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1. Anisotropic flow of identified hadrons in Xe-Xe collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ = 5.44 TeV

   https://doi.org/10.1007/JHEP10(2021)152  

   Acharya, S.; Adamová, D.; Adler, A.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Ahuja, I.; et al (October 2021, Journal of High Energy Physics)

   A bstract Measurements of elliptic ( v 2 ) and triangular ( v 3 ) flow coefficients of π ± , K ± , p+ $$ \overline{\mathrm{p}} $$ p ¯ , $$ {\mathrm{K}}_{\mathrm{S}}^0 $$ K S 0 , and Λ+ $$ \overline{\Lambda} $$ Λ ¯ obtained with the scalar product method in Xe-Xe collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5 . 44 TeV are presented. The results are obtained in the rapidity range | y | < 0 . 5 and reported as a function of transverse momentum, p T , for several collision centrality classes. The flow coefficients exhibit a particle mass dependence for p T < 3 GeV/ c , while a grouping according to particle type (i.e., meson and baryon) is found at intermediate transverse momenta (3 < p T < 8 GeV/ c ). The magnitude of the baryon v 2 is larger than that of mesons up to p T = 6 GeV/ c . The centrality dependence of the shape evolution of the p T -differential v 2 is studied for the various hadron species. The v 2 coefficients of π ± , K ± , and p+ $$ \overline{\mathrm{p}} $$ p ¯ are reproduced by MUSIC hydrodynamic calculations coupled to a hadronic cascade model (UrQMD) for p T < 1 GeV/ c . A comparison with v n measurements in the corresponding centrality intervals in Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5 . 02 TeV yields an enhanced v 2 in central collisions and diminished value in semicentral collisions. 

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2. On Weak Flexibility in Planar Graphs

   https://doi.org/10.1007/s00373-022-02564-1  

   Lidický, Bernard; Masařík, Tomáš; Murphy, Kyle; Zerbib, Shira (December 2022, Graphs and Combinatorics)

   Abstract Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs (J Graph Theory 92(3):191–206, 2019, https://doi.org/10.1002/jgt.22447 ). In this new setting, each vertex v in some subset of V ( G ) has a request for a certain color r ( v ) in its list of colors L ( v ). The goal is to find an L coloring satisfying many, but not necessarily all, of the requests. The main studied question is whether there exists a universal constant $$\varepsilon >0$$ ε > 0 such that any graph G in some graph class $$\mathscr {C}$$ C satisfies at least $$\varepsilon$$ ε proportion of the requests. More formally, for $$k > 0$$ k > 0 the goal is to prove that for any graph $$G \in \mathscr {C}$$ G ∈ C on vertex set V , with any list assignment L of size k for each vertex, and for every $$R \subseteq V$$ R ⊆ V and a request vector $$(r(v): v\in R, ~r(v) \in L(v))$$ ( r ( v ) : v ∈ R , r ( v ) ∈ L ( v ) ) , there exists an L -coloring of G satisfying at least $$\varepsilon |R|$$ ε | R | requests. If this is true, then $$\mathscr {C}$$ C is called $$\varepsilon$$ ε - flexible for lists of size k . Choi, Clemen, Ferrara, Horn, Ma, and Masařík (Discrete Appl Math 306:20–132, 2022, https://doi.org/10.1016/j.dam.2021.09.021 ) introduced the notion of weak flexibility , where $$R = V$$ R = V . We further develop this direction by introducing a tool to handle weak flexibility. We demonstrate this new tool by showing that for every positive integer b there exists $$\varepsilon (b)>0$$ ε ( b ) > 0 so that the class of planar graphs without $$K_4, C_5 , C_6 , C_7, B_b$$ K 4 , C 5 , C 6 , C 7 , B b is weakly $$\varepsilon (b)$$ ε ( b ) -flexible for lists of size 4 (here $$K_n$$ K n , $$C_n$$ C n and $$B_n$$ B n are the complete graph, a cycle, and a book on n vertices, respectively). We also show that the class of planar graphs without $$K_4, C_5 , C_6 , C_7, B_5$$ K 4 , C 5 , C 6 , C 7 , B 5 is $$\varepsilon$$ ε -flexible for lists of size 4. The results are tight as these graph classes are not even 3-colorable. 

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3. Type 𝐼𝐼 quantum subgroups of 𝔰𝔩_{𝔑}. ℑ: Symmetries of local modules

   https://doi.org/10.1090/cams/19  

   Edie-Michell, Cain (May 2023, Communications of the American Mathematical Society)

   This paper is the first of a pair that aims to classify a large number of the type I I II quantum subgroups of the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . In this work we classify the braided auto-equivalences of the categories of local modules for all known type I I quantum subgroups of C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . We find that the symmetries are all non-exceptional except for four cases (up to level-rank duality). These exceptional cases are the orbifolds C ( s l 2 , 16 ) Rep ⁡ ( Z 2 ) 0 \mathcal {C}(\mathfrak {sl}_{2}, 16)^0_{\operatorname {Rep}(\mathbb {Z}_{2})} , C ( s l 3 , 9 ) Rep ⁡ ( Z 3 ) 0 \mathcal {C}(\mathfrak {sl}_{3}, 9)^0_{\operatorname {Rep}(\mathbb {Z}_{3})} , C ( s l 4 , 8 ) Rep ⁡ ( Z 4 ) 0 \mathcal {C}(\mathfrak {sl}_{4}, 8)^0_{\operatorname {Rep}(\mathbb {Z}_{4})} , and C ( s l 5 , 5 ) Rep ⁡ ( Z 5 ) 0 \mathcal {C}(\mathfrak {sl}_{5}, 5)^0_{\operatorname {Rep}(\mathbb {Z}_{5})} . We develop several technical tools in this work. We give a skein theoretic description of the orbifold quantum subgroups of C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . Our methods here are general, and the techniques developed will generalise to give skein theory for any orbifold of a braided tensor category. We also give a formulation of orthogonal level-rank duality in the type D D - D D case, which is used to construct one of the exceptionals. We uncover an unexpected connection between quadratic categories and exceptional braided auto-equivalences of the orbifolds. We use this connection to construct two of the four exceptionals. In the sequel to this paper we will use the classified braided auto-equivalences to construct the corresponding type I I II quantum subgroups of the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . This will essentially finish the type I I II classification for s l n \mathfrak {sl}_n modulo type I I classification. When paired with Gannon’s type I I classification for r ≤ 6 r\leq 6 , our results will complete the type I I II classification for these same ranks. This paper includes an appendix by Terry Gannon, which provides useful results on the dimensions of objects in the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . 

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4. Character bounds for regular semisimple elements and asymptotic results on Thompson’s conjecture

   https://doi.org/10.1007/s00209-022-03193-3  

   Larsen, Michael; Taylor, Jay; Tiep, Pham Huu (February 2023, Mathematische Zeitschrift)

   Abstract For every integer k there exists a bound $$B=B(k)$$ B = B ( k ) such that if the characteristic polynomial of $$g\in \textrm{SL}_n(q)$$ g ∈ SL n ( q ) is the product of $$\le k$$ ≤ k pairwise distinct monic irreducible polynomials over $$\mathbb {F}_q$$ F q , then every element x of $$\textrm{SL}_n(q)$$ SL n ( q ) of support at least B is the product of two conjugates of g . We prove this and analogous results for the other classical groups over finite fields; in the orthogonal and symplectic cases, the result is slightly weaker. With finitely many exceptions ( p ,  q ), in the special case that $$n=p$$ n = p is prime, if g has order $$\frac{q^p-1}{q-1}$$ q p - 1 q - 1 , then every non-scalar element $$x \in \textrm{SL}_p(q)$$ x ∈ SL p ( q ) is the product of two conjugates of g . The proofs use the Frobenius formula together with upper bounds for values of unipotent and quadratic unipotent characters in finite classical groups. 

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5. J/ψ elliptic and triangular flow in Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ = 5.02 TeV

   https://doi.org/10.1007/JHEP10(2020)141  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; et al (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The inclusive J/ ψ elliptic ( v 2 ) and triangular ( v 3 ) flow coefficients measured at forward rapidity (2 . 5 < y < 4) and the v 2 measured at midrapidity (| y | < 0 . 9) in Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5 . 02 TeV using the ALICE detector at the LHC are reported. The entire Pb-Pb data sample collected during Run 2 is employed, amounting to an integrated luminosity of 750 μ b − 1 at forward rapidity and 93 μ b − 1 at midrapidity. The results are obtained using the scalar product method and are reported as a function of transverse momentum p T and collision centrality. At midrapidity, the J/ ψ v 2 is in agreement with the forward rapidity measurement. The centrality averaged results indicate a positive J/ ψ v 3 with a significance of more than 5 σ at forward rapidity in the p T range 2 < p T < 5 GeV/ c . The forward rapidity v 2 , v 3 , and v 3 /v 2 results at low and intermediate p T ( p T ≲ 8 GeV/ c ) exhibit a mass hierarchy when compared to pions and D mesons, while converging into a species-independent curve at higher p T . At low and intermediate p T , the results could be interpreted in terms of a later thermalization of charm quarks compared to light quarks, while at high p T , path-length dependent effects seem to dominate. The J/ ψ v 2 measurements are further compared to a microscopic transport model calculation. Using a simplified extension of the quark scaling approach involving both light and charm quark flow components, it is shown that the D-meson v n measurements can be described based on those for charged pions and J/ ψ flow. 

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