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Semiclassical Entropy of BPS States in 4d N=2 Theories and Counts of Geodesics
[article]

2019
*
arXiv
*
pre-print

We relate a number

arXiv:1906.11839v2
fatcat:m4phhsohofdi7jryh27gzvvnua
*of*results*in*the theory*of*flat surfaces to BPS spectra*of*a class*of*4d*N*=*2*supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces –A_1 class S theories ...*In*particular, we apply classic results*of*Eskin and Masur,*which*determine the asymptotic growth*of*geodesic counts at large length on flat surfaces, as well as more recent progress*in*the mathematics ... We also thank Jayadev Athreya for helpful comments on an earlier draft*of*this paper. ...##
###
Fixed points of local actions of nilpotent Lie groups on surfaces

2016
*
Ergodic Theory and Dynamical Systems
*

non-zero for sufficiently small$t>0$,then$\mathsf{

doi:10.1017/etds.2015.73
fatcat:rxxg43mh5ndspdupi2eeubseey
*Fix*}(*G*)\*cap*K\neq \varnothing$. ... Assume$K$is a compact set*of**fixed*points*of*$\unicode[STIX]{x1D711}$and$U$is a neighborhood*of*$K$containing no other*fixed*points.Theorem.If the Dold*fixed*-point index*of*$\unicode[STIX]{x1D711}_{t}|U$is ... (a) The set*N*(X, U,*g*) := Y ∈*g*: U is isolating for Y and i(Y, U) = i(X, U) Lemma 4.*2*.*2*If dim (*g*) ≥*2*, every element*of**g*lies*in*an ideal*of**codimension*one. ...##
###
Linear nonbinary covering codes and saturating sets in projective spaces
[article]

2009
*
arXiv
*
pre-print

Let A_R,q denote a family

arXiv:0904.3835v1
fatcat:2mwv6j2mmrhtjmlpnovwxp2gcy
*of*covering codes,*in**which*the covering radius R and the size q*of*the underlying Galois field are*fixed*, while the code length tends to infinity. ... ,A_R,q^(R-1) such that, for*all*u >= u_0, the family A_R,q^(v) contains codes*of**codimension*r_u=Ru+v and length f_q^v(r_u) where f_q^v(r)=O(q^(r-R)/R) and u_0 is a constant. ... J.Östergård for useful discussions*of*problems on codes with covering radius three. ...##
###
Positively curved metrics on symmetric spaces with large symmetry rank
[article]

2012
*
arXiv
*
pre-print

We prove an obstruction at the level

arXiv:1209.4627v1
fatcat:dcmlcjvvu5b2lmjjzabtommywe
*of*rational cohomology*in*small degrees to the*existence**of*positively curved metrics with large symmetry rank. ... The symmetry rank bound is logarithmic*in*the dimension*of*the manifold. ... If,*in*fact, dk(M σ x ) ≤ 1, then Lemma 2.5 implies cod M σ x <*n*−*n*√*2*<*n*3 . Otherwise,*there**exists*a*2*-torus inside T*which**fixes*M σ x . ...##
###
Capelli identities on algebras with involution or graded involution

2022
*
Turkish Journal of Mathematics
*

*In*the associative case, the asymptotic equality between the

*codimensions*

*of*the T -ideal generated by the Capelli polynomial

*of*rank k

*2*+ 1 and the

*codimensions*

*of*the matrix algebra M k (F ) was proved ... Recently, similar results have been determined by the authors

*in*the case

*of*algebras with involution and superalgebras with graded involution. ... Regev

*in*[35] showed that if A is an associative P I -algebra, then c

*n*(A) is exponentially bounded, i.e.

*there*

*exist*constants α , β

*which*depend on A such that c

*n*(A) ≤ αβ

*n*for any

*n*≥ 1 . ...

##
###
Abelian gerbes, generalized geometries and foliations of small exotic R^4
[article]

2014
*
arXiv
*
pre-print

*In*the paper we prove the

*existence*

*of*the strict but relative relation between small exotic R^4 for a

*fixed*radial family

*of*DeMichelis-Freedman type, and cobordism classes

*of*

*codimension*one foliations ... For a

*fixed*radial family, we will show that the isotopy classes (invariance w.r.t. small diffeomorphisms or coordinate transformations)

*of*

*all*members

*in*this family are distinguished by the Godbillon-Vey ... Last but not least we acknowledged

*all*critical remarks

*of*the referees increasing strongly the readability

*of*the paper. ...

##
###
Positively curved manifolds with symmetry

2006
*
Annals of Mathematics
*

*There*are very few examples

*of*Riemannian manifolds with positive sectional curvature known.

*In*fact

*in*dimensions above 24

*all*known examples are diffeomorphic to locally rank one symmetric

*spaces*. ... Secondly, we show that

*in*dimensions above 18(k + 1)

*2*each M is tangentially homotopically equivalent to a rank one symmetric

*space*, where k > 0 denotes the cohomogeneity, k = dim(M/ Iso(M,

*g*)). ... Therefore

*there*

*exists*a number

*n*(l) such that L hk = L hk for

*all*k, k ≥

*n*(l) and h = 0, . . . , dim l i=1 S

*2*V ⊗ S i V . ...

##
###
Linear nonbinary covering codes and saturating sets in projective spaces

2011
*
Advances in Mathematics of Communications
*

A new concept

doi:10.3934/amc.2011.5.119
fatcat:2gz3nalzarbchgp2xmyov3fx3q
*of**N*-fold strong*blocking*set is introduced. ... Let A R,q denote a family*of*covering codes,*in**which*the covering radius R and the size q*of*the underlying Galois field are*fixed*, while the code length tends to infinity. ... By Theorem 3.7,*in*P*G*(3, q)*there**exists*a 3-fold strong*blocking*set*of*size 4q + 4. ...##
###
Free CR distributions

2012
*
Central European Journal of Mathematics
*

Indeed, the homogeneous model turns out to be (

doi:10.2478/s11533-012-0090-y
fatcat:dkcsuobznrcxdjuoxqtt6ug2ze
*n*+1,*n*)/P with a suitable parabolic subgroup P. We study the geometric properties*of*such real (2n+*n*^*2*)-dimensional submanifolds*in*C^*n*+*n*^*2*for*all**n*>1. ... The cases*of*CR dimensions*n*and*codimensions**n*^*2*are among the very few possibilities*of*the so called parabolic geometries. ... As well known,*there*is just the imaginary part*of*the center*of*the Levi component*g*0*in*p*which*is not*in*q. ...##
###
Large Arrays of Linearly Coupled Josephson Junctions: A Survey
[article]

2017
*
arXiv
*
pre-print

The works summarized here are devoted to the study

arXiv:1707.00038v1
fatcat:l4rb54jnm5gfpfvfqj32rhkocm
*of*where*in*parameter*space*the*in*-phase oscillations are stable and how the stability is lost. ...*In*this note I survey the extensive literature on the dynamics*of*large series arrays*of*identical current biased Josephson junctions coupled through various shared loads. ... Then if l =*N*/M*there**exists*an (l, M,*N*)-SWFS to (1),(*2*). . Q with*N*and normalize by the condition ψ*N*(0) = 0 for*all**N*. ...##
###
Approximation of holomorphic maps with a lower bound on the rank
[article]

2006
*
arXiv
*
pre-print

Let K be a closed polydisc or ball

arXiv:math/0610220v1
fatcat:tks2wafx7vbljmsnc4e5mdn5oi
*in*^*n*, and let Y be a quasi projective algebraic manifold*which*is Zariski locally equivalent to ^p, or a complement*of*an algebraic subvariety*of**codimension*>*2**in*... If r is an integer satisfying (*n*-r+1) (p-r+1)≥*2*then every holomorphic map from a neighborhood*of*K to Y with rank > r at every point*of*K can be approximated uniformly on K by entire maps ^*n*→ Y with ... Given ǫ > 0*there**exists*an automorphism Ψ*of*C*n**of*the form Ψ(z ′ , z ′′ ) = (z ′ , ψ(z ′ , z ′′ )) (z ′ ∈ C*n*−*2*, z ′′ ∈ C*2*) such that (i) |Ψ(z) − z| < ǫ for all z ∈ K, and (ii) Ψ(D × L) ⊂ C n \Σ. ...##
###
Approximation of holomorphic maps with a lower bound on the rank

2007
*
Proceedings of the American Mathematical Society
*

Let K be a closed polydisc or ball

doi:10.1090/s0002-9939-07-08956-3
fatcat:74xlom6ulrhffkp67thp3cpmqi
*in*C*n*, and let Y be a quasiprojective algebraic manifold*which*is Zariski locally equivalent to C p , or a complement*of*an algebraic subvariety*of**codimension*≥*2*...*n*→ Y with rank ≥ r at every point*of*C*n*. ... License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-*of*-use ...##
###
On the bounded compact approximation property and measures of noncompactness

1987
*
Journal of Functional Analysis
*

The Banach

doi:10.1016/0022-1236(87)90118-2
fatcat:5g2qgzcvkfevtklpiscubmqbse
*spaces*with the bounded compact approximation property are characterized by the completeness*of*measures*of*noncompactness. ... Applications to the theory*of*semi-Fredholm operators and to the algebraic properties*of*their canonical images*in*the Calkin algebra are discussed. 'T-J ... On the other hand, if F does not have the A-*CAP*for any*2*>O, by Theorem 2.3*there**exists*for each*n*E*N*a Banach*space*E, fP-sum*of*the*spaces*E,, 1 <p < cc (cf. [ 15, p. xii]). ...##
###
On some minimal supervarieties of exponential growth

2012
*
Journal of Algebra
*

*In*the present paper we investigate minimal supervarieties

*of*given superexponent over fields

*of*characteristic zero. ... We show that any minimal supervariety

*of*finite basic rank is generated by one

*of*the minimal superalgebras, introduced by Giambruno and Zaicev

*in*2003. ... For every variety V and for every

*n*1 the

*n*-th

*codimension*c

*n*(V)

*of*V is the dimension

*of*the vector

*space*P

*n*P

*n*∩Id(V) , where P

*n*is the

*space*

*of*multilinear polynomials

*of*degree

*n*

*in*a

*fixed*set ...

##
###
Positively curved cohomogeneity one manifolds and 3-Sasakian geometry

2008
*
Journal of differential geometry
*

The description yields a complete classification

doi:10.4310/jdg/1197320603
fatcat:enrnvomp7ngx5nbihtc4dlzwni
*in**all*dimensions but 7, where*in*addition to known examples, our list contains one exceptional*space*and two infinite families not yet known to carry metrics ... We provide an exhaustive description*of**all*simply connected positively curved cohomogeneity one manifolds. ... Then: (a) If L 1 and L*2*are two simple normal subgroups*of*H,*there**exists*an irreducible subrepresentation*of*H*in**G*on*which*both L 1 and L*2*act non-trivially. ...
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