A5027217863- Algebraic structures and combinatorial models
- Homotopy and Cohomology in Algebraic Topology
- Geometric and Algebraic Topology
- Advanced Operator Algebra Research
- Advanced Topics in Algebra
- Advanced Combinatorial Mathematics
- Ruminant Nutrition and Digestive Physiology
- Topological and Geometric Data Analysis
- Milk Quality and Mastitis in Dairy Cows
- Meat and Animal Product Quality
- Nonlinear Waves and Solitons
- Electromagnetic Compatibility and Measurements
- Coccidia and coccidiosis research
- Soil, Finite Element Methods
- Advanced Algebra and Geometry
- Media, Journalism, and Communication History
- Hygrothermal properties of building materials
- Silymarin and Mushroom Poisoning
- Soil Mechanics and Vehicle Dynamics
- EEG and Brain-Computer Interfaces
- Magnetism in coordination complexes
- Natural Products and Biological Research
- Biotin and Related Studies
- Metal complexes synthesis and properties
- Metal-Organic Frameworks: Synthesis and Applications
Université de Montpellier
2022-2024
Centre National de la Recherche Scientifique
2018-2024
University of Zurich
2021-2023
Azienda-Unita' Sanitaria Locale Di Cesena
2022
Université Paris Cité
2018-2022
Institut de Mathématiques de Jussieu-Paris Rive Gauche
2017-2022
Waseda University
2018-2022
Sorbonne Université
2020
Utah State University
2018
Sorbonne Paris Cité
2018
We develop the general theory for construction of Extended Topological Quantum Field Theories (ETQFTs) associated with Costantino-Geer-Patureau quantum invariants closed 3-manifolds. In order to do so, we introduce relative modular categories, a class ribbon categories which are modeled on representations unrolled groups, and can be thought as non-semisimple analogue categories. Our approach exploits 2-categorical version universal introduced by Blanchet, Habegger, Masbaum, Vogel. The...
We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for construction 1+1+1-TQFTs extending CGP invariants, which non-semisimple invariants closed 3-manifolds decorated with ribbon graphs and cohomology classes. When we consider zero class, these shown coincide renormalized Hennings coming from corresponding small groups.
In [M. De Renzi, A. Gainutdinov, N. Geer, B. Patureau-Mirand and I. Runkel, 3-dimensional TQFTs from non-semisimple modular categories, preprint (2019), arXiv:1912.02063[math.GT]], we constructed topological quantum field theories (TQFTs) using not necessarily semisimple categories. Here, study projective representations of mapping class groups surfaces defined by these TQFTs, express the action a set generators through algebraic data underlying category [Formula: see text]. This allows us...
An observational study was conducted on 18 dairy farms located in the area of Parmigiano Reggiano cheese production with aim to supply some recommendations regarding more efficient TMR physical form. The effects particle size distributions digestion process and productivity were investigated. Lower appeared improve resulted increased DMI, milk yield, casein level without affecting fat. Routinary measurement PSPS could be a good practice standardize distribution maximize DMI productivity.
Vitamin E, known for its great nutritional importance, is normally included in animal diets as DL-α-tocopherol acetate. The authors propose a method that makes it possible to determine the concentration of vitamin E plasma without saponification. This enable avoid aggressive treatments on analyte and complex procedures; detects only form DL-α-tocopherol.Lipoproteins analysed were denaturised by methanol. was extracted petroleum ether presence NaCl. extract dried rotavapor at 45 °C,...
In vitro” Dry Matter (IVDMD) and fiber degradability (IVNDFD) dynamics were determined for Total Mixed Rations (TMR) typical of Parmigiano Reggiano cheese area. The same parameters estimated on some these ration also “in vivo” a group fresh cows. “In trial showed values 62.21 44.82% DMD NDFD respectively, while average IVDMD was 67.48 74.33% at 24 48 hours respectively. At the intervals IVNDFD 49.32 62.61%, indicating an high digestibility cow. Based equations values, ruminal retention time...
We construct a braided monoidal functor $J_4$ from Bobtcheva and Piergallini's category $4\mathrm{HB}$ of connected 4-dimensional 2-handlebodies (up to 2-deformations) an arbitrary unimodular ribbon $\mathcal{C}$, which is not required be semisimple. The main example target provided by $H$-mod, the left modules over Hopf algebra $H$. source freely generated, as category, BPH (short for Bobtcheva-Piergallini algebra), this sent Kerler-Lyubashenko end $\int_{X \in \mathcal{C}} X \otimes X^*$...
Starting from an abelian group $G$ and a factorizable ribbon Hopf $G$-bialgebra $H$, we construct TQFT $J_H$ for connected framed cobordisms between surfaces with boundary decorated cohomology classes coefficients in $G$. When restricted to the subcategory of trivial decorations, our functor recovers special case Kerler-Lyubashenko TQFTs, namely those associated algebras. Our result is inspired by work Blanchet-Costantino-Geer-Patureau, who constructed non-semisimple TQFTs admissible using...
For a root of unity $\zeta$ odd prime order, we restrict coefficients non-semisimple quantum representations mapping class groups associated with the small group $\mathfrak{u}_\zeta \mathfrak{sl}_2$ from $\mathbb{Q}(\zeta)$ to $\mathbb{Z}[\zeta]$. We do this by exhibiting explicit bases states spaces that span $\mathbb{Z}[\zeta]$-lattices are invariant under projective actions groups.
We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories functors in their image.The circle category an ETQFT produced by our construction is equivalent to the full subcategory projective objects underlying category.In particular, it need not be semisimple.
This survey covers some of the results contained in papers by Costantino, Geer and Patureau (https://arxiv.org/abs/1202.3553) Blanchet, (https://arxiv.org/abs/1404.7289). In first one authors construct two families Reshetikhin-Turaev-type invariants 3-manifolds, $\mathrm{N}_r$ $\mathrm{N}^0_r$, using non-semisimple categories representations a quantum version $\mathfrak{sl}_2$ at $2r$-th root unity with $r \geqslant 2$. The secondary $\mathrm{N}^0_r$ conjecturally extend original...
We recover the family of non-semisimple quantum invariants closed oriented 3-manifolds associated with small group \mathfrak{sl_2} using purely combinatorial methods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These can be understood as a first-order extension Witten–Reshetikhin–Turaev invariants, which reformulated following our approach in case rational homology spheres.
Interventional cardiologists' mental workload may impact on their performance as well patients' outcome. Nevertheless, little attention is paid to the monitoring and optimization of status. Electroencephalogram (EEG)-based neural-interfaces can estimate fatigue sleepiness through spectral analysis techniques amplitude alpha waves a widely validated indicator engagement's level.The present study aims describe variation psychometrics neurometrics during work shift in population 7...
We provide a homological model for family of quantum representations mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives new geometric point view on these representations, and it gathers into one theory two the most promising constructions investigating linearity groups. More precisely, if $\varSigma_{g,1}$ is surface genus $g$ with $1$ boundary component, we consider (crossed) action its group $\mathrm{Mod}(\varSigma_{g,1})$...
We provide a combinatorial description of the monoidal category generated by fundamental representation small quantum group $\mathfrak{sl}_2$ at root unity $q$ odd order. Our approach is diagrammatic, and it relies on an extension Temperley-Lieb specialized $\delta = -q-q^{-1}$.