing them. These results are considered very original by Prof. Terwilliger himself. Later in this extensive dissertation, Dr. Fernandez deals in detail with properties of distance-balanced graphs. He managed to establish their partial classification, as well as construct families of examples that provide answers to conjectures previously hypothesized by other mathematicians.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]SZYMON CYGAN<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”608″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: \u201cPatterns in\u00a0nonlocal and degenerate models from mathematical biology\u201d, The Dissertation by Dr. Cygan studies mathematical models of biological phenomena. In the first part of the dissertation the model Kondo is considered which, from a mathematical point of view, leads to a differential equation with an additional non-linear term depending on the variable function via an operator with an integral kernel. This quite intricate situation becomes simplified if only stationary solutions are sought. The existence of such solutions is demonstrated by means of the fixed point theorem, stability conditions are given, as well as the construction of solutions of a specific type together with a numerical implementation. This part of the dissertation characterizes with great independence. In the second part of the dissertation, models of diffusion-reaction type are considered. It is shown that stationary solutions near equilibrium are unstable. Further results concern the existence of discontinuous weak solutions and conditions of their stability. The strength of the results obtained is illustrated by their application to a series of classically known models such as the Grey-Scott model, Fitz-Nagumo model, Brusselator and Oregonator.<\/p>\n [\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_separator type=”normal” border_style=””][vc_empty_space][vc_column_text]<\/p>\n Laureates of the International Banach Prize – edition 2022<\/b><\/p>\n [\/vc_column_text][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]MAIN PRIZE<\/strong>[\/vc_column_text][vc_column_text]MARCIN SROKA<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”552″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: \u201cMonge-Amp\u00e8re\u2019s equation in hypercomplex geometry\u201d, The dissertation of dr. Marcin Sroka concerns solutions of the Monge-Amp\u00e8re equation on a pseudoconvex domain in Hn<\/sup><\/em> (i.e., with n<\/em> quaternion variables), and on compact manifolds with quaternion structure and equipped with a hyper-K\u00e4hler metric with torsion (HKT).<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The subject-matter stems from quantum mechanics and became an object of mathematical studies around 20 years ago. Leading names in the theory include Alesker, Verbitsky, Harvey and Lawson.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n In the context of Hn<\/sup><\/em>, dr. Sroka in his dissertation proved the existence of solutions of the Dirichlet problem with the right hand side in Lp<\/sup> <\/em>for p<\/em> > 2. This is an optimal result and significantly improves an earlier one, obtained by Harvey and Lawson, which required continuity.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n In the context of HKT, the dissertation provides a new and simpler proof of the so-called a priori C<\/em>0<\/sup>–estimate<\/em>, obtained by Alesker and Shelukhin via a long and complicated argument.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n The significance for geometric analysis of these results (which improve earlier achievements of leading specialists) is unquestionable. The community’s reaction is close to enthusiasm, which is best manifested in the recommendation letter by Valentino Tosatti from Courant Institute. Finally, an evidence of the authors own contribution is the fact that the results are published as single-authored papers in leading mathematical journals.<\/p>\n [\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]Presentation at the PTM Miniconference, June 2-3, 2023<\/a>[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]AGNIESZKA HEJNA<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”554″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: <\/strong>\u201cHarmonic analysis and Hardy spaces in the rational Dunkl setting\u201d, The dissertation concerns harmonic analysis in the Dunkl setting. Generally speaking, Dunkl analysis is a non-standard approach to analysis based on a modified notion of directional derivative involving an additional, non-local factor, proportional to a function invariant under a symmetry group. Such an approach is natural in studying some models in particle physics. In this setting one can define and investigate objects alternative to those lying at the base of classical analysis, such as exponential function, Fourier transform, convolution, Laplace operator, heat semigroup, Schr\u00f6dinger operator or Hardy spaces. Reconstruction of harmonic analysis in the Dunkl setting is the subject-matter of the extensive dissertation of dr. Hejna. The problem is highly nontrivial even if only for the non-local character of the operators or lack of the Leibniz integral rule. This work requires great originality and courage, as the success of such a research program was a priori far from obvious.<\/p>\n [\/vc_column_text][vc_empty_space][vc_column_text]Presentation at the PTM Miniconference, June 2-3, 2023<\/a>[\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]DOMINIK BUREK<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”553″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: \u201cArithmetic properties of finite quotients of Calabi-Yau type manifolds\u201d, The dissertation concerns algebraic geometry, in particular, construction and properties of Calabi-Yau manifolds. These were known earlier in complex dimension 2, where they are hyper-K\u00e4hler and have been called by Weil K3 surfaces <\/em>(partly after the names of three mathematicians involved in their investigation, partly as an allusion to K2 – one of the peaks hardest to conquer). Calabi-Yau manifolds are their higher-dimensional generalizations. They have rich geometric properties but effective constructions are far from obvious. The right away noticeable opening result of the dissertation is exactly such a construction of a rich class of Calabi-Yau manifolds as quotients under actions of finite groups. The construction is valid in any dimension. For the examples so constructed, dr. Burek provides a formula for the Hodge number, and, what is most impressive, an expression for the Weil zeta function describing the distribution of rational points.<\/p>\n [\/vc_column_text][vc_empty_space][vc_column_text]Presentation at the PTM Miniconference, June 2-3, 2023<\/a>[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][vc_column_text]<\/p>\n Laureates of the International Banach Prize – edition 2021<\/b><\/p>\n [\/vc_column_text][vc_empty_space][vc_separator type=”normal” border_style=””][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]MAIN PRIZE<\/strong>[\/vc_column_text][vc_column_text]MICHA\u0141 MI\u015aKIEWICZ<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”502″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: “Singularities of minimizing harmonic maps into closed manifolds”,<\/strong> Micha\u0142 Mi\u015bkiewicz’s dissertation concerns the set of singularities of transformations minimizing the Dirichlet functional between manifolds. The subject matter goes back to the 80’s, when Schoen and Hlenbeck have shown that such transformations are regular except on a set of codimension 3. Since then, properties of the set of singularities attracted the attention of many outstanding mathematicians, such as Brezis, Eells, Lieb, Lin or Yau. The problem is mathematically interesting because the fact that the set of singularities is nonempty is by itself already unexpected, let alone that it has rich analytic and geometric properties. One can thus say that the subject matter fits in the mainstream of interests of modern geometric analysis.<\/p>\n [\/vc_column_text][vc_empty_space][vc_column_text]Presentation at the PTM Miniconference, June 2-3, 2023<\/a>[\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]TOMASZ D\u0118BIEC<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”503″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The dissertation title: “Weak convergence methods for equations of mathematical physics and biology”,<\/strong> The dissertation of Tomasz D\u0119biec is concerned with weak solutions in a multitude of important models of dynamics of continua and hydrodynamics. The applications of these models, apart from mathematical physics, also reach biology. The cases under consideration include, among others, the Euler-Korteweg equations, compressible Euler and Navier-Stokes equations, and the cancer growth model with two cell types.<\/p>\n
\nInstitute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
\n<\/strong>supervisors: dr hab. Piotr Achinger, prof. dr hab. Adrian Langer<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]In his Ph.D. dissertation, Feliks R\u0105czka studies \ud835\udc9f-modules (sheaf-theoretic analogues of systems of linear PDEs) within the formalism of nonarchimedean geometry. As in the classical setting of \ud835\udc9f-modules on smooth complex algebraic varieties, in this setting there is a well-defined notion of a holonomic \ud835\udc9f-module, but contrary to the classical case the de Rham cohomology groups of these modules are rarely finitely dimensional in the nonarchimedean case. The main result of R\u0105czka\u2019s thesis asserts that the de Rham cohomology groups of holonomic \ud835\udc9f-modules over smooth, quasi-compact, quasi-projective rigid-analytic varieties defined over the field \u2102((t)) of formal Laurent series do have finite dimensions. This result is quite remarkable, for example because its analogue over the fields \u211ap<\/sub> of p-adic numbers is easily seen to be false. In the proof, the author uses a variety of techniques from different branches of mathematics, such as nonarchimedean geometry and functional analysis, commutative, non-commutative, and homological algebra, and the theory of algebraic \ud835\udc9f-modules.[\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner row_type=”row” type=”full_width” use_row_as_full_screen_section_slide=”no” text_align=”left” css_animation=””][vc_column_inner width=”1\/4″][vc_column_text]DISTINCTION<\/b>[\/vc_column_text][vc_column_text]DAMIAN G\u0141ODKOWSKI<\/strong><\/span>[\/vc_column_text][vc_empty_space][vc_single_image image=”715″ img_size=”100×100″ style=”vc_box_circle_2″ qode_css_animation=””][vc_empty_space][\/vc_column_inner][vc_column_inner width=”3\/4″][vc_column_text]The\u00a0dissertation title: \u201cSome applications of Set Theory in Banach Spaces and Operator Algebras\u201d
\nInstitute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
\nsupervisor: prof. dr hab. Piotr Koszmider<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]The dissertation is devoted to selected problems in functional analysis whose solutions rely on set-theoretic and topological methods.[\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\nphoto Pawe\u0142 Piotrowski<\/span><\/h6>\n
\nFaculty of Mathematics and Computer Science, University of Wroc\u0142aw, Poland
\nsupervisor: prof. dr hab. B\u0142a\u017cej Wr\u00f3bel<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]The dissertation of Maciej Kucharski concerns Lp<\/sup> norm estimates for Riesz transforms with focus on dimension-free estimates for both classical Riesz transforms and Riesz transforms associated with Schr\u00f6dinger operators.[\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]The main result of the first part is a dimension-free estimate of the Lp<\/sup> norm of the vector of classical higher order Riesz transforms, which was obtained using methods of Fourier analysis and the real and complex method of rotations.[\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]In the second part dr. Kucharski used probabilistic methods to prove that the Riesz transforms associated with Schr\u00f6dinger operators are bounded on L1<\/sup> and L\u221e<\/sup> as long as the potential satisfies a certain condition related to its growth at infinity. Moreover, he obtained a dimension-free estimate of the norms of Riesz transforms for potentials with at most quadratic growth acting independently on each coordinate.[\/vc_column_text][vc_empty_space][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][\/vc_row][vc_row row_type=”row” use_row_as_full_screen_section=”no” type=”full_width” text_align=”left” background_animation=”none” css_animation=””][vc_column][vc_separator type=”normal” border_style=””][vc_empty_space][vc_column_text]<\/p>\n
\nDepartment of Mathematical Analysis, Charles University, Prague, Czech Republic
\n<\/strong>supervisor: prof. RNDr. Lubo\u0161 Pick, CSc., DSc.<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nFaculty of Mathematics and Computer Science, University of Wroc\u0142aw
\nsupervisors: prof. dr hab. Aleksander Iwanow, dr Damian Osajda<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]The dissertation by Dr. Duda concerns two areas of geometric group theory.[\/vc_column_text][vc_empty_space height=”12px”][vc_column_text]<\/p>\n
\nInstitute of Mathematics, Polish Academy of Sciences, Warsaw
\nsupervisor: Prof. dr hab. Piotr Gwiazda<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: Prof.\u00a0Dr. \u0160tefko Miklavi\u010d, University of\u00a0Primorska<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: prof. dr hab. Grzegorz Karch, University of Wroclaw<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: prof. S\u0142awomir Ko\u0142odziej, Jagiellonian University in Cracow<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: prof. Jacek Dziuba\u0144ski<\/strong>, University of Wroc\u0142aw<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: prof. S\u0142awomir Cynk, Jagiellonian University in Cracow<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: dr hab. Anna Zatorska-Goldstein, prof. UW, University of Warsaw<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n
\nsupervisor: dr hab. Agnieszka \u015awierczewska-Gwiazda, prof. UW, University of Warsaw<\/strong>[\/vc_column_text][vc_empty_space][vc_column_text]<\/p>\n