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

Shamit Kachru, Richard Nally, Arnav Tripathy, Max Zimet
2019 arXiv   pre-print
We relate a number 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.  ... 
arXiv:1906.11839v2 fatcat:m4phhsohofdi7jryh27gzvvnua

Fixed points of local actions of nilpotent Lie groups on surfaces

MORRIS W. HIRSCH
2016 Ergodic Theory and Dynamical Systems  
non-zero for sufficiently small$t>0$,then$\mathsf{Fix}(G)\cap K\neq \varnothing$.  ...  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.  ... 
doi:10.1017/etds.2015.73 fatcat:rxxg43mh5ndspdupi2eeubseey

Linear nonbinary covering codes and saturating sets in projective spaces [article]

Alexander A. Davydov, Stefano Marcugini Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russian Federation, Department of Mathematics and Informatics, Perugia University, Perugia, Italy)
2009 arXiv   pre-print
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.  ...  ,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.  ... 
arXiv:0904.3835v1 fatcat:2mwv6j2mmrhtjmlpnovwxp2gcy

Positively curved metrics on symmetric spaces with large symmetry rank [article]

Lee Kennard
2012 arXiv   pre-print
We prove an obstruction at the level 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 < nn2 < n 3 . Otherwise, there exists a 2-torus inside T which fixes M σ x .  ... 
arXiv:1209.4627v1 fatcat:dcmlcjvvu5b2lmjjzabtommywe

Capelli identities on algebras with involution or graded involution

FRANCESCA SAVIELLA BENANTI, ANGELA VALENTI
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 .  ... 
doi:10.55730/1300-0098.3223 fatcat:pnyx5qa4qfesrdhgefguorvjie

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

Torsten Asselmeyer-Maluga, Jerzy Król
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.  ... 
arXiv:0904.1276v5 fatcat:3j423xv2vjdifg2g5t3jf3lidq

Positively curved manifolds with symmetry

Burkhard Wilking
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 .  ... 
doi:10.4007/annals.2006.163.607 fatcat:aod7wkh5urglzf34sahkd2c5iu

Linear nonbinary covering codes and saturating sets in projective spaces

Fernanda Pambianco, Stefano Marcugini, Massimo Giulietti, Alexander Davydov
2011 Advances in Mathematics of Communications  
A new concept 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.  ... 
doi:10.3934/amc.2011.5.119 fatcat:2gz3nalzarbchgp2xmyov3fx3q

Free CR distributions

Gerd Schmalz, Jan Slovák
2012 Central European Journal of Mathematics  
Indeed, the homogeneous model turns out to be (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.  ... 
doi:10.2478/s11533-012-0090-y fatcat:dkcsuobznrcxdjuoxqtt6ug2ze

Large Arrays of Linearly Coupled Josephson Junctions: A Survey [article]

D. G. Aronson
2017 arXiv   pre-print
The works summarized here are devoted to the study 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.  ... 
arXiv:1707.00038v1 fatcat:l4rb54jnm5gfpfvfqj32rhkocm

Approximation of holomorphic maps with a lower bound on the rank [article]

Kolarič Dejan
2006 arXiv   pre-print
Let K be a closed polydisc or ball 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 n2 , z ′′ ∈ C 2 ) such that (i) |Ψ(z) − z| < ǫ for all z ∈ K, and (ii) Ψ(D × L) ⊂ C n \Σ.  ... 
arXiv:math/0610220v1 fatcat:tks2wafx7vbljmsnc4e5mdn5oi

Approximation of holomorphic maps with a lower bound on the rank

Dejan Kolarič
2007 Proceedings of the American Mathematical Society  
Let K be a closed polydisc or ball 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 codimension2  ...  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  ... 
doi:10.1090/s0002-9939-07-08956-3 fatcat:74xlom6ulrhffkp67thp3cpmqi

On the bounded compact approximation property and measures of noncompactness

Kari Astala, Hans-Olav Tylli
1987 Journal of Functional Analysis  
The Banach 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]).  ... 
doi:10.1016/0022-1236(87)90118-2 fatcat:5g2qgzcvkfevtklpiscubmqbse

On some minimal supervarieties of exponential growth

Onofrio Mario Di Vincenzo, Ernesto Spinelli
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  ... 
doi:10.1016/j.jalgebra.2012.07.005 fatcat:qdrdr4kpu5gbzieki42r6qhmh4

Positively curved cohomogeneity one manifolds and 3-Sasakian geometry

Karsten Grove, Burkhard Wilking, Wolfgang Ziller
2008 Journal of differential geometry  
The description yields a complete classification 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.  ... 
doi:10.4310/jdg/1197320603 fatcat:enrnvomp7ngx5nbihtc4dlzwni
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