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PROGRAM SEMINARIUM – SEMESTR ZIMOWY 2025/26
| 2.10.2025 |
Asier López-Gordón (IMPAN) |
Homogeneous Darboux and Frobenius theorems |
Abstract: There are several contexts in physics and differential geometry where a grading appears (the spin of particles, intensive/extensive variables, the exterior product of differential forms, etc.). It is thus natural to seek coordinates which are simultaneously homogeneous (i.e. respecting the grading) and adapted to the geometric structure under consideration. In the first part of my talk, I shall present a Frobenius theorem for involutive homogeneous distributions. In the second part, I shall present Darboux theorems for homogeneous presymplectic and Pfaffian forms. This is a work in progress with Prof. J. Grabowski.
| 9.10.2025 |
Jan Chwedeńczuk (IFT FUW) |
Conveyor belt for quantum information |
Abstract: This talk is focused on a transfer of information across a many-body system. It will be shown that a single qubit can play the role of an antenna that gathers vast amounts of information from a complex system. Moreover, single-particle measurements performed on this antenna can provide information about the speed of signal propagation in the system. This way, one can access the Lieb-Robinson bound without measuring the two-body correlations. A condition will be formulated under which the antenna, far apart from the source and embedded in a many-body interacting medium, can still collect the complete information. A striking feature of this setup is that a single-qubit antenna can accommodate even the full signal amplified by the entanglement of the source. In consequence, the retrieval of this information can be performed with simple one-qubit operations on the antenna (which will be fully characterized) rather than multi-qubit measurements of the source.
| 16.10.2025 |
Michał Oszmaniec (CFT PAN) |
Long-Time Properties of Many-Body Quantum Dynamics |
Abstract: In this talk, I will discuss recent results on the long-time dynamics of strongly interacting many-body quantum systems, focusing on two settings: local random quantum circuits and the unitary time evolution of closed quantum systems. For random quantum circuits, I will show that the circuit complexity of states and unitaries saturates after exponential time and undergoes recurrence after double-exponential time (in the system size). For unitary dynamics of closed quantum systems, I will present a doubly exponential upper bound on recurrence times and give examples of Hamiltonians and states that saturate this bound.
| 23.10.2025 |
Antonio Maglio (IMPAN) |
Shifted Contact Structures on Differentiable Stacks |
Abstract: Lie groupoids and their Morita equivalence classes (differentiable stacks) provide geometric models for singular spaces such as orbifolds, quotient spaces, and leaf spaces. Contact geometry, the odd-dimensional analogue of symplectic geometry, can be naturally studied in this context.In the past decade, Getzler’s notion of shifted symplectic structures on differentiable stacks has inspired major developments in derived and higher differential geometry. In the first part of the talk, we recall the definitions of Lie groupoids, their Morita equivalence, and differentiable stacks. In the second part, we introduce the notion of shifted contact structures on differentiable stacks, discuss their relation to shifted symplectic structures, and present several illustrative examples.The talk is based on a joint work with A. Tortorella and L. Vitagliano.
| 30.10.2025 |
Wojciech Niedziółka (KMMF) |
Ferromagnetism in the Hubbard model |
Abstract: One of the long-standing and only partially solved problems of theoretical condensed matter physics and mathematical physics is to demonstrate that ground states of some of the versions of the Hubbard model can exhibit a ferromagnetic ordering. In my talk I will present a result showing that crucial for this is the character of the lattice on which the Hubbard model is formulated: while on simple cubic lattices no ferromagnetic ordering seems to be possible, it can naturally arise, for low densities of magnetic moment carriers, on so-called frustrated lattices.
| 6.11.2025 |
Lorenzo Pettinari (Universita di Trento) |
New uniqueness results for high temperature KMS states |
Abstract: Lattice spin systems model particles whose positions are confined to the vertices of a graph, representing either crystalline or disordered structures. In such systems, only the internal degrees of freedom are relevant for describing the dynamics. These models can be formulated in the framework of quasi-local C*-algebras, obtained as the inductive limit oflocal algebras associated with finite subsets of vertices. Thermodynamic equilibrium states are then described by algebraic states—positive, normalized linear functionals—satisfying the KMS condition at a given temperature. After introducing this setting, I will present two new results establishing the uniqueness of KMS states at sufficiently high temperatures. Both results apply to classical and quantum spin systems and hold independently of the number of local degrees of freedom. The first isbased on an expansion of the spin space in terms of spherical harmonics and their quantized counterparts, while the second relies on a decomposition of observables into components with vanishing partial trace over finite regions of the lattice. If time allows it, Iwill discuss possible extensions to models with infinite number of single site degrees of freedom and problematic aspects of our approach.
| 13.11.2025 |
Christian Gérard (Paris-Sud) |
Quantization of Linearized Gravity |
| 20.11.2025 |
Paweł Strzelecki (MIM UW) |
Regularność i osobliwości równań eliptycznych z krytyczną nieliniowością: przekształcenia harmoniczne i nie tylko |
Abstract: Przedstawię przeglądowy wykład na temat regularności rozwiązań układów nieliniowych równań eliptycznych, takich jak równania powierzchni o zadanej średniej krzywiźnie lub odwzorowania harmoniczne in-harmoniczne w zwarte rozmaitości riemannowskie. Powiem trochę o historii problemu i omówię znane wyniki, od artykułów Richarda Schoena i Karen Uhlenbeck, które ukazały się 40+ lat temu, poprzez prace F.Heleina na temat odwzorowań harmonicznych na płaszczyźnie (jeden zwykładów ICM'1998), aż po najnowsze wyniki A. Schikorry i moich młodych współpracowników, M. Miśkiewicza i B. Petraszczuka. Przedstawię również nowy, właśnie opublikowany przykład, autorstwa Petraszczuka, który udowodnił, że pewien konkretny, stosunkowo prostyukład dwóch równań eliptycznych na płaszczyźnie (z kwadratową nieliniowością) - rozważany już przez Jensa Frehsego w 1973 r. - ma następującą zaskakującą własność: dla dowolnego zbioru zwartego K w dysku istnieje ograniczone słabe rozwiązanie o pochodnych całkowalnych z kwadratem, które jest nieciągłe w każdym (!) punkcie K, a gładkie wszędzie poza K. Co ciekawe, to rozwiązanie jest dane konkretnym wzorem, jako granica pewnego ciągu funkcyjnego; N-ty wyraz tego ciągu to rozwiązanie, które ma N punktowych osobliwości w zadanych punktach zbioru K. Na koniec przedstawię kilka pytań otwartych. Postaram się, żeby wykład był przystępny dla słuchaczy ze stosunkowo niewielkim przygotowaniem matematycznym.
| 27.11.2025 |
Andriy Panasyuk (UKSW) |
Dispersionless Hirota system and hidden symmetries of heavenly equation |
Abstract: In 2021 Konopelchenko, Schief and Szereszewski observed that solutions of 4D dispersionless Hirota system also solve the general heavenly equation describing self-dual vacuum Einstein metrics in neutral signature. They also noticed that the symmetry f → ϕ(f) of the Hirota system essentially change the properties of the corresponding metric.Joint work with Adam Szereszewski.In this paper we restate these observations in the context of II Plebański heavenly equation (IIPHE). Namely, we first extend to 5D the hierarchy for this equation found by Dunajski and Mason in 2000 for even dimensions. We then consider the corresponding 5D system with a special type of symmetry generalizing the tri-holomorphic symmetry of IIPHE. The reduction with respect to this symmetry (which in a sense imitates the reduction of self-dual vacuum Einstein metrics with respect to a tri-holomorphic symmetry ending in special Einstein--Weyl structures) gives an analogue of the dispersionless Hirota system for IIPHE. Such a point of view allows to reinterpret the symmetry f → ϕ(f) mentioned and obtain explicit formulas for the metric depending on ϕ. We present some examples showing how the Weyl spinor changes along with ϕ.
| 4.12.2025 |
Giovanni Moreno (KMMF) |
Signature tensors, ChatGPT and ODEs |
Abstract: The signature of a path X in R^d is a noncommutative formal power series σ(X) that uniquely characterizes X up to a mild equivalence. Signature tensors have been introduced by Kuo-Tsai Chen in 1954 and, after decades of oblivion, have recently risen again in the context of topological data analysis. In this talk, based on a recent preprint written in collaboration with F. Galuppi (MiMUW) and P. Santarsiero (University of Bologna), I will show that a path X is the solution of a given (system of) ODE(s) if and only if its signature σ(X) fulfills a certain system of algebraic equations. As a "pretext" for introducing signature tensors, I will briefly recall how ChatGPT predicts the next token for a given prompt and show that the so-called "attention" mechanism is nothing but a vector field on the space where signature tensors live.
| 11.12.2025 |
Joonas Mikael Vättö (Aalto University) |
Segal’s axioms of conformal field theory and the massless free boson |
Abstract: In Segal’s axiomatisation, a chiral conformal field theory (CFT) is a projective, monoidal functor from compact Riemann surfaces to the category of Hilbert spaces and Hilbert-Schmidt maps, satisfying natural compatibility conditions under gluing and boundary reparametrisations. The formalism is constructed to capture key properties of the path integral while avoiding measure-theoretic difficulties.Once a CFT is shown to satisfy Segal’s prescriptions, analytic control over central objects in alternative axiomatisation schemes (e.g. vertex operator algebras) is expected to follow. However, Segal CFTs are notoriously difficult to construct with concrete examples being few and far between. In this talk, I will review Segal’s framework and present a construction of the massless free boson CFT.
| 18.12.2025 | Christmas Meeting | - |
| 8.1.2026 |
Michał Suchorowski (IFT UW) |
From Scale Invariance to Universal Droplets: A Framework for 2D Attractive Bose Gases |
Abstract: Ultracold two-dimensional (2D) Bose gases exhibit behaviour that differs markedly from their three-dimensional counterparts, making them a sensitive setting for studying symmetry and interaction effects.In the idealized Gross-Pitaevskii equation (GPE), scale invariance gives rise to unique phenomena such as Townes solitons, ‘strong’ self-similar collapse, and interaction-independent breathing-mode frequencies intightly trapped systems. However, realistic bosonic systems exhibit a strong quantum anomaly, namely, a breaking of scale invariance and, in consequence, the formation of universal droplets. It remains unclearwhether a simple, unified theoretical framework exists to analyse these phenomena. To address that, we introduce a density-dependent coupling into the GPE, which successfully describes this behaviour, whilepreserving a structure suitable for intuitive analytical and numerical exploration.In this talk, I will focus on the mathematical structure of the Gross-Pitaevskii description of attractive 2D Bose gases. I will discuss the origin and consequences of scale invariance, its breakdown in realisticsystems, and the limitations of the standard GPE. I will then show how these limitations can be overcome using a generalized GPE, and how this framework connects collapse dynamics, Townes solitons, and self-bound droplets. The lecture will emphasize analytical arguments, scaling properties, and their relevance for current experiments.
| 15.1.2026 |
Mathieu Lewin (CEREMADE, CNRS) |
Gross-Pitaevskii theory of supersolids |
Abstract: Supersolids have been the subject of much recent experimental work on ultra-cold Bose gases. In this talk I will explain the mathematical model behind it (the Gross-Pitaevskii equation) and state some recent rigorous results obtained in collaboration with P.T. Nam (Munich). I will explain how to mix tools from PDEs and statistical mechanics to study the phase diagram of this nonlinear equation. The main result is that there is a unique freezing transition for interaction potentials that are stable but not positive definite.
| 22.1.2026 |
Jerzy Łusakowski (IFD) |
THz radiation - phenomena and applications |
Abstract: THz radiation, which involves a part of the electromagnetic spectrumsituated between microwaves and infrared, has been attracting more andmore attention of researchers working in many areas of basic andapplied sciences. To name a few, one can mention, e.g., quantum optics,solid state physics, technology of metamaterials, fast communication ormedicine. During the presentation, I will describe the status ofscientific activity based on THz radiation and currently used laboratoryequipment. A particular attention will be paid to a 30-years oldtechnique, the THz time domain spectroscopy, which is the source ofunquestionable rapid development of THz-related activities. I will alsodescribe a few examples of a basic research in which THz techniqueswere used in quantum optics, semiconductor physics and medicine.
PROGRAM SEMINARIUM – SEMESTR LETNI 2025/26
| 26.2.2026 |
Tomasz Smołka (KMMF UW) |
Electromagnetic and Gravitational Hopfion-like solutions in de Sitter spacetime |
Abstract: Hopfions are a family of `solitonic’ field solutions that have a non-trivial topological structure associated with the Hopf fibration. I will present a generalisation of such solutions, based on conformal transformations, to de Sitter spacetime. Topological charges will be discussed.
| 5.3.2026 |
Piotr Mucha (MIMUW) |
Regular Solutions in the Framework of Besov Spaces |
Abstract: In this talk, I would like to present arguments explaining why theapproach based on Besov spaces provides some of the strongest results inthe analysis of systems of partial differential equations. I will focus ontheir fundamental properties and demonstrate how they can be effectivelyapplied to systems arising in fluid mechanics, in particular to theNavier–Stokes equations.I will also discuss a simple example related to the heat equation in orderto illustrate the relative simplicity and transparency of this approach.Alongside the basic definitions and properties of Besov spaces, I willoutline the main directions of development of this method, as well as itslimitations.The central role in this framework is played by Fourier analysis, whichprovides the most natural and intuitive description of Besov spaces andtheir structure.This will be a blackboard talk, and I will aim to keep close contact withthe audience throughout the presentation.
| 12.3.2026 |
Magdalena Stobińska-Moretto (FUW) |
Long-range photonic device-independent quantum key distribution using SPDC sources and linear optics |
Abstract: We address the question of the implementation of long-distance device-independent quantum key distribution (DI QKD) by proposing two experimentally viable schemes. Those schemes only use spontaneous parametric down-conversion (SPDC) sources and linear optics. They achieve favorable key rate scaling proportional to the square root of channel transmittance $\eta_t$, matching the twin-field protocol advantage. We demonstrate positive asymptotic key rates at detector efficiencies as low as 80\%, bringing DI QKD within the reach of current superconducting detector technology. Our security analysis employs the Entropy Accumulation Theorem to establish rigorous finite-size bounds, achieving finite-key rates at a detector efficiency of 89%. This work represents a critical milestone toward device-independent security in quantum communication networks, providing experimentalists with practical implementation pathways while maintaining the strongest possible security guarantees against quantum adversaries.
| 19.3.2026 |
Marcel Majocha (KMMF) |
Ruelle Bounds. The thermodynamic limit of superstable interacting systems |
Abstract: We discuss the classical theorem of D. Ruelle (1970), later refined by M. Lewin, concerning bounds on correlation functions in classical systems. The theorem states that for systems with superstable and lower-regular pairwise interactions, the correlation functions are uniformly bounded by a constant independent of the system size. Moreover, particle number fluctuations in subsystems are also bounded by constants that do not depend on the total volume of the system. These bounds play a fundamental role in the analysis of the thermodynamic limit and provide useful estimates in classical statistical physics.
| 26.3.2026 |
Robert Budzyński (OKWF) |
Numerical simulation of physical models on personal computers |
Abstract: How far can we get with physics simulations on modern consumer grade computer hardware? I explore the limits of the capabilities of computers most of us have at hand on the examples of lattice models of statistical physics, and simple nonlinear dynamical systems with many (10^4 - 10^6) degrees of freedom. The goal is interactive simulations with real time visualization of model behavior.
| 9.4.2026 |
Piotr Szymczak (IFT UW) |
On the ideal shapes of stalagmites |
Abstract: Stalagmites are column-like formations that rise from the floor of caves. They are formed by the buildup of minerals deposited from water dripping from the ceiling. The water dissolves minerals, such as calcium carbonate, from the rock above. As the water drips down, it loses carbon dioxide to the cave air. This causes the minerals to come out of solution and precipitate onto the cave floor, slowly building up the stalagmite. Nearly sixty years ago, Franke formulated a mathematical model for the growth of stalagmites. In this model, the local growth rate of a stalagmite is proportional to the oversaturation of calcium ions in the solution dripping down the stalagmite's surface. Franke postulated that - provided the physical conditions in the cave remain constant - after a sufficiently long period, the stalagmite will assume an ideal shape, which in later stages of growth will only move upwards without further change in its form. These conclusions were later confirmed in computer simulations yet the mathematical form of this ideal shape was not discovered. As we will show, Franke's model for stalagmite growth can be solved analytically, finding invariant, Platonic forms of stalagmites that could be observed in an "ideal cave", under constant physical conditions and with a constant flow of water dripping from an associated stalactite. Interestingly, it turns out that the shape numerically found in previous numerical studies is just one of a whole family of solutions. These new solutions describe stalagmites with a flat area at their peak of a certain fixed diameter, and conical stalagmites, with sharply pointed tops. All of these forms are observed in caves.
| 16.4.2026 |
Wojciech Kamiński (IFT UW) |
Charges in asymptotically de Sitter spacetimes |
Abstract: Einstein's equations are not conformally invariant, but they exhibit surprising relations to conformal geometry. Many of these conformal properties can be understood using fact that important tensor in conformal geometry, Fefferman-Graham obstruction tensor vanishes on every solution of Einstein gravity. Vanishing of Fefferman-Graham obstruction tensor (Anderson-called Fefferman-Graham equations, AFG) shares many similarities to Einstein's equations for example it is a Lagrangian theory. The problem of charges definition in asymptotically de Sitter spacetimes attracted recently some attention and it is interesting to analyze if AFG equations can be useful also in this context. I will describe relation of Wald-Zoupas charges to AFG equations which touches many interesting results in conformal geometry: for example Alexakis decomposition of global conformal invariants, Yang-Mills currents for conformal normal Cartan connection etc.
| 23.4.2026 |
Haipan Shi (Huzhou University) |
Differential Formula and Uncertainty principles of the Clifford-Fourier transform |
Abstract: The Clifford analysis extends the theory of complex variable functions to high-dimensional spaces, which mainly studies the properties of functions defined on R^n with values in Clifford algebra Cl{0,n}. More precisely, the quaternion algebra H is isomorphic to the Clifford algebra Cl_{0,2}.I will present the differential formulas and the uncertainty principles of the quaternion fractional Fourier transform, the Clifford-Fourier transform, and the fractional Clifford-Fourier transform.
| 30.4.2026 |
Alex Bols (ETH Zurich) |
Anyons in quantum spin systems : Superselection sectors and how to compute them |
Abstract: The theory of superselection sectors, first developed in algebraic quantum field theory and more recently adapted to quantum spin systems by Naaijkens and Ogata, provides a rigorous description of the anyonic excitations hosted by gapped ground states of (2+1)-dimensional quantum systems. After a brief introduction to the general framework, I will sketch how the sector theory can be computed explicitly in a class of exactly solvable models. The talk is based on joint work with Mahdie Hamdan, Boris Kjær, Pieter Naaijkens, and Siddarth Vadnerkar : arXiv:2310.19661, arXiv:2503.15611, arXiv:2511.21521, arXiv:2603.01936
| 7.5.2026 |
Piotr Sołtan (KMMF FUW) |
Non-local games and their algebras |
Abstract: I will give a survey of the theory of non-local games touching on its connections to various branches of mathematics. Time permitting I will conclude by showing how some quantum games give rise to quantum semigroups nd groups.
| 14.5.2026 |
Tomasz Taylor (Northeastern University & Uniwersytet Warszawski) |
Yang Mills theory in de Sitter spacetime |
Abstract: I will discuss the quantization of Yang-Mills theory in global de Sitter spacetime. I will describe the Hilbert space and discuss the properties of scattering amplitudes.
| 21.5.2026 |
Rafal Demkowicz-Dobrzański (IFT UW) |
Elusive quantum states - or, on quantum measurement and estimation theory |
Abstract: How to optimally extract information encoded in quantum states? What are the optimal measurements and estimators? What is the natural metric in the space of quantum states resulting from such considerations? What are the tensions, due to potential incompatibility of different measurement strategies? Can you go around them? All the answers to these questions and more are provided by quantum measurement and estimation theory!
| 28.5.2026 |
Krzysztof Wiśniewski (KMMF) |
Geometric Quantization: Basic Notions and New Perspectives |
Abstract: Geometric quantization is a procedure of assigning operators acting on a suitable classes of functions to functions on phase space in a geometrically meaningful way. We aim to present geometric quantization in a trivial setting, accessible to everyone knowing the basics of symplectic geometry. We also aim to highlight various relations between geometric quantization and Weyl quantization.
| 11.6.2026 |
Małgorzata Flis (KMMF) |
On the Lie Groupoid Approach to the Integration of Ordinary Differential Equations |
Abstract: We introduce Lie groupoids, Lie algebroids and Lie pseudogroups and we describe their relation with differential equations and, in particular, the problem of integration of vector fields.
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