International Seminar on Quantization, Geometry, and Dynamics (ISQGD)

About the Seminar

The International Seminar on Quantization, Geometry, and Dynamics (ISQGD) is a global scholarly platform devoted to advancing research across a wide spectrum of interconnected mathematical disciplines. ISQGD brings together mathematicians working in quantization theory, fractal geometry, dynamical systems, geometric analysis, ergodic theory, geometric optimization, optimal transport, variational methods, geometric measure theory, and numerous related fields. The seminar is designed to foster international collaboration, highlight emerging developments, and create a sustained environment for scholarly exchange among researchers at every stage of their academic careers.

Although ISQGD is currently conducted online, the word “online” is intentionally omitted from its title to allow the seminar to evolve naturally into hybrid or fully in-person formats as resources and opportunities permit. Talks are scheduled with attention to global time zones, allowing researchers from diverse regions to participate. Recordings of most presentations are made available on the official ISQGD YouTube channel, providing a lasting resource for the broader community.

A dedicated independent website for ISQGD will be developed once appropriate funding and infrastructure become available. At present, seminar information is maintained on a hosted webpage, and organizational responsibilities—including scheduling, programming, and speaker invitations—are handled collectively by the ISQGD organizing committee.

Researchers interested in presenting their work are warmly welcome to contact any member of the organizing committee. In addition to regular seminar lectures, ISQGD may organize thematic workshops, mini-courses, and special sessions in online or hybrid formats, depending on community needs and available support.

Research Areas Covered by ISQGD

Quantization Theory
Constrained and unconstrained quantization; optimal n-means for for continuous, discrete, singular, and self-similar distributions; error analysis, high-resolution asymptotics, convergence rates, and stability results; quantization dimension, quantization coefficients, and local dimension relationships; quantization on Euclidean spaces, Riemannian manifolds, spherical surfaces, fractal sets, and other nonlinear metric spaces; geometric, variational, and algorithmic methods for computing optimal sets; and quantization on graphs, networks, and combinatorial metric structures.
Fractal Geometry
Self-similar, self-affine, and random fractal sets; Moran constructions, generalized Moran structures, and iterated function systems (IFS) with or without overlap; fractal functions, fractal interpolation schemes, and IFS-generated curves and surfaces; classical and generalized dimensions (Hausdorff, packing, box-counting, Assouad, and lower dimensions); multifractal analysis and spectrum theory for measures and dynamical quantities; fractal boundaries, attractors, invariant sets, Julia sets, and limit sets; fractal geometry on manifolds, spheres, and curved surfaces; and applications to dynamical systems, geometric structures, optimization, and measure-theoretic modeling.
Dynamical Systems
Uniformly hyperbolic, partially hyperbolic, and non-uniformly hyperbolic dynamical systems; symbolic dynamics, Markov partitions, and subshift spaces; thermodynamic formalism encompassing topological pressure, equilibrium measures, Gibbs states, and variational principles; invariant sets, attractors, repellers, and fractal limit sets; Lyapunov exponents, various notions of entropy, and stability theory; chaotic dynamics, mixing properties, and structural robustness; random, parametric, and skew-product dynamical systems; and fundamental links with smooth ergodic theory, geometric analysis, and quantization methods.
Geometric Analysis
Geometric analysis on smooth manifolds, including Riemannian and metric geometry; curvature-dependent geometric PDEs and variational problems; classical and sharp geometric inequalities with applications to quantization and optimization; Laplace–Beltrami operators, eigenvalue problems, and geometric spectral theory; structure and analysis of measure and metric-measure spaces; and spherical geometry involving small circles, spherical polygons, geodesic configurations, and geometric optimization on curved surfaces
Ergodic Theory
Ergodic measures, invariant transformations, and ergodic decompositions; unique ergodicity, rigidity phenomena, and classification of invariant measures; mixing, weak mixing, strong mixing, and quantitative decay of correlations; metric and topological entropy, recurrence theory, and orbit distributions; applications to quantization, information theory, and geometric measure structures; and deep connections with number theory, Diophantine approximation, and dynamical systems on homogeneous and arithmetic spaces.
Geometric Optimization
Centroidal Voronoi tessellations (CVTs) and related optimal tessellations; energy-minimizing and equilibrium point configurations on Euclidean domains, manifolds, and curved surfaces; classical and modern sphere packing, covering, and best-packing problems; geometric coding theory, spherical designs, and optimal spherical codes; optimal partitions and quantization of geometric and metric-measure spaces; and applications to quantization, geometric approximation, and optimization on curved and non-Euclidean spaces.
Optimal Transport
Wasserstein distances (Wp), optimal transport maps, and Kantorovich formulations; transport-based approaches to quantization, clustering, and geometric approximation; geometric, analytic, and dynamical applications of optimal transport; gradient flows and evolution equations in Wasserstein spaces; transport and functional inequalities, including Talagrand, HWI, and logarithmic Sobolev inequalities; curvature-dimension conditions and displacement convexity; and metric-measure structures and geometric analysis arising from optimal transport theory.
Variational Methods
Variational principles underlying quantization, geometric partitioning, and energy-based optimization; minimization of geometric and analytic energies on Euclidean spaces, manifolds, and fractal domains; classical and modern tools from the calculus of variations, including Euler–Lagrange equations and geometric functionals; and connections with elliptic and geometric partial differential equations, optimal transport, and geometric optimization on curved and singular spaces.
Geometric Measure Theory
Rectifiable and unrectifiable sets, Hausdorff measures, and geometric densities; projection theorems, slicing techniques, and dimension theory; measure-theoretic and geometric foundations of fractals, invariant sets, and dynamical systems; and applications to quantization, geometric approximation, and optimization on irregular, singular, or fractal geometric spaces.
Applications and Interdisciplinary Directions
Applications in data compression, signal processing, and information theory, where quantization originally emerged; machine-learning methods including vector quantizers, clustering algorithms, and prototype-based models; numerical approximation and discretization techniques on manifolds and geometric domains; geometric modeling, mesh generation, and computer graphics; mathematical physics problems involving minimal-energy particle systems, Coulomb/Riesz interactions, and discrete energies; and statistical-mechanical frameworks involving free energy, potentials, and equilibrium distributions.

Objectives

The International Seminar on Quantization, Geometry, and Dynamics (ISQGD) is guided by the following objectives:

Promote global research collaboration in quantization theory, geometric analysis, dynamical systems, fractal geometry, ergodic theory, geometric optimization, and other closely related mathematical fields, with emphasis on the deep structures that emerge from interactions among these areas.
Encourage broad, inclusive participation from researchers at all stages of their academic careers—established scholars, postdoctoral researchers, graduate students, and early-career mathematicians— thereby fostering a diverse and internationally engaged mathematical community.
Disseminate recent advances in quantization, geometry, dynamics, optimization on Euclidean and non-Euclidean spaces, geometric measure theory, and mathematical structures connected to these areas and to mathematical physics.
Provide a vibrant and sustained forum for exchanging ideas, promoting new collaborations, and inspiring thematic workshops, short courses, conferences, special sessions, and joint publications within the global research community.
Support expository, foundational, and interdisciplinary work that strengthens conceptual links between quantization, geometric optimization, dynamical and fractal structures, ergodic theory, and related areas—thereby advancing understanding across these interconnected disciplines.

Message from the Founding Chair, ISQGD

The vision of the International Seminar on Quantization, Geometry, and Dynamics (ISQGD) is to cultivate a truly global scholarly community in which meaningful mathematical exchange can flourish across continents, traditions, and research cultures. Mathematical progress grows not only from individual insight but also from sustained dialogue, shared exploration, and the collective pursuit of deeper understanding. ISQGD was founded to embody and advance these values, fostering connections that enrich both the present and future landscape of mathematical research.

The organizing committee is dedicated to fostering an environment where researchers can share new ideas, explore emerging directions, and engage with colleagues working across a wide spectrum of interconnected fields. ISQGD strives to cultivate a seminar series that remains accessible, inclusive, and intellectually vibrant, welcoming participation from mathematicians worldwide at every stage of their academic journey—from graduate students to senior researchers.

The continued growth of ISQGD is made possible by the dedication and enthusiasm of its speakers, participants, and supporters around the world. It is ISQGD’s aspiration that the seminar will continue to flourish, stimulate productive collaborations, inspire thematic workshops and related activities, and contribute meaningfully to the advancement of the global mathematical community for many years to come.

— Mrinal K. Roychowdhury, Founding Chair, ISQGD

Registration

Anyone interested in the International Seminar on Quantization, Geometry, and Dynamics (ISQGD) is welcome to join by subscribing using the button below. Subscribers will receive seminar announcements, Zoom links, updates, workshop and mini-course notices, special issue news, and other ISQGD-related communications.

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If you experience any difficulty registering or unsubscribing, please contact: mrinal.roychowdhury@utrgv.edu.

Speakers & Announcements (Chronological Order)

A chronological record of speaker announcements for the International Seminar on Quantization, Geometry, and Dynamics (ISQGD) appears below. This list is updated on an ongoing basis as new talks are confirmed.

Speaker: Professor Palle Jorgensen (University of Iowa, USA) — Webpage

Title:
Harmonic analysis, frames, and algorithms for fractal IFS L² spaces via infinite products of projections.

Date & Time:
GMT: Friday, December 5 — 3:00 PM
US Central Time (CST): Friday, December 5 — 9:00 AM
Speaker’s Local Time (CST): Friday, December 5 — 9:00 AM

Zoom Meeting Link:
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Meeting ID: 882 8369 3708

Abstract:
We present new results at the crossroads of spectral theory for operators in Hilbert space, optimization, large sparse systems, geometry of fractals from iterated function systems (IFS), and new results in fractal harmonic analysis. In detail, we present a new recursive iteration scheme involving as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and their error-estimates.

Speaker: Professor Peter Massopust (Technical University of Munich, Germany) — Webpage

Title:
Fractal Interpolation and Quaternions

Date & Time:
GMT: Friday, December 12 — 3:00 PM
US Central Time (CST): Friday, December 12 — 9:00 AM
Speaker’s Local Time (Germany): Friday, December 12 — 4:00 PM

Zoom Meeting Link:
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Meeting ID: 882 8369 3708

Abstract:
In recent years, quaternionic methodologies have found their way into many applications, one of which is digital signal processing. The main idea is to use the multidimensionality of the quaternions to model signals with multiple channels or images with multiple color values, and to use the underlying algebraic structure of quaternions to operate on these signals or images. The results of these algebraic or analytic operations again produce quaternions. This holistic approach cannot be performed in ℝⁿ, as these vector spaces do not possess an intrinsic algebraic structure.

On the other hand, the concept of fractal interpolation has been employed successfully in numerous applied settings over the last decades. The main purpose of fractal interpolation or approximation is to take into account complex geometric self-referential structures and to employ approximants that are well suited to model these types of structures. These approximants or interpolants are elements of vector spaces and cannot be operated on in an algebraic way so as to produce the same type of object. Hence, there is a natural need for an extension of fractal interpolation to the quaternionic setting.

This talk focuses on fractal interpolation in the quaternionic setting. Properties and main results are presented.

Speaker: Professor Balázs Bárány (Budapest University of Technology and Economics, Hungary) — Webpage

Title:
Exponential separation of analytic self-conformal sets on the real line

Date & Time:
GMT: Friday, December 19 — 3:00 PM
US Central Time (CST): Friday, December 19 — 9:00 AM
Speaker’s Local Time (Budapest): Friday, December 19 — 4:00 PM

Zoom Meeting Link:
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Meeting ID: 882 8369 3708

Abstract:
In a recent article, Rapaport showed that there is no dimension drop for exponentially separated analytic IFSs on the real line. We show that the set of exponentially separated IFSs in the space of analytic IFSs contains an open and dense set in the C² topology. Moreover, we provide sufficient conditions for the IFS to be exponentially separated, thereby allowing us to construct explicit examples that are exponentially separated. The key technical tool is the introduction of the dual IFS, which we believe has significant interest in its own right. As an application, we also characterise when an analytic IFS can be conjugated to a self-similar IFS. This is a joint work with István Kolossváry and Sascha Troscheit.

Speaker: Professor Stefano Galatolo (Dipartimento di Matematica and Centro Interdipartimentale per lo Studio dei Sistemi Complessi, Università di Pisa, Italy) — Webpage

Title:
To be announced.

Date & Time:
GMT: Friday, January 16 — 3:00 PM
US Central Time (CST): Friday, January 16 — 9:00 AM
Speaker’s Local Time (Pisa, Italy): Friday, January 16 — 4:00 PM

Zoom Meeting Link:
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Meeting ID: 882 8369 3708