Descriptive complexity | Finite model theory | Computational complexity theory
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic needed to express the languages in them. For example, PH, the union of all complexity classes in the polynomial hierarchy, is precisely the class of languages expressible by statements of second-order logic. This connection between complexity and the logic of finite structures allows results to be transferred easily from one area to the other, facilitating new proof methods and providing additional evidence that the main complexity classes are somehow "natural" and not tied to the specific abstract machines used to define them. Specifically, each logical system produces a set of queries expressible in it. The queries – when restricted to finite structures – correspond to the computational problems of traditional complexity theory. The first main result of descriptive complexity was Fagin's theorem, shown by Ronald Fagin in 1974. It established that NP is precisely the set of languages expressible by sentences of existential second-order logic; that is, second order logic excluding universal quantification over relations, functions, and subsets. Many other classes were later characterized in such a manner. (Wikipedia).
Mathematical modeling of evolving systems
Discover the multidisciplinary nature of the dynamical principles at the core of complexity science. COURSE NUMBER: CAS 522 COURSE TITLE: Dynamical Systems LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Enrico Borriello MODE: Online SEMESTER: Fall 2021 SESSION:
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Results and open problems in theory of quantum complexity - Anindya De
Andris Ambainis University of Latvia; Member, School of Mathematics April 22, 2014 I will survey recent results and open problems in several areas of quantum complexity theory, with emphasis on open problems which can be phrased in terms of classical complexity theory or mathematics but ha
From playlist Mathematics
Nicole Schweikardt: Databases and descriptive complexity – lecture 1
Recording during the meeting "Spring school on Theoretical Computer Science (EPIT) - Databases, Logic and Automata " the April 11, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by wor
From playlist Numerical Analysis and Scientific Computing
Said Hamoun (2/23/23): On the rational topological complexity of coformal elliptic spaces
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of the rational homotopy for some special families of
From playlist Topological Complexity Seminar
Geometric complexity theory from a combinatorial viewpoint - Greta Panova
Computer Science/Discrete Mathematics Seminar II Topic: Lattices: from geometry to cryptography Speaker: Greta Panova Affiliation: University of Pennsylvania; von Neumann Fellow, School of Mathematics Date: November 28, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Kolmogorov Complexity - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group
Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv
From playlist AATRN 2022
Knot Categorification From Mirror Symmetry (Lecture- 3) by Mina Aganagic
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
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Edward Witten: Mirror Symmetry & Geometric Langlands [2012]
2012 FIELDS MEDAL SYMPOSIUM Thursday, October 18 Geometric Langlands Program and Mathematical Physics 1.30am-2.30pm Edward Witten, Institute for Advanced Study, Princeton "Superconformal Field Theory And The Universal Kernel of Geometric Langlands" The universal kernel of geometric Langl
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Séminaire Bourbaki - 21/06/2014 - 4/4 - Thierry COQUAND
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Shannon 100 - 27/10/2016 - Jean Louis DESSALLES
Information, simplicité et pertinence Jean-Louis Dessalles (Télécom ParisTech) Claude Shannon fonda la notion d’information sur l’idée de surprise, mesurée comme l’inverse de la probabilité (en bits). Sa définition a permis la révolution des télécommunications numériques. En revanche, l’
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Self organized tissue architecture: morphogenesis in a dish by Maithreyi Narasimha & Vijaykumar....
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From playlist Winter School on Quantitative Systems Biology: Quantitative Approaches in Ecosystem Ecology 2020
Akhil Mathew - Some recent advances in syntomic cohomology (2/3)
Bhatt-Morrow-Scholze have defined integral refinements $Z_p(i)$ of the syntomic cohomology of Fontaine-Messing and Kato. These objects arise as filtered Frobenius eigenspaces of absolute prismatic cohomology and should yield a theory of "p-adic étale motivic cohomology" -- for example, the
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Black Holes- The Harmonic Oscillators ( 1 ) - Andrew strominger
Speaker : Andrew Strominger ( Havard University ) Date and Time : 04 Jan 2010, 04:00 PM Venue : AG 66, TIFR, Mumbai In the twentieth century, many problems across all of physics were solved by perturbative methods which reduced them to harmonic oscillators. Black holes are poised to play
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Haldun Özgür Bayindir : Adjoining roots to ring spectra and algebraic 𝐾-theory
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
PNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compac
From playlist PNWS 2014