Prossimi Seminari

19 Febbraio 2026

Aula Lagrange

ore 14:00

Tony Zorman

(Hamburg)

The reflection equation

and braided module categories

-------------------------------------------------------

ore 15:15

Sebastian Halbig

(Marburg)

Applications of category theory, representation theory, and geometry in (topological) quantum computing.

Abstract: 

Zorman: Solutions to the (quantum) Yang–Baxter equation, originally motivated by statistical mechanics and dynamical systems, have proven to be a powerful tool for generating (quantum) knot invariants, and the associated concept of a braided monoidal category has become foundational in representation theory and related fields.

In certain cases, these categorical structures can be described purely algebraically: a tensor product and a braiding on the category of modules of an algebra over a field may be completely described by putting additional structure on the algebra, which allows one to study "nice" braided monoidal categories purely algebraically.

A similar situation occurs when considering the reflection equation—a cousin of the Yang–Baxter equation arising in physical systems with boundary conditions. Solutions thereof instead lead to braided module categories, which may again be realised algebraically as additional conditions to put on a certain class of algebras.

In this talk, I will give an overview of the different constructions at work, with a view towards the categorical, rather than the algebraic, picture. Time permitting, I will talk about some ongoing joint work with Matti Stroiński to realise braided module categories  over a braided monoidal category as (lax) bimodule monads over its (lax) Drinfeld centre.

Halbig: In this informal talk, we are going to discuss different aspects of the mathematics underlying quantum computing and their connections to research topics in Torino. Specifically, we will give a brief overview of three closely related topics:

(a) anyonic quantum computing models and their connection to solutions of the Yang–Baxter equation,

(b) diagrammatic tools in quantum computing,

(c) a gauge-theoretic perspective on quantum computing.

If time permits, I will also briefly address recent progress made together with U. Krähmer towards extending the paradigm of topological quantum computing towards the non-semisimple realm.

Calendario Generale:

In rosso i seminari futuri.

• 19 febbraio 2026, S. Halbig (Marburg), Applications of category theory, representation theory, and geometry in (topological) quantum computing.

• 19 febbraio 2026, T. Zorman (Hamburg), The Reflection equation and braided module categories

• 5 febbraio 2026, T. Weber, Quantization of infinitesimal braidings

• 29 Gennaio 2026, H. Chen (Xi'an Jiatong-Liverpool Un.), The Iwasawa µ-invariant of fine Selmer groups associated to general Drinfeld modules.

• 16 Dicembre 2025, G. Rosso (Concordia Un.), A non-archimedean Ax–Lindemann theorem for Shimura varieties.

• 12 Dicembre 2025, M. Abreu (Un. Basilicata), Factors and Hamiltonicity in regular graphs

• 29 Ottobre 2025, M. Mula (Bundeswehr Un.), Modular polynomials for cryptography: zero-knowledge from genus-zero modular curves

• 19 Giugno 2025, C. Sava (Charles Un.),  ∞-Dold-Kan correspondence via representation theory

• 26 Maggio 2025, G. Rosso (Concordia Un.), Specialness for non-archimedean varieties

• 25 Marzo 2025, M. Rossi (Milano Bicocca), Some results on the geometry of arithmetic random waves

• 25 Marzo 2025, G. Cherubini (INdAM), Boyd’s probabilistic model for harmonic numbers divisible by p

• 13 Marzo 2025, G. Bogo (Bielefeld), Picard-Fuchs differential equations for families of abelian varieties with real multiplication 

• 28 Febbraio 2025, F.M. Saettone (Weizmann Inst. Sc.), Equidistribution of CM points via Drinfeld uniformization and automorphic forms

• 20 Febbraio 2025, M. Longo (Padova), On the Tamagawa number conjecture for motives of modular forms

• 29 Gennaio 2025, D. Spriano (Oxford), No finitely generated group is indigestible for the Loch-Ness monster.

• 16 Gennaio 2025, A. Conti (Heidelberg), Bogomolov property for Galois representations with big local image.

• 13 Novembre 2024; F. Cioffi (Napoli), Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases on Hilbert schemes.

• [Mathlab] 30 Ottobre 2024, Y. Bugeaud (Strasbourg), On the decimal expansion of e.

• 1 Ottobre 2024, L. De Feo (IBM Zürich), The isogeny toolbox

• 28 Maggio 2024, F. Pellarin (Roma I), Some remarks on the factorization of the sine function

• 15 Maggio 2024, A. Conti (Luxembourg), Prime power congruences between Galois representations

• 11 Aprile 2024, M. Gran (Louvain-la-neuve), On the naturalness of Mal'tsev categories

• 15 Marzo 2024, J. Jenvrin (Grenoble), On the height of some generators of Galois extensions with big Galois groups