204 research outputs found
İsmail Bey Gutgaşınlı, the one of the Azerbaijan Educators and his first story under the effect of Europe: Reşit Bey and Saadet Hanim
No full textl9th century was period during which mutual relations among cultures and literatures became strong and accelerated, and was session that Azerbaijani literature broke the patterns of regionalism, adapted to world literature in some degree. In the first quarter of l9th century, new generation of intellectuals grew, progress and development occurred in all areas of Cultural life in Azerbaijan. Changing people due to modernized life, forced literature to get new shape and new styles, thus new way opened in prose genre of Azerbaijani literature. İsmail Bey Gutgaşınlı was one of the first ambassadors of this newness. Author attach importance to show mental anguishes, feelings and thoughts about problems in social life of characters in his literary work "Reşit Bey ve Saadet Hanım" that author wrote in Warsaw during his military service. Author used commitment to soil and nature as motif. The author who has grasp of both eastern and western culture, made effort to synthesize the positive sides of this two dili'erent cultural systems in the personality of his characters. The work is important, For it played the first role in the rise of consciousness bound to realism in Azerbaijani literature.Kültürler ve edebiyatlar arası karşılıklı ilişkilerin güçlendiği ve hızlandığı bir dönem olan XIX. yüzyıl, Azerbaycan edebiyatının da mahalliliğin kalıplarını kırdığı, bir ölçüde de olsa dünya edebiyatına uyum sağlama sürecine girdiği bir devre olmuştur. XIX. yüzyılın ilk çeyreğinde Azerbaycan'da daha yeni bir aydın nesil yetişmiş, kültür hayatının bütün alanlarında bir ilerleme ve gelişme yaşanmıştır. Yenileşen hayatla birlikte belli bir değişime uğrayan insanlar, edebiyatı da yeni şekil ve yeni tarzlara zorlamış, böylece Azerbaycan edebiyatında nesir türünde yeni bir çığır açılmıştır. İsmail Bey Gutgaşınlı, bu yeniliğin ilk temsilcilerinden olmuştur. Yazarın Varşova'da askeri hizmetteyken kaleme aldığı "Reşit Bey ve Saadet Hanım" isimli eseri kahramanlarının ruhsal ıstıraplarının yanı sıra onların sosyal hayatla, yaşanılan zamanla, toplum içerisinde karşılaştıkları problemlerle ilgili duygu ve düşüncelerini yansıtmaya önem vermiştir. Yazar, eserde toprağa ve tabiata bağlılığı motif olarak kullanmıştır. Hem Doğu hem de Batı kültürüne vâkıf olan yazar, kendi kahramanlarının şahsında bu iki Farklı kültür sisteminin olumlu yönlerinin sentezine çaba göstermiştir. Eser, Azerbaycan edebiyatında realizme bağlı bir şuurun uyanmasında ilk rolü oynadığından önem taşımaktadır
Twisted sheaves and SU(r)/Z_r Vafa-Witten theory
No full textThe SU (r) Vafa–Witten partition function, which virtually counts Higgs pairs on a projective surface S, was mathematically defined by Tanaka–Thomas. On the Langlands dual side, the first-named author recently introduced virtual counts of Higgs pairs on μ r-gerbes. In this paper, we instead use Yoshioka’s moduli spaces of twisted sheaves. Using Chern character twisted by rational B-field, we give a new mathematical definition of the SU (r) / Z r Vafa-Witten partition function when r is prime. Our definition uses the period-index theorem of de Jong. S-duality, a concept from physics, predicts that the SU (r) and SU (r) / Z r partition functions are related by a modular transformation. We turn this into a mathematical conjecture, which we prove for all K3 surfaces and prime numbers r
Twisted sheaves and SU(r)/Z_r Vafa-Witten theory
No full textThe SU (r) Vafa–Witten partition function, which virtually counts Higgs pairs on a projective surface S, was mathematically defined by Tanaka–Thomas. On the Langlands dual side, the first-named author recently introduced virtual counts of Higgs pairs on μ r-gerbes. In this paper, we instead use Yoshioka’s moduli spaces of twisted sheaves. Using Chern character twisted by rational B-field, we give a new mathematical definition of the SU (r) / Z r Vafa-Witten partition function when r is prime. Our definition uses the period-index theorem of de Jong. S-duality, a concept from physics, predicts that the SU (r) and SU (r) / Z r partition functions are related by a modular transformation. We turn this into a mathematical conjecture, which we prove for all K3 surfaces and prime numbers r
Vafa-Witten theory on N=2 and N=4 twisted superspace in four dimensions
No full textWe construct a new off-shell twisted real form of the hypermultiplet with a scalar and an anti-self-dual tensor superfields. Using the N = 2 twisted superspace formalism, we construct a Donaldson-Witten theory coupled to the real form of the hypermultiplet. We show that this action possesses the Vafa-Witten type N = 4 twisted supersymmetry at the on-shell level. We also reconstruct the action using a N = 4 twisted superconnection formalism
A proof of a conjecture of Gukov-Pei-Putrov-Vafa
No full textIn this paper, we prove Gukov-Pei-Putrov-Vafa\u27s conjecture that the Witten-Reshetikhin-Turaev invariants are radial limits of homological blocks, which are -series introduced by them for plumbed -manifolds with negative definite linking matrices. In our previous work, the author attributed this conjecture to the holomorphy of certain rational functions by developing an asymptotic formula based on the Euler-Maclaurin summation formula. However, it is challenging to prove holomorphy for general plumbed manifolds. In this paper, we address this challenge using induction on a sequence of trees obtained by repeating pruning trees.18 pages, 2 figure
Cohomological X-independence for Higgs bundles and Gopakumar–Vafa invariants
No full textThe aim of this paper is two-fold. Firstly, we prove Toda’s X-independence conjecture for Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison’s work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank r and Euler characteristic X which are not necessary coprime, and show that it does not depend on X. This result extends the Hausel–Thaddeus conjecture on the X-independence of E-polynomials proved by Mellit, Groechenig–Wyss–Ziegler and Yu in two ways: We obtain an isomorphism of mixed Hodge modules on the Hitchin base rather than an equality of E-polynomials, and we do not need the coprime assumption. The proof of these results is based on a description of the moduli stack of one-dimensional coherent sheaves on a local curve as a global critical locus which is obtained in the companion paper by the first author and Naruki Masuda
G(2) holonomy, Taubes' construction of Seiberg-Witten invariants and superconducting vortices
No full textUsing a reformulation of topological N = 2 QFT’s in M-theory setup, where QFT is realized via M5 branes wrapping co-associative cycles in a G2 manifold constructed from the space of self-dual 2-forms over a four-fold X, we show that superconducting vortices are mapped to M2 branes stretched between M5 branes. This setup provides a physical explanation of Taubes’ construction of the Seiberg-Witten invariants when X is symplectic and the superconducting vortices are realized as pseudo-holomorphic curves. This setup is general enough to realize topological QFT’s arising from N = 2 QFT’s from all Gaiotto theories on arbitrary 4-manifolds. © 2020, The Author(s)
Some analytic aspects of Vafa-Witten twisted N̳ = 4 supersymmetric Yang-Millseory theory
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.In title on title page, double underscored "N" appears as upper case script. Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 118-121).Given an oriented Riemannian four-manifold equipped with a principal bundle, we investigate the moduli spaceMVW of solutions to the Vafa-Witten equations. These equations arise from a twist of N = 4 supersymmetric Yang-Mills theory. Physicists believe that this theory has a well-defined partition function, which depends on a single complex parameter. On one hand, the S-duality conjecture predicts that this partition function is a modular form. On the other hand, the Fourier coefficients of the partition function are supposed to be the "Euler characteristics" of various moduli spacesMASD of compactified anti-self-dual instantons. For several algebraic surfaces, these Euler characteristics were verified to be modular forms. Except in certain special cases, it's unclear how to precisely define the partition function. If there is a mathematically sensible definition of the partition function, we expect it to arise as a gauge-theoretic invariant of the moduli spaces MVW. The aim of this thesis is to initiate the analysis necessary to define such invariants. We establish various properties, computations, and estimates for the Vafa-Witten equations. In particular, we give a partial Uhlenbeck compactification of the moduli space.by Bernard A.Mares, Jr.Ph.D
Vafa-Witten invariants, Ramanujan's continued fractions, and cosmic strings
No full textWe conjecture a structure formula for the Vafa-Witten
partition function for surfaces with holomorphic 2-form. The conjecture is
based on -duality and a structure formula for the vertical contribution
previously derived by the third-named author using Gholampour-Thomas's theory
of virtual degeneracy loci.
For ranks , conjectural expressions for the partition function in
terms of the theta functions of and Seiberg-Witten
invariants were known. We conjecture new expressions for in terms of
the theta functions of , Seiberg-Witten invariants,
and continued fractions studied by Ramanujan. The vertical part of our
conjectures is proved for low virtual dimensions by calculations on nested
Hilbert schemes.
The horizontal part of our conjectures gives predictions for virtual Euler
characteristics of Gieseker-Maruyama moduli spaces of stable sheaves. In this
case, our formulae are sums of universal functions with coefficients in Galois
extensions of . The universal functions, corresponding to different
quantum vacua, are permuted under the action of the Galois group.
For we also find relations with Hauptmoduln of . We
present -theoretic refinements for involving weak Jacobi forms.Comment: 62 pages. Typos corrected. Published versio
- …
