Analysis Seminar of the Rényi Institute, Spring of 2025
May 29, Thursday, 12:15--13:15, Tondós lecture room
Speaker: József Pitrik, Wigner & Rényi & BME
Title: TBA
Abstract:
TBA.
May 22, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Tamás Titkos, Corvinus University & Rényi Institute
Title: TBA
Abstract:
TBA.
May 15, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Gergely Bunth, Rényi Institute
Title: TBA
Abstract:
TBA.
May 8, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Szergii Favorov, Karazin’s Kharkiv National University, Ukraine
Title: Crystalline measures, Fourier quasicrystals, their generalizations and some applications
Abstract: We give definitions of crystalline measure and Fourier quasicrystal, discuss the relationship between these notions, and show some sufficient conditions for a crystalline measure to be a Fourier quasicrystal. We then present the theorem of Olevskii and Ulanovskii on the 1-1 correspondence between zeros of exponential polynomials and Fourier quasicrystals with unit masses. We show generalizations of this result to the zeros of absolutely convergence Dirichlet series, to slowly growing measures with countable spectrum, to the zeros of almost periodic functions in a strip. The last result yields the simple criterion of representability of almost periodic entire functions of exponential growth (in particular exponential polynomials) as a finite product of sines.
April 17, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Mihály Weiner, Budapest University of Technology and Economics & Rényi Institute
Title: Hypothesis testing and a new characterization of matrix geometric means
Abstract:
Let A, B, C be three positive semidefinite matrices. I will show that there exists a subexponential function (e.g. a polynomial) p such that
A^{\otimes n} \leq p(n) (B^{\otimes n} + C^{\otimes n})
for all n = 1,2,3,.. if and only if there exists a t \in [0,1] such that
A \leq B #_t C
where B #_t C is the weighted geometric mean of B and C. I will also explain why this question appears in asymptotic quantum hypothesis testing. Joint work with P.E. Frenkel, M. Mosonyi and P. Vrana.
April 10, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Lajos Molnár, University of Szeged & Rényi Institute
Title: Isomorphisms of positive cones in operator algebras with respect to geometric means
Abstract:
In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we extend our existing result from the case of von Neumann factors to the case of more general algebras. As for the Fiedler-Pták geometric mean, we present the first satisfactory result that concerns the setting of finite factor von Neumann algebras.
April 3, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Ágota G. Horváth, Budapest University of Technology and Economics
Title: Removable Sets for Fractional Heat and Fractional Bessel-Heat Equations
Abstract:
We examine fractional heat-diffusion equations concerning to Laplace-
and the Bessel-Laplace operators. We give conditions for removability
which are sufficient and which are necessary, by $L^p$-capacities. Due
to taking average on the sphere, in the spirit of modulus of smoothness
we handle the Laplace and Bessel-Laplace cases together.
(It is a joint work with Mouna Chegaar.)
March 20, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Péter Vrana, Budapest University of Technology and Economics
Title: Error bounds for entanglement transformations from tensor degeneration
Abstract:
Pure states of multipartite quantum systems are described by tensors, and tensor restriction corresponds to a transformation between two states by local operations and classical communication that succeeds with a nonzero probability. By an asymptotic restriction we mean a sequence of restrictions between Kronecker powers of the tensors, which corresponds to a transformation between many copies, and in principle allows an arbitrarily rapid decay of the success probability as the number of copies is increased. In the simplest case, the asymptotic restriction arises from a single-copy probabilistic transformation, which gives a simple exponential lower bound on the success probability. However, it is also possible that a tensor asymptotically restricts to another while there is no restriction between their nth powers for any n. Tensor degeneration is a fundamental tool for proving asymptotic restriction when no single-copy transformation is possible. In this talk, I explain the construction of a family of asymptotic entanglement transformations from a given degeneration and determine its success probability in the many-copy limit. Based on joint work with Dávid Bugár.
March 13, Thursday, 12:15--13:15, Tondós lecture room
Speaker: András Gilyén, Rényi Institute
Title: Quantum generalizations of Glauber and Metropolis dynamics
Abstract:
Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with complex degrees of freedom. I will describe efficiently implementable continuous and discrete-time quantum counterparts to Metropolis sampling and Glauber dynamics that also enjoys the following desirable features: it is (i) exactly detailed balanced, (ii) efficiently implementable, and (iii) quasi-local for geometrically local systems. I will describe generic properties of all constructions, including the uniqueness of the fixed-point and the locality of the resulting operators.
Joint work with Chi-Fang Chen, Joao F. Doriguello, Michael J. Kastoryano.
February 27, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Balázs Maga, Rényi Institute
Title: Permutation limits and Shannon entropy
Abstract:
Studying analytic limit objects of discrete structures has become one of the main directions of combinatorics recently, which owes its success to the fact that quite often statements in the discrete world can be converted to analytic ones and vice versa, vastly enriching the available tools in dealing with important questions.
In my talk, I am going to discuss permutons, i.e., permutation limits, which are simply probability measures on the unit square with uniform marginals. Such a measure naturally gives rise to a distribution over the length n permutations for any n>0. We are interested in the asymptotic properties of the Shannon entropy of these distributions, which we call the pattern entropy sequence.
After discussing some simple examples, I am going to speak about an exciting connection to Kolmogorov-Sinai entropy for permutons supported by graphs of measure-preserving functions, demonstrating that given certain regularity conditions, the pattern entropy sequence has a linear growth rate.
I will also touch upon how one can prove via Baire category arguments the existence of irregular permutons, i.e., ones for which no natural normalization yields a convergent sequence.
A simple construction for random permutons comes from the random automorphism of the rooted $d$-ary tree. If time permits, I will also speak about some surprising probabilistic phenomena I encountered upon studying its pattern entropy sequence.
February 20, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Haojie Ren, Technion, Israel
Title: Hausdorff Dimension of Solenoidal Attractors
Abstract:
Solenoidal attractors are fractal sets arising in skew product systems. In this talk, I will introduce their definition, provide a simple geometric description, and give a brief overview of their research history. I will then focus on a special class of skew product maps, discussing my works on the SRB measures and the solenoidal attractors induced by these maps. The proofs draw on Hochman's entropy growth tools for convolutions and techniques from my recent collaboration with Shen. I will also introduce some open questions in the field.
February 13, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Geuntaek Seo, POSTECH, South Korea
Title: Nonconvex Wasserstein Gradient Flows: A Variational Problem and Asymptotic Convergence
Abstract:
This talk consists of two parts:
The first part deals with the geometry of minimizers for certain free energy functionals related to aggregation-diffusion equations. As shown by Lim and McCann [ARMA, 2021], the minimizers of the interaction energy with certain mildly repulsive potentials are equi-distributed on $\Delta^n$, the vertices of the $n$-simplex. Using $\Gamma$-convergence, we show that the minimizers of the free energy functional are compactly supported and equi-distributed near $\Delta^n$ when the diffusion effect corresponds to the porous medium diffusion. This is a joint work with Tongseok Lim (Purdue).
In the second part, we discuss the asymptotic convergence of nonlinear PDEs described by gradient flows for nonconvex functionals. Our goal in this research is to establish the generalization of the Lojasiewicz-Simon theory to nonconvex Wasserstein gradient flows. This is a joint work in progress with Beomjun Choi and Seunghoon Jeong (POSTECH).
February 6, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Sascha Troscheit, Uppsala University, Sweden
Title: Continuum trees of real functions and their graphs
Abstract:
The Brownian continuum tree (CRT) is an important random metric space that was extensively investigated in the 1990s. It can be constructed by a change of metric from a Brownian excursion function on [0,1]. This change of metric can be applied to all continuous circle mappings to give a continuum tree associated with the function. In 2008, Picard proved that analytic properties of the function are connected to the dimension theory of its tree: the upper box dimension of the continuum tree coincides with the variation index of the contour function. We will provide a short and direct proof of Picard's theorem through the study of packings. The methods used will inspire different notions of variations and variation indices, and we will link the dimension theory of the tree with the dimension theory of the graph of its contour function.
The title and abstract may be familiar to some of you who came to the one-day fractal meeting at BME about a year ago. This talk includes some updates and strengthened results. (Joint work with Maik Gröger.)
January 30, Thursday, 12:15--13:15, Tondós lecture room
Speaker: Zoltán Balogh, University of Bern, Switzerland
Title: Logarithmic Sobolev Inequality on Surfaces via OMT
Abstract:
In the first part of this talk I present a proof of the Logarithmic
Sobolov Inequality (LSI) in the Euclidean space, that is based on the
method of optimal mass transport (OMT). In the second part of
the talk I show, that this method is strong enough to obtain a version of the LSI
in curved spaces such as Euclidean surfaces.
In this case the statement of the LSI involves the mean curvature of the surface.
The talk is based on a joint work with Alexandru Kristaly.
Last modified: 25.03.2025