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mahdavi Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics. There is a convenient planar (or spherical) diagrammactic expression for this theory, that enables one to see how to extend many classical invariants to invariants of virtual knots, and to compare properties of virtual knots with classical knots. This algebraic technique can be applied to categories of tangles, and thus to knot theory. www2.potsdam.edu /honors/honors/clubs/MATH/mahdavk/abst.htm   (2164 words)

Mathematics My work blends Lie theory with elements of category theory and has connections to knot theory and Lie algebra cohomology. My other mathematical interests include algebraic coding theory, knot theory, the history of mathematics, and the relationship between music and mathematics.   Since the theory of conjugation can be regarded as the theory of quandles, we begin by describing the means by which we can treat our Lie groups as quandles in Diff*, the category of pointed, smooth manifolds. myweb.lmu.edu /acrans/research.html   (2164 words)

York University: Category seminar Under certain hypotheses, this simple remark may be extended to lax algebras, and leads by way of the Kleisli category of the associated monad to a certain "neighborhood presentation" of the theory of lax algebras. Surprisingly, their braided monoidal categories have played a starring role in the recent resurgence of interest n knot theory led by the work of Vaughan Jones. ABSTRACT: Following the description by Manes [1] of the category of compact Hausdorff spaces as the Eilenberg-Moore category for the ultrafilter monad, Barr [2] showed that by weakening the axioms for a monad and the subsequent algebras, the Eilenberg-Moore category could be seen to be isomorphic to the category of topological spaces. www.math.yorku.ca /Seminars/category   (2164 words)

York University: Category seminar Under certain hypotheses, this simple remark may be extended to lax algebras, and leads by way of the Kleisli category of the associated monad to a certain "neighborhood presentation" of the theory of lax algebras. Surprisingly, their braided monoidal categories have played a starring role in the recent resurgence of interest n knot theory led by the work of Vaughan Jones. ABSTRACT: Following the description by Manes [1] of the category of compact Hausdorff spaces as the Eilenberg-Moore category for the ultrafilter monad, Barr [2] showed that by weakening the axioms for a monad and the subsequent algebras, the Eilenberg-Moore category could be seen to be isomorphic to the category of topological spaces. www.math.yorku.ca /Seminars/category   (2145 words)

Book Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series) The braided monoidal category that arises in knot theory is a perfect example of this. Structures such as braided monoidal categories, operads, and Hopf algebras are familiar to those who have studied topological quantum field theory, knot theory, string theory, and the renormalization procedure in quantum field theory. Higher-dimensional category theory or `n-category theory,' is viewed as a generalization of the notion of category. store.worldsearch.com /higher_operads%2c_higher_categories-amco-0521532159.htm   (2145 words)

pa_schft.html Braided monoidal categories have important applications in knot theory, algebraic quantum field theory, and the theory of quantum groups and Hopf algebras. We generalize this construction to the category $\Mp$ of entwined modules, that is $A$-modules and $C$-comodules over Hopf algebras $A$ and $C$ where the structures are only related by an entwining map $\psi: C \tensor A \to A \tensor C$. As an application I will derive the well known result that the antipode of a Hopf algebra in a braided monoidal category is an algebra antihomomorphism which is expressed by the formulas $S(1) = 1$ and $S(ab) = \langle S(b)S(a),\tau \rangle$. www.mathematik.uni-muenchen.de /~pareigis/pa_schft.html   (2145 words)

Descriptions of fall 2003 courses in the Rutgers-New Brunswick Math Graduate Program This course is an introduction to the theory of tensor categories and its applications in representation theories, quantum groups, knot invariants and conformal field theories. The prerequisite for this course is a strong background on advanced calculus involving multivariables (esp. Green's Theorem and Divergence Theorem), the theory of ordinary differential equations(ODEs), and basic properties of Fourier transforms. The theory of tensor categories has recently become an important tool in the study of a number of mathematical and physical problems. www.math.rutgers.edu /grad/courses/fall_2003_descriptions.html   (3864 words)

Knot invariant - Wikipedia, the free encyclopedia This is a homology theory whose Euler characteristic is the Alexander polynomial of the knot. This category includes the crossing number, which is the minimum number of crossings for any diagram of the knot. Some knot invariants are worked out from a knot diagram, in which case they must be unchanged (that is to say, invariant) under the Reidemeister moves; knot polynomials are examples of this. en.wikipedia.org /wiki/Knot_invariant   (387 words)

Wikipedia:Requested articles/mathematics - Wikipedia, the free encyclopedia Autonomous category - Enriched limit (mathematics)- Kan extension - Tangle diagram - Tangle theory - Tricategory Braid word - Rational knot - Slice knot - Tangle diagram - Tangle theory Campbell's theorem - Probabilistic potential theory - Rasch en.wikipedia.org /wiki/Wikipedia:Requested_articles/Mathematics   (387 words)

Homotopy - Wikipedia, the free encyclopedia In practice homotopy theory is carried out by working with CW complexes, for technical convenience; or in some other reasonable category. In geometric topology- for example in knot theory - the idea of isotopy is used to construct equivalence relations. An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. en.wikipedia.org /wiki/Homotopy   (387 words)

Citations: Braided compact monoidal categories with applications to low dimensional topology - Freyd, Yetter (ResearchIndex) Tangles are important because they make clear the relation between knot theory and braided monoidal categories. The category of tangles in 3 dimensions is especially important, because it has a beautiful algebraic characterization in terms of a universal property. This special case serves as the basis of recent work on 3 dimensional topological quantum field theory. citeseer.ist.psu.edu /context/279249/0   (387 words)

Topological Quantum Field Theory (291) graduate course, Fall 2004 Other parts require a bit more abstract algebra, in particular Lie algebras and category theory. This discovery proved to be the tip of the iceberg: several other knot related knot polynomials (HOMFLY, Kauffman,...) were quickly discovered, and in 1989 Witten explained how this family of invariants should extend naturally to give lots of invariants for three-manifolds. The subject began in 1984 with Jones' discovery of his famous polynomial invariant of knots in the three-sphere. math.ucsd.edu /~justin/TQFT.html   (402 words)

The Maseeh Mathematics & Statistics Colloquium Series A specific set of relations, which correspond to the Reidemeister moves of knot theory, is then used to define, with this language, a specific strict monoidal category. In the remainder of the talk tangles are defined and tangle categories are constructed. The language of strict monoidal categories is then constructed using the concept of a graph with relations. www.mth.pdx.edu /Events/colloquium.asp?id=61   (402 words)

Read about Category:Geometric topology at WorldVillage Encyclopedia. Research Category:Geometric topology and learn about Category:Geometric topology here! In mathematics, geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups. Research Category:Geometric topology and learn about Category:Geometric topology here! It has come over time to be almost synonymous with low-dimensional topology, concerning in particular objects of three or four dimensions. encyclopedia.worldvillage.com /s/b/Category:Geometric_topology   (402 words)

Knot invariant - Wikipedia, the free encyclopedia This is a homology theory whose Euler characteristic is the Alexander polynomial of the knot. This category includes the crossing number, which is the minimum number of crossings for any diagram of the knot. The complement of a knot itself (as a topological space) is known to be a complete invariant of the knot, meaning that it distinguishes the given knot from all other knots up to isotopy. en.wikipedia.org /wiki/Knot_invariant   (402 words)

The Maseeh Mathematics & Statistics Colloquium Series A specific set of relations, which correspond to the Reidemeister moves of knot theory, is then used to define, with this language, a specific strict monoidal category. In particular, a strict monoidal category, braiding, and pivotal category are defined. This category is in fact a free braided pivotal category. www.mth.pdx.edu /Events/colloquium.asp?id=61   (402 words)

LookSmart - Directory - Topology Topology - Find out about the Moebius strip, knot theory and mazes. Browse a compendium of abstracts, papers, journals, conferences, teaching resources and employment opportunities in the field of topology. Online encyclopedia presents what was an important problem in topology, until solved recently by Grigory Perelman. search.looksmart.com /p/browse/us1/us317914/us328800/us574141/?&sn=10&...   (402 words)

Home Page of N.P. Landsman Lectures on von Neumann algebras, knot theory, and quantum field theory Mathematical tools include C*-algebras, von Neumann algebras, Poisson manifolds, category theory, Lie algebroids and Lie groupoids, symplectic reduction, operator-algebraic induction, Hilbert C*-modules, measure theory on infinite-dimensional spaces, etc. My research is mainly concerned with the connection between classical and quantum theory, from a mathematical perspective. www.math.ru.nl /~landsman   (402 words)

Mathematics My work blends Lie theory with elements of category theory and has connections to knot theory and Lie algebra cohomology.   A Lie 2-algebra is a category equipped with algebraic structure much like that of a Lie algebra, but where the laws involving the bracket only hold up to isomorphism. My other mathematical interests include algebraic coding theory, knot theory, the history of mathematics, and the relationship between music and mathematics. myweb.lmu.edu /acrans/research.html   (402 words)

mahdavi This workshop investigates the interactions between Representation Theories, Knot Theory, Topology, quantum Field Theory, Category Theory, and Mathematical Physics. Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics. This conference will be of great benefit to the researchers, recent Ph.Ds, and graduate students. www2.potsdam.edu /mahdavk/Conf.htm   (402 words)

2cats 5) Lowell Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory and its Ramifications 5 (1996), 569-587. My ultimate goal is to take you to an elegant understanding of Frobenius algebras by means of a 2-category called the "walking biadjunction", but first I'll play around a bit with a simpler but more famous 2-category called the "walking adjunction". So: one definition of a "Frobenius object" in a monoidal category is that it's a monoid object / comonoid object satisfying the I = N equations. www.math.niu.edu /~rusin/known-math/01_incoming/2cats   (2679 words)

DMS.MPS.a9102765.txt He will investigate the consequences for string theory, elliptic cohomology, algebraic K-theory, knot theory, and the problem of defining degree three, non-abelian, sheaf cohomology. The category will be constructed by deducing which geometric structure has a given gerb as its holonomy. Title : Mathematical Sciences: Construction of a Geometric Category Representing H4(M;Z), and Its Implications Abstract : Over the next three years, McLaughlin plans to find a category representing H4(M;Z), in a manner similar to the interpretation of H2(M;Z) as isomorphism classes of line bundles, and H3(M;Z) as equivalence classes of gerbs. www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9102765.txt   (391 words)

LRCI’s Left Turn: ‘No Coherent Middle Ground’ : Moribund No More? The moribund workers’ state theory is indeed absurd, but in seeking to change labels without drawing the programmatic conclusions, the LRCI’s current majority leaves their Gordian knot intact. The moribund workers’ state theory brought plenty of confusion and certainly deserves to be “cut away;” but in doing so, LRCI members must confront their support to the Yeltsinite counterrevolutionies in August 1991. On the question of defensism, the LRCI has concluded that its “moribund workers’ state” position lacks “theoretical and programmatic utility—it brings nothing but confusion to the issue.” Yet there is still confusion within the LRCI, even among the critics of the moribund theory. www.bolshevik.org /1917/no23/Finlrci.html   (2678 words)

Quantum Conformal Gravity and Higgs Masses By using the Crane ladder, you can study black holes with the methods of topological quantum field theory, knot theory, and category theory that are described by Baez in his series This Week's Finds in Mathematical Physics as well as in his books and papers. redefinition of classical general relativity in terms of new variables, the Ashtekar variables, and trying to use the new variables to construct a quantum theory of gravity. Therefore, although the quantum gravity methods of string theory cannot be used in the D4-D5-E6 model because the D4-D5-E6 model uses fundamental point particles at the classical level, methods based on Ashtekar variables are available. www.mathematik.uni-kl.de /~hunt/cnfGrHg.html   (1949 words)

Home Page of N.P. Landsman Mathematical tools include C*-algebras, von Neumann algebras, Poisson manifolds, category theory, Lie algebroids and Lie groupoids, symplectic reduction, operator-algebraic induction, Hilbert C*-modules, measure theory on infinite-dimensional spaces, etc. Lectures on von Neumann algebras, knot theory, and quantum field theory My research is mainly concerned with the connection between classical and quantum theory, from a mathematical perspective. www.math.ru.nl /~landsman   (1949 words)

Heriot-Watt Maths Research Report HWM99-23 P R Turner, M Brightwell, Representations of the homotopy surface category of a simply connected space, Journal of Knot Theory and its Ramifications, 9 No. 1, 855-864, (2000). We introduce the homotopy surface category of a space which generalizes the 1+1-dimensional cobordism category of circles and surfaces to the situation where one introduces a background space. We explain how for a simply connected background space, monoidal functors from this category to vector spaces can be interpreted in terms of Frobenius algebras with additional structure. www.ma.hw.ac.uk /maths/deptreps/HWM99-23.html   (95 words)

Gizem Karaali - Research Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics, Title: Combinatorics in Representation Theory - series of two lectures ; The title of my thesis was r-matrices on Lie Superalgebras. www.math.ucsb.edu /~gizem/research/research.html   (95 words)

Wikipedia:Requested articles/mathematics - Wikipedia, the free encyclopedia Autonomous category - Enriched limit (mathematics) - Kan extension - Tangle diagram - Tangle theory - Tricategory Braid word - Rational knot - Slice knot - Tangle diagram - Tangle theory Homeokinetics - Minimum degree spanning tree - Poisson Integral en.wikipedia.org /wiki/Wikipedia:Requested_articles/Mathematics   (95 words)

vkamg.txt One comment is from Bill Cockcroft a long time ago, saying that Victor's interest in knot theory and low dimensional topology in his thesis was very much ahead of his time, and perhaps most in the VKAMG nature, but was unfashionable when he went to the USA. K. Gugenheim, Cohomology theory in the category of Hopf algebras, in Colloque de Topologie (Brussels, 1964), 137--148, Librairie Universitaire, Louvain, 1966; MR0227251 (37 #2836) V. K. Gugenheim, Semisimplicial homotopy theory, in Studies in Modern Topology, 99--133, Math. www.maths.ed.ac.uk /~aar/surgery/uicc/vkamg.txt   (2381 words)

List of mathematical topics (P-R) - Gurupedia Primality test -- Prime -- Prime (order theory) -- Prime factor -- Prime factorization algorithm -- Prime ideal -- Prime knot -- Probability-generating function -- Probable prime -- Problem size -- Product (category theory) -- Product (mathematics) -- Product of groups -- Product of rings -- Product rule -- Product topology -- Pro-finite group -- Prognostic variable -- Programming -- Programming language -- Projection (linear algebra) -- Permanent -- Permutable prime -- Permutation -- Permutation group -- Permutation matrix -- Permutations and combinations -- Perpendicular -- Perrin pseudoprime -- Perron Integral -- Persistence of a number -- www.gurupedia.com /l/li/list_of_mathematical_topics_(p-r).htm   (1408 words)

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