Itinerant Quantum Math Meetings

Tuesday, October 27, 2026 - 11:00
Aula Seminari (3rd floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Alessandro Ferreri (Sapienza Università di Roma)

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Position-space invariants for topological crystalline insulators

The study of topological phases of crystalline insulators leads to the problem of characterizing homotopy classes of Fermi projections associated with gapped Schrödinger operators with space-group symmetries. The Bloch–Floquet decomposition provides a momentum-space description of the occupied states, in which crystalline symmetries give rise to topological invariants that distinguish phases under deformations preserving the spectral gap and the symmetries. The usual formulation of these invariants relies on this momentum-space description and on compatibility of the Fermi projection with the prescribed space-group. This motivates the search for a position-space formulation whose behavior can also be studied when a momentum-space description is unavailable or the symmetries are broken.

In this talk, I will present an operator-theoretic framework for expressing crystalline symmetry invariants directly in position space. The approach combines propagation properties and local trace-class regularity of Fermi projections with Fourier-analytic methods to derive reconstruction formulas relating position-space quantities to the invariants of a crystalline system. I will also discuss the stability of these quantities under perturbations of the Hamiltonian that preserve the spectral gap, highlighting the role of the spatial distribution of the perturbation.

Wednesday, June 3, 2026 - 15:00
Sala Consiglio (7th floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Maciej Zworski (University of California, Berkeley)

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Localised Davies generator for pseudodifferential operators

A classical Davies generator provides a Lindbladian for which the Gibbs state is stationary. Its construction involves precise knowledge of the Bohr spectrum or equivalently state evolution for all times. Recently Chen, Kastoryano and Gilyen proposed a construction involving localisation in time and carried it out in the case of finite dimensional Hilbert spaces. The resulting generators are called quantum Gibbs samplers as the corresponding Lindblad is expected to settle to the Gibbs state. In this note, we show that the construction also works for classes of unbounded operators, including pseudodifferential operators used in the study of classical/quantum correspondence in Lindblad evolution. We also show that the resulting jump operators are pseudo local.

Wednesday, June 3, 2026 - 11:00
Sala Consiglio (7th floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Stefan Teufel (University of Tübingen)

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Beyond linear response: an Ohm’s law for quantum Hall currents

I will present a recent result that establishes a form of Ohm’s law for the quantum Hall current in models of interacting fermions on a lattice at zero temperature. I will focus on two novel aspects: defining the Hall current properly in order to go beyond linear response calculations and computing this current to all orders in perturbation theory. These two aspects are both based on the concept of non-equilibrium almost stationary states, a form of ‘many-body resonances’ for infinite-volume quantum systems.

Tuesday, May 26, 2026 - 11:00
Sala Consiglio (7th floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Serena Federico (University of Bologna)

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Weyl calculus on graded Lie groups

In this talk, we shall discuss the existence of a Weyl pseudo-differential calculus on a graded Lie G.
To begin with, we will introduce a family of admissible quantizations on G and develop the corresponding pseudo-differential calculus. Afterwards, following classical criteria, we shall identify the suitable candidate Weyl quantization on G among all the admissible symmetric ones. Finally, we will show that in the case of the Heisenberg group, the Weyl quantization is uniquely determined.
This talk is based on a joint work with D. Rottensteiner and M. Ruzhansky.

Friday, May 8, 2026 - 11:00
Sala Consiglio (7th floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Yelena Guryanova (University of Basel / QuantumBasel)

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Cloning Quantum Channels

For states, the no-cloning theorem is one of the first encounters in quantum information: an arbitrary unknown pure state cannot be perfectly copied onto a waiting register. It’s simple then to infer that cloning N states onto M registers won’t work either, but by relaxing the problem to allow for imperfect (approximate) copying, one can investigate the rate and quality of N-to-M cloning. But what if we go further? Can we imagine cloning the cloner, in other words, cloning devices themselves? Questions around states have constituted decades of investigation and were, most recently, extended to cloning unitary gates. In this work we pose the question comprehensively and study general quantum channel cloning via a framework based on higher-order quantum operations. We establish necessary conditions for a family of channels to exhibit super-replication—those that can be cloned with a quadratic rate at high-quality (bounded error). Noisy phase-gate channels can be super-replicated but the full set of noisy unitaries; classical noise; and amplitude damping channels cannot. We present algorithms that search for channel cloners and study specific cloning strategies. In many cases, estimating and re-preparing is enough: for the unitary gates for which super-replication protocols were known, we construct simpler alternatives and establish a direct connection between channel cloning and Bayesian estimation.

Thursday, April 16, 2026 - 15:30
Aula Seminari (3rd floor) - Bd. 14 "Nave", Via Bonardi 9
Politecnico di Milano

Zoom link on request (contact Alessandro Olgiati by email)

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SPEAKER: Hynek Kovařík (Università degli studi di Brescia)

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Cwikel-Lieb-Rozenblum type estimates for magnetic Hamiltonians in dimension two

In this talk I will present Cwikel-Lieb-Rozenblum type inequalities for the number of negative eigenvalues of Pauli and Schroedinger operators in dimension two. The resulting upper bounds are sharp both in the weak as well as the strong coupling limit. In both cases, the nature of the inequality depends on whether the flux of the magnetic field is integer or not. The talk is based on a joint work with Matthias Baur.