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No occurrence obstructions in geometric complexity theory
[article]

2018
*
arXiv
*
pre-print

The permanent versus determinant conjecture is a major problem

arXiv:1604.06431v3
fatcat:7bnkt3tyvjb6jaubwrmpvuuhsi
*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 ...##
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On Geometric Complexity Theory: Multiplicity Obstructions Are Stronger Than Occurrence Obstructions

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. ...

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

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

arXiv:1102.1150v4
fatcat:borhcah5inbclai5gjsvmrir74
*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 ...##
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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). ...##
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Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes

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

doi:10.1515/crelle-2013-0037
fatcat:k7f5fzzszrcypiiuiv2xbtz7a4
*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 ...##
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On P vs. NP, Geometric Complexity Theory, and the Riemann Hypothesis
[article]

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 ...

##
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Even partitions in plethysms

2011
*
Journal of Algebra
*

Our investigation is motivated by questions of

doi:10.1016/j.jalgebra.2010.10.031
fatcat:bls2nllprnc2tmdhbaw3ku2vgu
*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*. ...##
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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. ...##
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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 ...##
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Towards an algebraic natural proofs barrier via polynomial identity testing
[article]

2017
*
arXiv
*
pre-print

We also discuss connections between this algebraic natural proofs barrier,

arXiv:1701.01717v1
fatcat:tfx54wjxcrdlpkm4kdkou3qthm
*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. ...##
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Moduli spaces of (bi)algebra structures in topology and geometry
[article]

2016
*
arXiv
*
pre-print

Derived geometry provides the appropriate framework to describe moduli spaces classifying objects up to weak equivalences and encoding

arXiv:1611.03662v2
fatcat:5hlpkm4ydngxjeyi4klcb5c6mq
*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*. ...##
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Moduli Spaces of (Bi)algebra Structures in Topology and Geometry
[chapter]

2018
*
MATRIX Book Series
*

Derived geometry provides the appropriate framework to describe moduli spaces classifying objects up to weak equivalences and encoding

doi:10.1007/978-3-319-72299-3_20
fatcat:mcwbsnyqozd53esasdci4jjox4
*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*. ...##
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Remedial Safety Treatment of Accident-Prone Locations

2015
*
International Journal of Technology
*

The present study adopts the combined approach of Systems

doi:10.14716/ijtech.v6i4.1097
fatcat:x6homd4tajb5nfw5r2lxhgsz5a
*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 ...##
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Geometric complexity theory and matrix powering

2017
*
Differential geometry and its applications
*

We prove that

doi:10.1016/j.difgeo.2017.07.001
fatcat:qqt6jaxvfraddcoqgqsvmxkndq
*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*. ...
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