Relevant bibliographies by topics / Equivariant localization

Academic literature on the topic 'Equivariant localization'

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Published: 14 March 2023

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Journal articles on the topic "Equivariant localization"

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Alekseev, A., E. Meinrenken, and C. Woodward. "Group-valued equivariant localization." Inventiones Mathematicae 140, no. 2 (May 1, 2000): 327–50. http://dx.doi.org/10.1007/s002220000056.

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Katz, Gabriel. "Localization in equivariant bordisms." Mathematische Zeitschrift 213, no. 1 (May 1993): 617–45. http://dx.doi.org/10.1007/bf03025741.

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Tirkkonen, Olav. "Equivariant BRST and localization." Theoretical and Mathematical Physics 98, no. 3 (March 1994): 344–49. http://dx.doi.org/10.1007/bf01102211.

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Kusakabe, Yuta. "An implicit function theorem for sprays and applications to Oka theory." International Journal of Mathematics 31, no. 09 (July 17, 2020): 2050071. http://dx.doi.org/10.1142/s0129167x20500718.

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We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields interpolation. This proof and Lárusson’s elementary proof of the converse give an elementary proof of the equivalence between approximation and interpolation. The second application concerns the Oka property of a blowup. We prove that the blowup of an algebraically Oka manifold along a smooth algebraic center is Oka. In the appendix, equivariantly Oka manifolds are characterized by the equivariant version of Gromov’s condition [Formula: see text], and the equivariant localization principle is also given.
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Bruzzo, Ugo, and Vladimir Rubtsov. "On localization in holomorphic equivariant cohomology." Central European Journal of Mathematics 10, no. 4 (April 19, 2012): 1442–54. http://dx.doi.org/10.2478/s11533-012-0054-2.

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Smithies, Laura. "Equivariant analytic localization of group representations." Memoirs of the American Mathematical Society 153, no. 728 (2001): 0. http://dx.doi.org/10.1090/memo/0728.

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Dykstra, Hans M., Joseph D. Lykken, and Eric J. Raiten. "Exact path integrals by equivariant localization." Physics Letters B 302, no. 2-3 (March 1993): 223–29. http://dx.doi.org/10.1016/0370-2693(93)90388-x.

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Karpenko, Nikita, and Alexander Merkurjev. "Equivariant connective 𝐾-theory." Journal of Algebraic Geometry 31, no. 1 (October 28, 2021): 181–204. http://dx.doi.org/10.1090/jag/773.

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For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective K K -theory mapping to the equivariant K K -homology of Guillot and the equivariant algebraic K K -theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.
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Duflot, J. "Erratum to "Localization of Equivariant Cohomology Rings"." Transactions of the American Mathematical Society 290, no. 2 (August 1985): 857. http://dx.doi.org/10.2307/2000321.

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Duflot, J. "Erratum to: ‘‘Localization of equivariant cohomology rings”." Transactions of the American Mathematical Society 290, no. 2 (February 1, 1985): 857. http://dx.doi.org/10.1090/s0002-9947-1985-0792834-5.

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Dissertations / Theses on the topic "Equivariant localization"

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Pedroza, Andrés. "Equivariant formality and localization formulas /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2004.

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Thesis (Ph.D.)--Tufts University, 2004.
Adviser: Loring W. Tu. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 43-45). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
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Hössjer, Emil. "Equivariant Localization in Supersymmetric Quantum Mechanics." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355329.

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We review equivariant localization and through the Feynman formalism of quantum mechanics motivate its role as a tool for calculating partition functions. We also consider a specific supersymmetric theory of one boson and two fermions and conclude that by applying localization to its partition function we may arrive at a known result that has previously been derived using different approaches. This paper follows a similar article by Levent Akant.
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Takeda, Yuichiro. "Localization theorem in equivariant algebraic K-theory." 京都大学 (Kyoto University), 1997. http://hdl.handle.net/2433/202419.

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Chen, Hua. "The localization theorems of S³-equivariant cohomologies /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108307745.

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Ronzani, Massimiliano. "Instanton counting on compact manifolds." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/3582.

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In this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.
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Books on the topic "Equivariant localization"

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Szabo, Richard J. Equivariant Cohomology and Localization of Path Integrals. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46550-2.

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Smithies, Laura. Equivariant Analytic Localization of Group Representations. American Mathematical Society, 2001.

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Szabo, Richard J. Equivariant Cohomology and Localization of Path Integrals. Springer, 2000.

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Szabo, Richard J. Equivariant Cohomology and Localization of Path Integrals. Springer London, Limited, 2003.

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Szabo, Richard J. Equivariant Cohomology and Localization of Path Integrals. Springer, 2014.

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Tu, Loring W. Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.001.0001.

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Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah–Bott and Berline–Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, the book begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
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Balchin, Scott, David Barnes, Magdalena Kędziorek, and Markus Szymik, eds. Equivariant Topology and Derived Algebra. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108942874.

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This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.
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Paradan, Paul-Emile, and Michele Vergne. Witten Non Abelian Localization for Equivariant K-Theory, and the $[Q,R]=0$ Theorem. American Mathematical Society, 2019.

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McDuff, Dusa, and Dietmar Salamon. Symplectic group actions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0006.

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The chapter begins with a discussion of circle actions and their relation to 2-sphere bundles. It continues with a section on general Hamiltonian group actions and moment maps, then proceeds to discuss various explicit examples in both finite and infinite dimensions, and introduces the Marsden–Weinstein quotient, together with new examples that explain its relation to the construction of generating functions for Lagrangians. Further sections give a proof of the Atiyah–Guillemin–Sternberg convexity theorem about the image of the moment map in the case of torus actions, and use equivariant cohomology to prove the Duistermaat–Heckman localization formula for circle actions. It closes with an overview of geometric invariant theory which grows out of the interplay between the actions of a real Lie group and its complexification.
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Book chapters on the topic "Equivariant localization"

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Alekseev, Anton. "Notes on Equivariant Localization." In Geometry and Quantum Physics, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46552-9_1.

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Guillemin, Victor W., Shlomo Sternberg, and Jochen Brüning. "The Abstract Localization Theorem." In Supersymmetry and Equivariant de Rham Theory, 173–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03992-2_11.

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Guillemin, Victor W., Shlomo Sternberg, and Jochen Brüning. "The Thom Class and Localization." In Supersymmetry and Equivariant de Rham Theory, 149–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03992-2_10.

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Schürmann, Jörg. "Localization results for equivariant constructible sheaves." In Topology of Singular Spaces and Constructible Sheaves, 141–205. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8061-9_4.

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Niemi, Antti J. "Localization, Equivariant Cohomology, and Integration Formulas." In Particles and Fields, 211–50. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1410-6_6.

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Miličić, Dragan, and Pavle Pandžić. "Equivariant Derived Categories, Zuckerman Functors and Localization." In Progress in Mathematics, 209–42. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-4162-1_12.

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Zhang, Chao, Ignas Budvytis, Stephan Liwicki, and Roberto Cipolla. "Rotation Equivariant Orientation Estimation for Omnidirectional Localization." In Computer Vision – ACCV 2020, 334–50. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69538-5_21.

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Tu, Loring W. "Localization Formulas." In Introductory Lectures on Equivariant Cohomology, 238–44. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0030.

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This chapter highlights localization formulas. The equivariant localization formula for a torus action expresses the integral of an equivariantly closed form as a finite sum over the fixed point set. It was discovered independently by Atiyah and Bott on the one hand, and Berline and Vergne on the other, around 1982. The chapter describes the equivariant localization formula for a circle action and works out an application to the surface area of a sphere. It also explores some equivariant characteristic classes of a vector bundle. These include the equivariant Euler class, the equivariant Pontrjagin classes, and the equivariant Chern classes.
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Tu, Loring W. "Some Applications." In Introductory Lectures on Equivariant Cohomology, 252–58. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0032.

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This chapter explores some applications of equivariant cohomology. Since its introduction in the Fifties, equivariant cohomology has found applications in topology, symplectic geometry, K-theory, and physics, among other fields. Its greatest utility may be in converting an integral on a manifold to a finite sum. Since many problems in mathematics can be expressed in terms of integrals, the equivariant localization formula provides a powerful computational tool. The chapter then discusses a few of the applications of the equivariant localization formula. In order to use the equivariant localization formula to compute the integral of an invariant form, the form must have an equivariantly closed extension.
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Tu, Loring W. "Rationale for a Localization Formula." In Introductory Lectures on Equivariant Cohomology, 232–38. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0029.

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This chapter offers a rationale for a localization formula. It looks at the equivariant localization formula of Atiyah–Bott and Berline–Vergne. The equivariant localization formula of Atiyah–Bott and Berline–Vergne expresses, for a torus action, the integral of an equivariantly closed form over a compact oriented manifold as a finite sum over the fixed point set. The central idea is to express a closed form as an exact form away from finitely many points. Throughout his career, Raoul Bott exploited this idea to prove many different localization formulas. The chapter then considers circle actions with finitely many fixed points. It also studies the spherical blow-up.
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Conference papers on the topic "Equivariant localization"

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BYTSENKO, A. A., and F. L. WILLIAMS. "LOCALIZATION OF EQUIVARIANT COHOMOLOGY – INTRODUCTORY AND EXPOSITORY REMARKS." In Proceedings of the 2000 Londrina Workshop. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810366_0004.

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Bruzzo, U. "Equivariant Cohomology and Localization for Lie Algebroids and Applications." In Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0009.

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Gong, Guoqiang, Liangfeng Zheng, Wenhao Jiang, and Yadong Mu. "Self-Supervised Video Action Localization with Adversarial Temporal Transforms." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/96.

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Weakly-supervised temporal action localization aims to locate intervals of action instances with only video-level action labels for training. However, the localization results generated from video classification networks are often not accurate due to the lack of temporal boundary annotation of actions. Our motivating insight is that the temporal boundary of action should be stably predicted under various temporal transforms. This inspires a self-supervised equivariant transform consistency constraint. We design a set of temporal transform operations, including naive temporal down-sampling to learnable attention-piloted time warping. In our model, a localization network aims to perform well under all transforms, and another policy network is designed to choose a temporal transform at each iteration that adversarially brings localization result inconsistent with the localization network's. Additionally, we devise a self-refine module to enhance the completeness of action intervals harnessing temporal and semantic contexts. Experimental results on THUMOS14 and ActivityNet demonstrate that our model consistently outperforms the state-of-the-art weakly-supervised temporal action localization methods.
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Reports on the topic "Equivariant localization"

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Naber, Gregory L. Equivariant Localization and Stationary Phase. GIQ, 2012. http://dx.doi.org/10.7546/giq-4-2003-88-124.

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