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No occurrence obstructions in geometric complexity theory [article]

Peter Bürgisser and Christian Ikenmeyer and Greta Panova
2018 arXiv   pre-print
The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP_ws and VNP. Mulmuley and Sohoni (SIAM J.  ...  In that paper it was also proposed to separate these orbit closures by exhibiting occurrence obstructions, which are irreducible representations of GL_n^2(C), which occur in one coordinate ring of the  ...  Acknowledgments This work, as well as [26] , are an outcome of the program "Algorithms and Complexity in Algebraic Geometry", held at the Simons Institute for the Theory of Computing in Berkeley in 2014  ... 
arXiv:1604.06431v3 fatcat:7bnkt3tyvjb6jaubwrmpvuuhsi

On Geometric Complexity Theory: Multiplicity Obstructions Are Stronger Than Occurrence Obstructions

Julian Dörfler, Christian Ikenmeyer, Greta Panova
2020 SIAM Journal on applied algebra and geometry  
Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001 , 2008 aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate  ...  ACM Subject Classification Theory of computation → Algebraic complexity theory  ...  Acknowledgements This work was done in part while CI and GP were visiting the Simons Institute for the Theory of Computing.  ... 
doi:10.1137/19m1287638 fatcat:2ybwbv6s2rbmdfbbghz5jtphia

Page 956 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
Some final remarks concern the occurrence of bicategories in the Chern- Simons field theory of Witten and the analogous construction for finite groups. {For the entire collection see MR 94m:57002.}  ...  In fact, some of the general structure theory carries over to the Bockstein spectral sequences which arise in Morava K-theory for BSpin(n).  ... 

Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes [article]

Timo Schürg, Bertrand Toën, Gabriele Vezzosi
2011 arXiv   pre-print
We show how a quasi-smooth derived enhancement of a Deligne-Mumford stack X naturally endows X with a functorial perfect obstruction theory in the sense of Behrend-Fantechi.  ...  Ext's, and show how this map induces a morphism of the corresponding obstruction theories when X is a Calabi-Yau threefold.  ...  Our initial interest in the possible relationships between reduced  ... 
arXiv:1102.1150v4 fatcat:borhcah5inbclai5gjsvmrir74

Page 1946 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
An obstruction to embedding a simplicial n-complex into a 2n-manifold. (English summary) Topology Appl. 122 (2002), no. 3, 581-591.  ...  These graded vector spaces are important in representation theory because they “count” the occurrences of F(A,n) as a submodule and as a composition factor, respectively, in R(n).  ... 

Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes

Timo Schürg, Bertrand Toën, Gabriele Vezzosi
2015 Journal für die Reine und Angewandte Mathematik  
AbstractA quasi-smooth derived enhancement of a Deligne–Mumford stack 𝒳 naturally endows 𝒳 with a functorial perfect obstruction theory in the sense of Behrend–Fantechi.  ...  We apply this result to moduli of maps and perfect complexes on a smooth complex projective variety.ForWe give two further applications toAn important ingredient of our construction is a  ...  Our initial interest in the possible relationships between reduced  ... 
doi:10.1515/crelle-2013-0037 fatcat:k7f5fzzszrcypiiuiv2xbtz7a4

On P vs. NP, Geometric Complexity Theory, and the Riemann Hypothesis [article]

Ketan D. Mulmuley
2009 arXiv   pre-print
Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems.  ...  No background in algebraic geometry, representation theory or quantum groups is assumed.  ...  Introduction This article gives a mathematical overview of geometric complexity theory (GCT), an approach towards the fundamental lower bound problems in complexity theory, such as ( Figure 1 ): (1) The  ... 
arXiv:0908.1936v2 fatcat:mmttkmgzmvgftpxrwk5rp5jy5y

Even partitions in plethysms

Peter Bürgisser, Matthias Christandl, Christian Ikenmeyer
2011 Journal of Algebra  
Our investigation is motivated by questions of geometric complexity theory and uses ideas from quantum information theory.  ...  We prove that for all natural numbers k,n,d with k <= d and every partition lambda of size kn with at most k parts there exists an irreducible GL(d, C)-representation of highest weight 2*lambda in the  ...  Connection to geometric complexity theory.  ... 
doi:10.1016/j.jalgebra.2010.10.031 fatcat:bls2nllprnc2tmdhbaw3ku2vgu

Page 93 of Mathematical Reviews Vol. , Issue 90G [page]

1990 Mathematical Reviews  
B 216 (1989), no. 1-2, 68-74. Summary: “The complex geometry and the geometric quantization for bosonic strings are discussed.  ...  Nuclear Phys. 13 (1989), no. 5, 419-428. Summary: “Geometric quantization for bosonic strings is discussed in this paper.  ... 

Page 1887 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
B 194 (1987), no. 2, 267-270; MR 89c:81 106]. 81T Quantum field theory; related classical field theories 96c:81212 The 3-cocycles in chiral gauge theory then arise as obstructions preventing the existence  ...  Summary: “We analyze the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a  ... 

Towards an algebraic natural proofs barrier via polynomial identity testing [article]

Joshua A. Grochow and Mrinal Kumar and Michael Saks and Shubhangi Saraf
2017 arXiv   pre-print
We also discuss connections between this algebraic natural proofs barrier, geometric complexity theory, and (algebraic) proof complexity.  ...  This is analogous to the Razborov-Rudich natural proofs barrier in Boolean circuit complexity, in that we rule out a large class of lower bound techniques under a derandomization assumption.  ...  We thank Amir Shpilka for conversations related to Section 4.1 and for his encouragement to publicize our thinking, even in light of the results of [14] which (independently) supercede ours.  ... 
arXiv:1701.01717v1 fatcat:tfx54wjxcrdlpkm4kdkou3qthm

Moduli spaces of (bi)algebra structures in topology and geometry [article]

Sinan Yalin
2016 arXiv   pre-print
Derived geometry provides the appropriate framework to describe moduli spaces classifying objects up to weak equivalences and encoding in a geometrically meaningful way their deformation and obstruction  ...  To understand the classification and deformation theory of these structures on a given object, a relevant idea inspired by geometry is to gather them in a moduli space with nice homotopical and geometric  ...  complexes and obstruction theory.  ... 
arXiv:1611.03662v2 fatcat:5hlpkm4ydngxjeyi4klcb5c6mq

Moduli Spaces of (Bi)algebra Structures in Topology and Geometry [chapter]

Sinan Yalin
2018 MATRIX Book Series  
Derived geometry provides the appropriate framework to describe moduli spaces classifying objects up to weak equivalences and encoding in a geometrically meaningful way their deformation and obstruction  ...  To understand the classification and deformation theory of these structures on a given object, a relevant idea inspired by geometry is to gather them in a moduli space with nice homotopical and geometric  ...  complexes and obstruction theory.  ... 
doi:10.1007/978-3-319-72299-3_20 fatcat:mcwbsnyqozd53esasdci4jjox4

Remedial Safety Treatment of Accident-Prone Locations

Martha Leni Siregar, Tuti Alawiyah, Tri Tjahjono
2015 International Journal of Technology  
The present study adopts the combined approach of Systems Theory which proposes that accidents are the result of maladjustments in the interaction between the components of complex systems, and the Causal  ...  The remedial safety treatment therefore focuses on geometric redesigning of the roundabout in compliance with geometric standards and traffic demand.  ...  ; Systems Theory which proposes that accidents are the result of maladjustments in the interaction between the components of complex systems; and Causal Accident Theory, which states that accidents can  ... 
doi:10.14716/ijtech.v6i4.1097 fatcat:x6homd4tajb5nfw5r2lxhgsz5a

Geometric complexity theory and matrix powering

Fulvio Gesmundo, Christian Ikenmeyer, Greta Panova
2017 Differential geometry and its applications  
We prove that in this homogeneous formulation there are no orbit occurrence obstructions that prove even superlinear lower bounds on the complexity of the permanent.  ...  This is the first no-go result in geometric complexity theory that rules out superlinear lower bounds in some model.  ...  This is the first time that the possibility of superlinear lower bounds is ruled out in geometric complexity theory.  ... 
doi:10.1016/j.difgeo.2017.07.001 fatcat:qqt6jaxvfraddcoqgqsvmxkndq
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