A group blog on math, physics and philosophy

*A Higher Stacky Perspective On Chern-Simons Theory*(Dec 28, 2012)- A contribution for a book on mathematical aspects of QFT, on extended (“multi-tiered”) prequantum Chern-Simons theory formulated in terms of higher geometry.
*TwoVect*(Nov 19, 2012)- Jamie Vicary on a software for handling 2-categorical linear algebra.
- Tangency (Oct 9, 2012)
- Thoughts by Andrew Stacey on the notion of tangency.
- General Covariance in Homotopy Type Theory (Sep 8, 2012)
- A natural formalization of generally covariant field theory in the formal language of homotopy type theory.
*From Poisson To String Geometry*(Sep 4, 2012)- A conference in Erlangen on Poisson geometry, String geometry, and some relations.
*Quantum Gauge Field Theory in Cohesive Homotopy Type Theory*(Aug 20, 2012)- A survey article on the formalization of aspects of quantum gauge field theory in the formal language of cohesive homotopy type theory.
*Strings and Automorphic Forms in Topology*(Aug 13, 2012)- A conference on mathematical issues in higher string geometry.
*Extended higher Chern-Simons theories*(Jul 20, 2012)- A discussion of “extended” or “multi-tiered” prequantum higher-dimensional higher gauge theories of Chern-Simons type.
- Notes from
*String-Math 2012*(Jul 16, 2012) - Notes from String-Math 2012, a conference on mathematical aspects of string theory.
- Geometric Quantization on Moduli ∞-Stacks (Jul 9, 2012)
- A talk on higher geometric quantization on higher moduli stacks.
- Flat Ehresmann connections in Cohesive HoTT (Jun 28, 2012)
- The formalization of flat Ehresmann connections in higher geometry.
- Principal ∞-Bundles -- general theory and presentations (Jun 25, 2012)
- Notes on the theory of principal and twisted bundles in higher geometry.
- Segal-Completeness and Univalence (May 18, 2012)
- An observation about the relation between Segal-completeness in internal infinity-category theory and univalence in homotopy type theory.
- What is Homotopy Type Theory Good For? (May 10, 2012)
- An example in mathematical string theory where appeal to homotopy type theory helps solve a subtle problem.
- Twisted Higher Bundles in Münster (May 5, 2012)
- A workshop that happens to have some talks on twisted higher bundles.
- Principal ∞-Bundles (Apr 23, 2012)
- A preview of an article on principal bundles in higher geometry.
*Higher Structures in Topology and Geometry VI*(Apr 20, 2012)- Part VI of the series of workshops on Higher Structures in Göttingen.
- Research Network
*String Geometry*(Apr 16, 2012) - We won a reaserch network grant on the topic of String Geometry, the higher differential geometry of differential string structures.
*CATS 4*(Apr 16, 2012)- Meeting in Luminy about Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra
*New Perspectives in Topological Field Theories*(Mar 16, 2012)- A conference in Hamburg on mathematical physics, with an emphasis on TQFT, representation theory and categorification.
- Prequantization in Cohesive Homotopy Type Theory (Feb 27, 2012)
- A proposal for axiomatics of geometric prequantization formulated in cohesive homotopy type theory.
- ESI Program
*K-Theory and Quantum Fields*(Feb 22, 2012) - A program at the ESI institute in Vienna including two weeks of lectures on cohomological structures in quantum field theory and string theory.
- In Göttingen (Feb 21, 2012)
- Am in Göttingen, talking about higher differential geometry and higher gauge theory.
- Workshop on Formal Topology, Higher Dimensional Algebra, Categories and Types (Feb 15, 2012)
- A workshop or two on topics in topology, type theory and homotopy theory.
- Modern Perspectives in Homotopy Theory (Feb 14, 2012)
- A school on modern developments in homotopy theory.
- The Moduli 3-Stack of the C-Field (Feb 9, 2012)
- An article discussing the moduli 3-stack of the C-field in 11-dimensional supergravity.
- Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory (Jan 21, 2012)
- An article on 7-dimensional Chern-Simons theory of nonabelian String 2-form fields.
- Mathematical Aspects of String and M-Theory in Cambridge (Jan 11, 2012)
- A workshop in Cambridge on mathematical aspects of string theory.
*4th Odense Winter School on Geometry and Mathematical Physics*(Dec 18, 2011)- A winter school on gauge theoretic aspects of theoretical physics.
*Basic Ideas of Homotopy Axiomatic Cohesion*(Dec 6, 2011)- Slides for a course on basic ideas of axiomatic cohesion in homotopy type theory.
- Some Job Offers (Dec 5, 2011)
- Below are various recent job offers in maths that colleagues are asking me to circulate. One in Liverpool on motives. One in Prague, on geometry and algebra. One in Erlangen, on higher categories and TQFT. One in Adelaide, on…
*Higher Structures Along The Lower Rhine*(Nov 29, 2011)- A workshop in Bonn on higher structures in geometry.
*Higher Structures 2011*(Nov 28, 2011)- The 2011 meeting of the annual workshop on
*Higher structures in mathematics and physics*. *Publications of the nLab*(Nov 23, 2011)- A web-based journal for publications in mathematics and physics for topics that are usefully viewed from the point of view of higher category theory and homotopy theory.
*Chern-Simons Terms on Higher Moduli Stacks*(Nov 15, 2011)- A talk on Chern-Simons functionals defined on higher moduli stacks of higher connections.
- HoTT Cohesion -- Exercise II (Nov 9, 2011)
- How to code in homotopy type theory the intrinsic definition of ordinary differential cohomology and the proof of its basic properties?
- HoTT Cohesion -- Exercise I (Nov 2, 2011)
- de Rham coefficient objects and Maurer-Cartan forms in cohesive homotopy type theory.
- WZW Models in a Cohesive ∞-Topos (Oct 31, 2011)
- A talk on (higher dimensional) Wess-Zumino-Witten models internal to a cohesive infinity-topos.
*Prequantum Physics in a Cohesive ∞-Topos*(Oct 26, 2011)- Slides for a talk at “Quantum Physics and Logic 2011”.
- Theoretical Physics -- Stack Exchange (Oct 5, 2011)
- A new question-and-anwers site for research-level theoretical physics.
- QVEST, Autumn 2011 (Sep 17, 2011)
- The next meeting of our Quarterly Seminar on Topology and Geometry
- AKSZ-Models in Higher Chern-Weil Theory (Aug 6, 2011)
- The class of AKSZ-sigma models has a natural origin in abstract higher Chern-Weil theory.
- AKSZ Sigma-Models (Aug 5, 2011)
- The original definition of AKSZ sigma-model quantum field theories.
- Local and Global Supersymmetry (Jul 27, 2011)
- On the concept of supersymmetry and its experimental verification.
- Bohr Toposes (Jul 25, 2011)
- The quantum phase space as a ringed topos.
- Nikolaus on
*Higher Categorical Structures in Geometry*(Jul 1, 2011) - Thomas Nikoluas’s PhD thesis on topics in higher geometry and gauge theory.
*Towards the Mathematics of Quantum Field Theory*(Jun 21, 2011)- A book on modern attempts at formalizing quantization and quantum field theory.
- Differential Characteristic Cocycles (Jun 16, 2011)
- Notes on refined differential characteristic maps.
- String Topology Operations as a Sigma-Model (Jun 6, 2011)
- The origin of string topology operation in extended QFT and the derivation of the spaces of states from higher line bundles.
- ∞-Dijkgraaf-Witten Theory (May 12, 2011)
- In another thread Tom Leinster would like to learn what a sigma-model in quantum field theory is. Here I want to explain this in a way that will make perfect sense to Tom, and hopefully even intrigue him. To…
- QVEST, Summer 2011 (May 11, 2011)
- The fourth QVEST meeting.
- Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff (Apr 21, 2011)
- A workshop in Cardiff on higher gauge theory and quantum field theory.
- Segal on
*Three roles of quantum field theory*(Apr 14, 2011) - Graeme Segal lectures on quantum field theory at the HIM institute in Bonn.
- Axioms for Infinitesimal Cohesion (Apr 12, 2011)
- Simple homotopy theoretic axioms for differential geometry/cohomology with explicit (synthetic) infinitesimals.
- Deformation Theory of Algebras and Modules (Mar 7, 2011)
- A conference on deformation theory.
- QVEST, Spring 2011 (Mar 1, 2011)
- The second QVEST seminar meeting
- Differential Cohomology in a Cohesive Topos (Feb 28, 2011)
- A text on general abstract and concrete differential geometry and cohomology.
- 4d QFT for Khovanov Homology (Feb 23, 2011)
- The identification of the 4d TQFT that has Khovanob homology as its observables.
- Structured Ring Spectra 2011 (Feb 18, 2011)
- A conference on stable homotopy theory.
- Lurie: Higher Algebra (Feb 7, 2011)
- Jacob Lurie has made his new book available.
- String-Math 2011 (Feb 4, 2011)
- Announcement of the first _String-Math_ conference.
- Higher Structures in Topology and Geometry V (Jan 31, 2011)
- Part V of the Goettingen/Hamburg Higher Structures meetings.
- Stasheff:
*Parallel Transport -- Revisited*(Jan 7, 2011) - A note by Jim Stasheff on a homotopical notion of parallel transport.
- QVEST, Winter 2010 (Dec 16, 2010)
- A seminar on aspects of higher category theory.
- Hochschild Homology As Cohomology of Loop Space Objects (Dec 2, 2010)
- Notes on Hochschild homology in terms of functions on higher loop space objects.
- Cocycles for Differential Characteristic Classes (Nov 7, 2010)
- Some aspects of Chern–Weil theory for higher bundles over higher Lie groups.
- Structures in a Cohesive ∞-Topos (Nov 6, 2010)
- Inside any cohesive infinity-topos there exists a wealth of geometric and differential geometric structures.
- Cohesive ∞-Toposes (Oct 14, 2010)
- Some words on the notion of toposes of cohesion.
- Function
*T*-Algebras on ∞-Stacks (Sep 1, 2010) - Herman Stel’s master thesis on Function Algebras on Infinity-Stacks.
- Minicourse on
*Nonabelian Differential Cohomology*(Aug 19, 2010) - A course on nonabelian differential cohomology.
*Copenhagen Meeting on Differential Characters*(Aug 1, 2010)- A workshop on differential characters and Deligne cohomology.
*Day on Higher Category Theory*in Utrecht (Jul 5, 2010)- A workshop on higher category theory.
- Dutch
*Geometry and Quantum Theory*Conference 2010 (Jun 28, 2010) - Foruth annual conference of the Durch Geometriy And Quantum Theory Cluster.
- Alan Carey's 60th Birthday Conference (Jun 25, 2010)
- This week at MPI Bonn is (or has been) taking place a conference in honor of Alan Carey’s 60th birthday. on “noncommutative geometry and index theory, statistical models, geometric issues in quantum field theory. Hamiltonian anomalies and bundle n-gerbes”….
- At "Geometry, Quantum Fields, and Strings: Categorial Aspects" (Jun 8, 2010)
- An Oberwolfach workshop on higher categorical aspects of quantum field and string theory.
- Nonabelian Cohomology in Three (∞,1)-Toposes (May 26, 2010)
- On nonabelian sheaf cohomology with constant coefficients in petit and gros (oo,1)-toposes.
- We Have Moved (At Least Temporarily) (Mar 18, 2010)
- The nCategory Cafe has moved to a different installation.
- Comment Bug (Mar 15, 2010)
- The nCafé is currently affected by a bug that prevents comments to be posted. Here is a link to discussion on the nForum to alleviate this problem for the moment.
- Séminaire Itinérant de Catégories (Mar 11, 2010)
- A workshop on category theory and higher category theory.
- Summer School on Mathematical String Theory (Mar 9, 2010)
- Summer school involving higher category theory in mathematical string theory.
- Algebraic Models for Higher Categories (Mar 2, 2010)
- On (oo,1)-categories of algebraic oo-groupoids and algebraic (oo,1)-categories.
- Rational Homotopy Theory in an (oo,1)-Topos (Mar 2, 2010)
- On rational homotopy theory and differential cohomology from the point of view of oo-topos theory.
- 3000 and One Things to Think About (Feb 25, 2010)
- Latest activity on the nLab, on occasion of entry number 3000.
- Higher Structures in Göttingen IV (Feb 15, 2010)
- Announcement of the fourth workshop “Higher Structures in Göttingen”.
- Intrinsic Naturalness (Feb 12, 2010)
- On naturalness and kludgyness, on concepts and tools in higher category theory.
- Derived Synthetic Differential Geometry (Feb 2, 2010)
- The geometry of structured infinity-toposes induced by starting from the pregeometry given by the site of smooth loci.
- 6th Workshop on Categories, Logic and Foundations of Physics (Jan 25, 2010)
- The 6th Workshop in a series organized by Bob Coecke and Andreas Döring.
- Quasicoherent ∞ -Stacks (Jan 8, 2010)
- On the notion of quasicoherent sheaves and vector bundles in higher category theory.
- Combinatorial Model Categories (Nov 25, 2009)
- The theory of combinatorial model categories is currently scattered over the literature. Here is a collection of some links.
- Notions of Space (Nov 4, 2009)
- A survey of Jacob Lurie’s “Structured Spaces”.
- Mathematical Foundations of Quantum Field and Perturbative String Theory (Oct 24, 2009)
- A Call for Comments on a Call for Papers on an issue on Mathematical Foundations of Quantum Field and Perturbative String Theory.
- Path-Structured Smooth (∞,1)-Toposes (Oct 13, 2009)
- A talk on a context for higher synthetic differential geometry.
- D'Auria-Fré-Formulation of Supergravity (Sep 30, 2009)
- An nLab entry on the D’Auria-Fre formulation of supergravity and its interpretation as a higher gauge theory.
- A Seminar on a Geometric Model for TMF (Sep 21, 2009)
- A seminar on geometric models for tmf cohomology theory by Stephan Stolz and Peter Teichner.
- A Seminar on Gromov-Witten Invariants (Sep 17, 2009)
- A mathematician’s seminar on Gromov-Witten theory.
*n*Lab - Latest Changes (Sep 17, 2009)- Trying to install better software support for logging latest changes to the nLab.
- Inbound Citations (Sep 15, 2009)
- A list of citations of entries at the nCafé blog and/or at the nLab wiki.
- Interactive Science Symposium (Sep 8, 2009)
- A sympositum on the use of web technology for communication among scientists.
- A Seminar on a Survey of Elliptic Cohomology (Sep 6, 2009)
- An nLab entry accompanying a seminar on elliptic cohomology.
- Traces in Bicategories (Sep 4, 2009)
- An article by Ponto and Shulman on traces in bicategories.
*n*Lab Migration Done (Sep 1, 2009)- The
*n*Lab wiki has successfully migrated to a better server. - Notes on Differential Nonabelian Cohomology (Aug 21, 2009)
- Notes on differential nonabelian cohomology.
*n*Lab Migration (Aug 19, 2009)- Request for help with testing the migrated nLab wiki installation.
- Question about ∞-Colimits (Aug 10, 2009)
- What can one say about hocolimits over domains that are themselves hocolimits?
- Question on Synthetic Differential Forms (Aug 3, 2009)
- On a realization of differential forms as cosimplicial generalized smooth algebras.
- Question on Models for (∞,1)-Functor Categories (Jul 29, 2009)
- How and under which conditions are (∞,1)–functor categories modeled my simplicial model structures on functor categories.
- Verity on Descent for Strict ω-Groupoid Valued Presheaves (Jul 23, 2009)
- Dominc Verity characterizes the descent condition for infinity-groupoid valued presheaves that happen to take values in strict infinity-groupoids.
- nLab -- How to get started (Jul 23, 2009)
- Quick easy information on how to make use of the nLab.n
- Laubinger on Lie Algebras for Frölicher Groups (Jul 1, 2009)
- Martin Laubinger studies Lie algebras of groups with generalized smooth manifold structure: Froelicher groups.
- Strings, Fields, Topology in Oberwolfach (Jun 8, 2009)
- Notes and material on Oberwolfach workshop on Strings, Fields and Topology
- Alm on Quantization as a Kan Extension (May 26, 2009)
- An observation on a relation between Kan extensions and path integral quantization – by Johan Alm.
- TFT at Northwestern (May 19, 2009)
- Reports from a conference on extended topological quantum field theory at Northwestern University.
- Journal Club -- Geometric Infinity-Function Theory -- Week 4 (May 18, 2009)
- Chris Brav reviews technical details about tensor products and integral transforms of quasi-coherent sheaves on perfect stacks.
- Journal Club -- Geometric Infinity-Function Theory -- Week 3 (May 11, 2009)
- This week in our Journal Club on [[geometric ∞\infty-function theory]] Bruce Bartlett talks about section 3 of “Integral Transforms”: perfect stacks. So far we had Week 1: Alex Hoffnung on Introduction Week 2, myself on Preliminaries See here for…
- Journal Club -- Geometric Infinity-Function Theory -- Week 2 (May 5, 2009)
- Preliminaries for the discussion of geometric infinity-function theory: higher categories, higher sheaves, higher algebra, higher traces and what it all means.
- Journal Club -- Geometric Infinity-Function Theory -- Week 1 (Apr 27, 2009)
- Journal Club on Geometric oo-Function theory part I: Introduction to integral transforms.
- Master in Mathematical Physics at Hamburg University (Apr 20, 2009)
- A new master program in mathematical physics at University of Hamburg.
- Report on 88th Peripatetic Seminar on Sheaves and Logic (Apr 11, 2009)
- Mike Shulman reports on the 88th Peripatetic Seminar on Sheaves and Logic
- Journal Club -- Geometric Infinity-Function Theory (Apr 10, 2009)
- A place to discuss and learn about the work by Ben-Zvi/Francis/Nadler on geometric infinity-function theory and its application in infinity-quantum field theory.
- Graphical Category Theory Demonstrations (Apr 7, 2009)
- On computer aided diagrammatic reasoning.
- Cohomology (Apr 4, 2009)
- On the general (infinity,1)-categorical notion of cohomology.
- Twisted Differential String- and Fivebrane-Structures (Mar 20, 2009)
- An article on twisted differential nonabelian cohomology and its application to anomaly cancellation in string theory.
- Question on Homotopical Structure on SimpSet (Mar 5, 2009)
- A question on (directed) path objects in Kan complexes and weak Kan complexes.
- Question on Geometric Function Theory (Feb 27, 2009)
- On the choice of “nice generalized geometric functions” in a general context of oo-stacks.
- Moerdijk on Infinity-Operads (Feb 6, 2009)
- Ieke Moerdijk on (infinity,1)-operads.
- Dendroidal Sets and Infinity-Operads (Feb 5, 2009)
- Notes from a talk by Ieke Moerdijk on dendroidal sets, with a few remarks on presheaves on the category of posets.
- Ben-Zvi on Geometric Function Theory (Jan 8, 2009)
- An exposition by David Ben-Zvi on central ideas of geometric function theory, its categorification and relation to groupoidification.
*n*Lab -- General Discussion (Jan 4, 2009)- A place for general discussion concerning the nLab.
- Groupoidification from sigma-Models? (Dec 30, 2008)
- On constructing sigma-models from differential nonabelian cocycles and how this gives rise to methods of groupoidification.
- Question on Infinity-Yoneda (Dec 4, 2008)
- What is known about the Yoneda lemma in a higher categorical context?
- Zhu on Lie's Second Theorem for Lie Groupoids (Dec 3, 2008)
- On Lie integration of Lie algebroids.
*n*Lab (Nov 28, 2008)- We have set up a Wiki accompanying the n-Category Cafe.
- Mathematics, Physics and Philosophy (Nov 26, 2008)
- An essay, or the like, on motivations for interdisciplinary research at the boundary of math, physics and philosophy.
- Bär on Fiber Integration in Differential Cohomology (Nov 26, 2008)
- On fiber integration in differential cohomology and the notion of generalized smooth spaces used for that.
*Higher and Graded Geometric Structures*in Göttingen (Nov 19, 2008)- A workshop on higher bundles, gerbes, groupoids and supermanifolds.
- Local Nets and Co-Sheaves (Nov 14, 2008)
- Co-sheaf condition (codescent) for Haag-Kastler nets of local quantum observables?
- Frobenius Algebras and the BV Formalism (Nov 14, 2008)
- Bruce Bartlett is looking at the latest article by Cattaneo and Mnev on BV-quantization of Chern-Simons theory.
- Baković on
*Bigroupoid 2-Torsors*(Nov 13, 2008) - Bakovic on G-principal bundles for G a bigroupoid.
- Talk:
*Local Nets from Parallel Transport 2-Functors*(Nov 12, 2008) - A talk on the relation between AQFT and extended functorial QFT.
- Lie 3-Algebras on the Membrane (?) (Nov 6, 2008)
- Recently a trinary bracket appears in the study of the supermembrane which is sometimes addressed as a homotopy algebraic structure.
*Higher Structures in Math and Physics*in Lausanne (Nov 2, 2008)- A workshop in Lausanne on Higher Structures in Mathematics and Physics
- Twisted Differential Nonabelian Cohomology (Oct 30, 2008)
- Work on theory and applications of twisted nonabelian differential cohomology.
- Hopf Algebraic Renormalization (Oct 23, 2008)
- The starting point and basic idea of combinatorial Hopf algebraic techniques in perturbative quantum field theory.
- Codescent and the van Kampen Theorem (Oct 21, 2008)
- On codescent, infinity-co-stacks, fundamental infinity-groupoids, natural differential geometry and the van Kampen theorem
- Hepworth on 2-Vector Bundles and the Volume of a Differentiable Stack (Oct 20, 2008)
- Hepworth on the idea of volume forms on a stack in terms of sections of 2-vector bundles.
- Talk in Göttingen:
*Second Nonabelian Differential Cohomology*(Oct 19, 2008) - A talk on second nonabelian differential cohomology.
- String- and Fivebrane-Structures (Oct 14, 2008)
- A new article on String- and Fivebrane structures and some previous articles on Fivebrane structures.
- Freely Generated ω-Categories (Oct 14, 2008)
- The notion of strict infinity-categories which are “freely generated”.
- Semistrict Infinity-Categories and ω-Semi-Categories (Oct 8, 2008)
- On strict infinity categories with weak identities.
- Yet Another Model ω-Question (Oct 7, 2008)
- On the relation between the model category structure on smooth infinity-groupoids and on differential algebras.
- More Model ω-Questions (Oct 2, 2008)
- More questions on model category theory in general and the model structure on omega-categories in particular.
- (ω+ω)-Categories (?) (Sep 30, 2008)
- A tentative suggestion for weak oo-categories.
- Some Model ω-Questions (Sep 27, 2008)
- The model structure on omega-categories should induce a model structure on omega-category valued presheaves. What can be said about this?
- Group Cocycles and Simplices (Sep 22, 2008)
- Question on simplicial group cocycles.
- Back and Catching Up (Sep 21, 2008)
- A list of things to read.
- Planar Algebras, TFTs with Defects (Sep 11, 2008)
- On planar algebras interpreted as 2D TFTs with defect lines.
- Smooth Differential Graded Algebra? (Sep 9, 2008)
- What is the right definition of generalized smooth differential graded-commutative algebras?
- Equivariant deRham Cohomology and Action Lie Algebroids (Sep 7, 2008)
- The relation between equivariant deRham cohomology and the Weil algebra of the corresponding action Lie algebroid.
- Waldorf on
*Transport Functors and Connections on Gerbes*(Sep 6, 2008) - A talk on parallel 2-transport.
- Homotopical Algebra with Applications to Mathematical Physics (Aug 21, 2008)
- A workshop on homotopical methods in mathematical physics.
- Bergman on Infinity-Vector Bundles Coupled to Topological Strings (Aug 17, 2008)
- topological string, B-model, derived category, B-brane, infinity-vector space, infinity connection
- Differential Graded Clifford Algebra (Aug 17, 2008)
- On Clifford-defomrations of Chevalley-Eilenberg and Weil algebras.
- Connections on Nonabelian Gerbes and their Holonomy (Aug 15, 2008)
- An article on transport 2-functors.
- Pre- and Postdictions of the NCG Standard Model (Jul 30, 2008)
- Some predictions and postdictions derived from the NCG Kaluza-Klein standard model.
- Some ω-Questions (Jul 18, 2008)
- Questions on omega-categorical constructions in the context of descent and cohomology.
- News on Measures on Groupoids? (Jul 17, 2008)
- Benjamin Bahr apparently thought about measures on groupoids of connections.
- Talk on
*AQFT from FQFT and Applications*(Jul 10, 2008) - On local nets constructed from transport 2-functors and examples relating to lattice models, Hopf spin chains, asymptotic inclusion of subfactors. And some remarks on the relation between conformal nets and vertex operator algebras.
- Basics of Poisson Reduction and BV, I (Jul 7, 2008)
- Basics of symplectic reduction and Poisson reduction.
- The Manifold Geometries of QFT, II (Suijlekom on Renormalization, Hopf Algebra and BV-Formalism) (Jul 1, 2008)
- Walter Suijlekom explains a relation between Connes-Kreimer Hopf algebras of Feynman diagrams with the master equation in BV-formalism.
- Block on L-∞ Module Categories (Jun 30, 2008)
- On Jonathan Block’s concept of modules over differential graded algebras.
- The Manifold Geometries of QFT, I (Jun 30, 2008)
- Some notes on the first day at “The manifold geometries of QFT” at the MPI in Bonn.
- AQFT from Lattice Models (?) (Jun 27, 2008)
- On lattice AQFT models such as Hopf spin chains and their derivation of 2-C*-algebra valued 2-functors.
- Eli Hawkins on Geometric Quantization, II (Jun 27, 2008)
- Eli Hawkins explains his method of getting a quantum algebra from the convolution algebra of sections on a symplectic groupoid.
- Category Algebras (Jun 26, 2008)
- On an interpretation of the category algebra of a category in terms of pull-push of finite sets through correspondence spaces.
- Behrang Noohi on Butterflies and Morphisms Between Weak 2-Groups (Jun 23, 2008)
- A talk by Behrang Noohi.
- Aldrovandi on Non-Abelian Gerbes and 2-Bundles (Jun 23, 2008)
- A talk by Aldrovandi on different perspectives on gerbes and 2-bundles.
- Landsman on Quantization of Poisson Algebras Associated to Lie Algebroids (Jun 22, 2008)
- A quick review of Landsman’s result on strict deformation quantization of Poisson manifolds dual to Lie algebroids: the quantum algebra is nothing but the groupoid algebra of the Lie groupoid integrating the Lie algebroid.
- Eli Hawkins on Geometric Quantization, I (Jun 20, 2008)
- Some basics and some aspects of geometric quantization. With an emphasis on the geometric quantization of duals of Lie algebras and duals of Lie algebroids.
- Schommer-Pries on Classification of 2-Dimensional Extended TFT (Jun 18, 2008)
- Chris Schommer-Pries classifies 2-functors from a 2-category of 2-dimensional cobordisms.
- Teleman on Topological Construction of Chern-Simons Theory (Jun 17, 2008)
- A talk by Constant Teleman on extended Chern-Simons QFT and what to assign to the point.
- An Exercise in Groupoidification: The Path Integral (Jun 13, 2008)
- A remark on the path integral in view of groupoidification and Sigma-model quantization.
- A Groupoid Approach to Quantization (Jun 12, 2008)
- On Eli Hawkins’ groupoid version of geometric quantization.
- Urban Myths in Contemporary Cosmology (Jun 6, 2008)
- On urban-myth-like memes in the contemporary theoretical cosmology community.
- HIM Trimester on Geometry and Physics, Week 4 (May 29, 2008)
- Talk in Stanford on nonabelian differential cohomology.
- Workshop: Non-Commutative Constructions in Arithmetic and Geometry (May 22, 2008)
- Conference in London on non-commutative constructions in arithmetic and geometry
- Hopkins-Lurie on Baez-Dolan (May 20, 2008)
- Hopkins and Lurie give a proof of the Baez-Dolan hypothesis on tangles and extended TQFT.
- Relation between AQFT and Extended Functorial QFT (May 20, 2008)
- On how to obtain from any extended d-dimensional QFT a local net of observables.
- Integrals and Valuations using Geometric Logic (May 19, 2008)
- Bas Spitters on the theory of integration in a topos.
- Harrison's Geometric Calculus (May 18, 2008)
- On Harrison’s generalized formalism for differential calculus and differential geometry.
- Electric-Magnetic-Duality and Hodge Duality Extended to Differental Cocycles (May 17, 2008)
- On the electric-magnetic dual formulation of higher abelian Yang-Mills theory.
- HIM Trimester Geometry and Physics, Week 1 (May 14, 2008)
- On vertex operator algebras, operads and Segals QFT axioms. On integration over supermanifolds, supergroupoids and the two notions of supercategories.
- E
_{8}Quillen Superconnection (May 10, 2008) - On Quillen superconnections on E8-bundles and on the mathematical interpretation of the connection appearing in an article by A. Lisi.
- On Lie oo-Theory (May 8, 2008)
- Talk on the Lie infinity-algebroid perspective on the BRST complex and its relation to the integrated picture of action infinity-groups.
- Integrability of Lie Brackets (May 7, 2008)
- Crainic and Fernandes on integration of Lie algebroids to Lie groupoids.
- Ambimorphic? (May 6, 2008)
- On adjunctions between spaces and n-groupoids induced by homming out of the fundamental n-groupoid.
- FQXi (May 4, 2008)
- The Foundational Questions Institute runs its second grant competition.
- Dual Formulation of String Theory and Fivebrane Structures (Apr 28, 2008)
- An article which discusses lifts through the 7-fold connected cover of the structure group of the tangent bundle in the context of electric-magnetic duality in string theory.
- Charges and Twisted Bundles, IV: Anomaly Cancellation (Apr 27, 2008)
- How the fermionic anomaly may cancel against the charge anomaly in higher gauge theory: the Green-Schwarz mechanism
- Charges and Twisted Bundles, III: Anomalies (Apr 25, 2008)
- On the anomalies arising in (higher) gauge theories in the presence of electric and magnetic charges.
- Thoughts (Mostly on Super ∞-Things) (Apr 22, 2008)
- Thoughts while travelling and talking.
- Higher Hochschild Cohomology and Differential Forms on Mapping Spaces (Apr 18, 2008)
- On “brane topology”, the higher order generalization of Hochschild cohomology. And on Chen iterated integrals.
- A Topos for Algebraic Quantum Theory (revised) (Apr 15, 2008)
- Bas Spitters on topos-theory of noncommutative C*-algebras and quantum physics.
- Sigma-Models and Nonabelian Differential Cohomology (Apr 11, 2008)
- Notes on nonabelian differential cohomology and its application to classical and qantum parallel transport.
- Limits and Push-Forward (Mar 31, 2008)
- Question on the relation between push-forward of functors and (indexed) limits.
- What Has Happened So Far (Mar 27, 2008)
- A review of one of the main topics discussed at the Cafe: Sigma-models as the pull-push quantization of nonabelian differential cocycles.
- Nonabelian Differential Cohomology in Street's Descent Theory (Mar 22, 2008)
- A discussion of differential nonabelian cocycles classifying higher bundles with connection in the context of the general theory of descent and cohomology with coefficients in infnity-category valued presheaves as formalized by Ross Street.
- Crossed Menagerie (Mar 21, 2008)
- Detailed notes by Tim Porter on “crossed gadgetry and cohomology in algebra and topology”.
- Slides:
*On Nonabelian Differential Cohomology*(Mar 13, 2008) - On the notion of nonabelian differential cohomology.
- Chern-Simons Actions for (Super)-Gravities (Mar 12, 2008)
- On Chern-Simons actions for (super-)gravity.
- Space and Quantity (Mar 6, 2008)
- Notes on spaces and smooth spaces, function algebras and smooth function algebras.
- Sections of Bundles and Question on Inner Homs in Comma Categories (Mar 4, 2008)
- On inner homs in comma categories, motivated from a description of spaces of sections of bundles in terms of such.
- Charges and Twisted n-Bundles, II (Mar 4, 2008)
- Rephrasing Freed’s action functional for differential cohomology in terms of L-oo connections in a simple toy example.
- Infinity-Groups with Specified Composition (Mar 3, 2008)
- On infinity-groups and infinity-categories with specified composition, and their closedness.
- Charges and Twisted n-Bundles, I (Feb 29, 2008)
- Generalized charges are very well understood using generalized differential cohomology. Here I relate that to the nonabelian differential cohomology of n-bundles with connection.
- (Generalized) Differential Cohomology and Lie Infinity-Connections (Feb 27, 2008)
- On generalized differential cohomology and its relation to infinity-parallel transport and Lie-infinity connections.
- Impressions on Infinity-Lie Theory (Feb 26, 2008)
- Thoughts on infinity Lie theory.
- What I learned from Urs (Feb 26, 2008)
- Bruce Bartlett talks about some aspects of the program of systematically understanding the quantization of Sigma-models in terms of sending parallel transport n-functors to the cobordism representations which encode the quantum field theory of the n-particles charged under them.
- Lurie on Extended TQFT (Feb 21, 2008)
- Jacob Lurie on extended TQFT and the Baez-Dolan Cobordism Hypothesis
- Categories, Logic and Physics in London, II (Feb 19, 2008)
- Second workshop on “Categories, Logic and Foundations of Physics” in London.
- Slides:
*L-Infinity Connections and Applications*(Feb 15, 2008) - Talks on L-infinity algebra connections.
- Construction of Cocycles for Chern-Simons 3-Bundles (Feb 12, 2008)
- On how to interpret the geometric construction by Brylinksi and McLaughlin of Cech cocycles classified by Pontrjagin classes as obstructions to lifts of G-bundles to String(G)-2-bundles.
- Question on Smooth Functions (Feb 11, 2008)
- On morphisms of algebras of smooth functions coming from pullback along smooth maps.
- Smooth 2-Functors and Differential Forms (Feb 6, 2008)
- An article on the relation between smooth 2-functors with values in strict 2-groups, and an outline of the big picture that this sits in.
- Chern-Simons States from L-infinity Bundles, III: States over the Circle (Feb 4, 2008)
- On computing the states of Chern-Simons theory over the circle from the L-infinity algebraic model of the Chern-Simons 3-bundle over BG.
- States of Chern-Simons Theory (Feb 1, 2008)
- A list of selected literature discussing Chern-Simons theory and its space of states.
- L-infinity Associated Bundles, Sections and Covariant Derivatives (Jan 30, 2008)
- Associated L-infinity structures are obtained from Lie action infinity-algebroids, leading to a concept of sections and covariant derivatives in this context.
- Differential Forms and Smooth Spaces (Jan 28, 2008)
- On turning differential graded-commutative algebras into smooth spaces, and interpreting these as classifying spaces.
- Integration Without Integration (Jan 24, 2008)
- On how integration and transgression of differential forms is realized in terms of inner homs applied to transport n-functors and their corresponding Lie oo-algebraic connection data.
- Spaceoids (Jan 17, 2008)
- Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul on categorified spaces and the many-object version of C-star algebras.
- Slides:
*On the BV-Formalism*(BV Part XI) (Jan 16, 2008) - A discussion of BV-formalism from a Lie oo-algebraic perspective.
- BV-Formalism, Part X: Symplectic Structures (Jan 14, 2008)
- A Lie oo-algebraic perspective on the antibracket.
- Ginot and Stiénon on Characteristic Classes of 2-Bundles (Jan 11, 2008)
- Stinot and Stienon on 2-bundles and their characteristic classes.
- The Concept of a Space of States, and the Space of States of the Charged
*n*-Particle (Jan 9, 2008) - On the notion of topos-theoretic quantum state objects, the proposed definition by Isham and Doering and a proposal for a simplified modification for the class of theories given by charged n-particle sigma-models.
- Dijkgraaf-Witten and its Categorification by Martins and Porter (Jan 4, 2008)
- On Dijkgraaf-Witten theory as a sigma model, and its categorification by Martins and Porter.
- On BV Quantization, Part IX: Antibracket and BV-Laplacian (Jan 4, 2008)
- The meaning of antibracket, BV-Laplacian and master equation in BV-formalism: Clifford structures on generalized smooth spaces.
- Comparative Smootheology (Jan 3, 2008)
- A survey and comparison of the various notions of generalized smooth spaces, by Andrew Stacey.
- Transgression of
*n*-Transport and*n*-Connections (Dec 30, 2007) - On the general idea of transgression of n-connections and on the underlying machinery of generalized smooth spaces and their differential graded-commutative algebras of differential forms.
- BF-Theory as a Higher Gauge Theory (Dec 29, 2007)
- On interpreting BF-theory as a higher gauge theory.
- Lie oo-Connections and their Application to String- and Chern-Simons
*n*-Transport (Dec 25, 2007) - A discussion of connections for general L-infinity algebras and their application to String- and Chern-Simons n-transport.
- Non-Commutative Structures in Arithmetic and Geometry (Dec 21, 2007)
- A conference on non-commutative structures.
- Basic Bundle Theory and K-Cohomology Invariants (Dec 17, 2007)
- A book on bundle theory and K-cohomology.
- Program
*Geometry and Physics*at HIM (Dec 11, 2007) - A program on geometry and physics takes place summer 2008 at the HIM on Bonn.
- Local Nets from 2-Transport (Dec 9, 2007)
- How to obtain a local net of observables from an extended functorial QFT.
- A Topos for Algebraic Quantum Theory (Dec 6, 2007)
- A summary of some key points of Chris Heunen’s and Bas Spitters’ article.
- The Principle of General Tovariance (Dec 5, 2007)
- Landsmann proposes that physical laws should be formulated such that they may be internalized into any topos.
- On BV Quantization, Part VIII (Nov 29, 2007)
- Towards understading BV by computing the charged n-particle internal to Z-categories, secretly following AKSZ.
- Concordance (Nov 23, 2007)
- On the notion of concordance of 2-bundles and, more generally, on a notion of omega-anafunctor and a possible closed structure on the category of omega-categories with omega-anafunctors between them.
- Something Like Lie-Rinehart ∞-pairs and the BV-complex (BV, part VII) (Nov 20, 2007)
- Notes on something like Lie ∞-algebroids in the light of the BV complex.
- Modules for Lie infinity-Algebras (Nov 13, 2007)
- On modules for Lie infinity algebras in general and the definition given by Lars Kjeseth in particular.
- 2-Vectors in Trondheim (Nov 5, 2007)
- On line 2-bundles.
*n*-Bundle Obstructions for Bruce (Nov 4, 2007)- On the global description of n-bundles obstructing lifts through shifted central extensions.
- On Noether's Second (BV, Part VI) (Oct 31, 2007)
- On Noether’s second theorem and ghost/antighost pairing.
- BV for Dummies (Part V) (Oct 30, 2007)
- Some elements of BV formalism, or rather of the Koszul-Tate-Chevalley-Eilenberg resolution, in a simple setup with ideosyncratic remarks on higher vector spaces.
- On String- and Chern-Simons
*n*-Transport (Oct 23, 2007) - Slides on String- and Chern-Simons n-Transport.
- On Lie
*N*-tegration and Rational Homotopy Theory (Oct 20, 2007) - On the general ideal of integrating Lie n-algebras in the context of rational homotopy theory, and about Sullivan’s old article on this issue in particular.
- Advanced Course on Simplicial Methods in Higher Categories (Oct 19, 2007)
- Lectures on simplicial methods in higher category theory.
- On Weak Cokernels for 2-Groups (Oct 17, 2007)
- On weak cokernels of 2-groups.
*n*-Curvature, Part III (Oct 16, 2007)- Curvature is the obstruction to flatness. Believe it or not.
- Loday and Pirashvili on Lie 2-Algebras (secretly) (Oct 16, 2007)
- On the non-standard monoidal structure on 2-term chain complexes induced from the monoidal structure on Baez-Crans 2.vector spaces.
- What is the Fiber? (Oct 15, 2007)
- On bundle gerbes and whether or not they “are” 2-bundles.
- Obstructions to
*n*-Bundle Lifts Part II: The BIG Diagram (Oct 12, 2007) - A big diagram illustrating the situation of lifting a bundle through a String-like extension.
- BV-Formalism, Part IV (Oct 11, 2007)
- Lie algebroids of action groupoids and their relation to BRST formalism.
- Question on Weak Pullbacks along Sequences (Oct 11, 2007)
- How to weakly pull a functor along a short sequence of groupoids?
- Categorified Clifford Algebra and weak Lie
*n*-Algebras (Oct 9, 2007) - On weak Lie n-algebras, differential graded Clifford algebra and Roytenberg’s work on weak Lie 2-algebras.
- Report on AIM Workshop: Towards Relative Symplectic Field Theory (Oct 5, 2007)
- James Stasheff reports on the AIM workshop Towards Relative Symplectic Field Theory
- Cohomology of the String Lie 2-Algebra (Oct 2, 2007)
- On the Lie 2-algebra cohomlogy of the String Lie 2-algebra and its relation to twisted K-theory.
- Detecting Higher Order Necklaces (Sep 27, 2007)
- Nils Baas on higher order structures, Enrico Vitale on weak cokernels and a speculation on weak Lie
*n*-algebras triggered by discussion with Pavol Severa. - An Invitation to Higher Dimensional Mathematics and Physics (Sep 25, 2007)
- A public talk supposed to illustrate some of the basic reasoning underlying higher dimensional algebra.
- Obstructions, Tangent Categories and Lie
*N*-tegration (Sep 24, 2007) - Thoughts on n-bundle theory in terms of Lie n-algebras.
- Groupoidfest 07 (Sep 14, 2007)
- A conference on groupoids.
- Obstructions for
*n*-Bundle Lifts (Sep 12, 2007) - On obstructions to lifting the structure n-group of n-bundles.
- Notes by Jurčo on generalized Bundle Gerbes (Sep 10, 2007)
- Branislav Jurco has some notes on nonabelian bundle 2-gerbes and on associated bundle 1-gerbes.
- Lie n-Algebra Cohomology (Sep 7, 2007)
- On characteristic classes of n-bundles.
- Arrow-Theoretic Differential Theory IV: Cotangents (Sep 3, 2007)
- Cotangents and morphisms of Lie n-algebroids from arrow-theoretic differential theory.
- On Hess and Lack on Bundles of Categories (Aug 30, 2007)
- On Hess and Lack’s notion of “bundles of categories”.
- Question about von Neumann Algebras (Aug 30, 2007)
- On von Neumann algebras and their bimodules.
- Arrow-Theoretic Differential Theory III: Higher Morphisms (Aug 28, 2007)
- Using arrow-theoretic differential theory to understand higher morphisms of Lie n-algebras.
- The G and the B (Aug 25, 2007)
- How to get the bundle governing Generalized Complex Geometry from abstract nonsense and arrow-theoretic differential theory.
- That Shift in Dimension (Aug 24, 2007)
- What makes the Kontsevich-Cattaneo-Felder theorem tick? How can it be that an n-dimensional quantum field theory is encoded in an (n+1)-dimensional one?
- Wilson Loop Defects on the String (Aug 23, 2007)
- On Alekseev and Monnier’s work on quantizing Wilson loop observables for the WZW model.
- Lyakhovich and Sharapov on QFT (On BV-Quantization, Part III) (Aug 22, 2007)
- On Lyakhovich and Sharapov’s insights into mechanics, holography and BV formalism.
- More on Tangent Categories (Aug 21, 2007)
- More comments on the nature of tangent categories and their relation to the notion of shifted tangent bundles to differential graded spaces.
- On BV Quantization, Part II (Aug 18, 2007)
- A review of elements of the Batalin-Vilkovisky formalism, with an eye towards my claim that this describes configuration spaces which are Lie n-algebroids.
- On BV Quantization. Part I. (Aug 17, 2007)
- On BV-formalism applied to Chern-Simons theory and its apparent relation to 3-functorial extentended QFT.
- On Roberts and Ruzzi's Connections over Posets (Aug 16, 2007)
- On J. Roberts and G. Ruzzi’s concept of G-bundles with connection over posets and its relation to analogous notions discussed at length at the n-Cafe.
- The Canonical 1-Particle, Part II (Aug 14, 2007)
- More on the canonical quantization of the charged n-particle for the case of a 1-particle propagating on a lattice.
- Lazaroiu on G-Flows on Categories (Aug 14, 2007)
- Lazaroiu’s concept of a “graded category wiuth shifts” is the same as that of a category “with G-flow”.
- Question about Tensor Categories (Aug 13, 2007)
- Hendryk Pfeiffer asked me to forward the following question to the Café. Dear nn-category people, I have a question about tensor categories on which I would appreciate comments and references. As probably several people are interested in this, I…
- String and Chern-Simons Lie 3-Algebras (Aug 10, 2007)
- A talk on Chern-Simons Lie n-algebras.
- Arrow-Theoretic Differential Theory, Part II (Aug 8, 2007)
- A remark on maps of categorical vector fields, inner derivations and higher homotopies of L-infinity algebras.
- Adinkras (Aug 7, 2007)
- The concept of an “Adinkra” - a graph used to describe representations of N-extended d=1 supersymmetry algebras - remarkably resembles some categorical structures which appear in the context of supersymmetry.
- Gauge Tranformations of n-Bundles and (n-1)-Gerbes (Aug 4, 2007)
- The notion of gauge transformation of n-bundles and (n-1)-gerbes.
- QFT of Charged n-Particle: Towards 2-Functorial CFT (Aug 3, 2007)
- Towards a 2-functorial description of 2-dimensional conformal field theory. A project description.
- QFT of Charged n-Particle: Extended Worldvolumes (Aug 2, 2007)
- Passing from locally to globally refined extended QFTs by means of the adjointness property of the Gray tensor product of the n-particle with the timeline.
- Arrow-Theoretic Differential Theory (Jul 27, 2007)
- We propose and study a notion of a tangent (n+1)-bundle to an arbitrary n-category. Despite its simplicity, this notion turns out to be useful, as we shall indicate.
- Physical Systems as Topoi, Part III (Jul 23, 2007)
- The third part of the talk.
- Physical Systems as Topoi, Part II (Jul 22, 2007)
- Second part of the talk.
- Physical Systems as Topoi, Part I (Jul 22, 2007)
- Doering on his work with Isham on topos theoretic models of quantum theory and general theories of physics.
- Making AdS/CFT Precise (Jul 22, 2007)
- The last session of Recent Developments in QFT in Leipzig was general discussion, which happened to be quite interesting for various reasons….
- Deformation Quantization of Surjective Submersions (Jul 22, 2007)
- Waldman on noncommutative deformations of total spaces of fiber bundles.
- Tangent Categories (Jul 21, 2007)
- An arrow-theoretic formulation of tangency and its relation to inner automorphisms.
- Multiplicative Structure of Transgressed n-Bundles (Jul 5, 2007)
- On how to think of multiplicative structures on n-bundles with connection.
- Supercategories (Jul 4, 2007)
- A proposal for a definition of “supercategory” and an arrow-theoretic understanding of some elements of supersymmetry.
- The Inner Automorphism 3-Group of a Strict 2-Group (Jul 4, 2007)
- On the definition and construction of the inner automorphism 3-group of any strict 2-group, and how it plays the role of the universal 2-bundle.
- Conference on Categories in Geometry and Physics (Jun 28, 2007)
- A conference on categories and their application in geometry and physics, taking place in Split, Croatia.
- Colorings of Graphs (Jun 26, 2007)
- Dmitry Kozlov on understanding the graph coloring problem by looking at simplicial Hom-complexes of graphs.
- Some Recreational Thoughts on Super-Riemannian Cobordisms (Jun 23, 2007)
- On super-Riemannian structure on cobordisms in terms of super-Poincaré connections.
- Curvature, the Atiyah Sequence and Inner Automorphisms (Jun 20, 2007)
- On the notion of curvature 2-functor in light of morphisms from the path sequence of the base to the Atiyah sequence of the bundle.
- Waldorf on Parallel Transport Functors (Jun 18, 2007)
- Review of parallel transport functors by Konrad Waldorf.
- Generalized Geometric Langlands is False (Jun 18, 2007)
- C. Teleman on a counter example to the generalised geometric Langlands conjecture.
- Polyvector Super-Poincaré Algebras (Jun 14, 2007)
- Superextension of Poincare algebras and how these give rise to brane charges.
- Spectral Triples and Graph Field Theory (Jun 12, 2007)
- Yan Soibelman is thinking about spectral stringy geometry.
- Extended QFT and Cohomology II: Sections, States, Twists and Holography (Jun 10, 2007)
- How transformations of extended d-dimensional quantum field theories are related to (d-1)-dimensional quantum field theories. How this is known either as twisting or as, in fact, holography.
- Extended Quantum Field Theory and Cohomology, I (Jun 8, 2007)
- On understanding extended quantum field theory and generalized cohomology.
- Large Smooth Categories (Jun 8, 2007)
- Stacks versus categories internal to sheaves.
- The n-Café Quantum Conjecture (Jun 8, 2007)
- Why it seems that quantum mechanics ought to be the de-refinement of a refined theory which lives in one categorical degree higher than usual.
- Connections on String-2-Bundles (Jun 3, 2007)
- On connections on String 2-bundles.
- On the Bar Construction (May 31, 2007)
- Todd Trimble on the bar construction.
- The Second Edge of the Cube (May 31, 2007)
- Differentiating parallel transport anafunctors to Cartan-Ehresmann connections.
- Kock on Higher Connections (May 31, 2007)
- Anders Kock gives a synthetic differential description of parallel n-transport using strict n-fold categories.
- What is a Lie Derivative, really? (May 31, 2007)
- On the arrow-theory behind Lie derivatives.
- Derivation Lie 1-Algebras of Lie n-Algebras (May 25, 2007)
- On ordinary Lie algebras “of derivations” of Lie n-algebras.
- Chern Lie (2
*n*+1)-Algebras (May 19, 2007) - Generalizing Baez-Crans Lie 2n-algebras to Chern and to Chern-Simons Lie (2n+1)-algebras.
- Calculations Inside Semisimple Categories (May 18, 2007)
- Bruce Bartlett on computations in semisimple categories.
- Zoo of Lie n-Algebras (May 10, 2007)
- A menagerie of examples of Lie n-algebras and of connections taking values in these, including the String 2-connection and the Chern-Simons 3-connection.
- Workshop on Elliptic Cohomology in Hamburg (May 9, 2007)
- A little workshop on elliptic cohomology, mainly the functorial QFT approach by Stolz and Teichner, in Hamburg, June 2007.
- Report from "Workshop on Higher Gauge Theory" (May 9, 2007)
- Report-back on a little symposium titled “Higher Gauge Theory” (but concerned just with abelian gerbes) that took place at the AEI in Golm.
- The First Edge of the Cube (May 4, 2007)
- The notion of smooth local i-trivialization of transport n-functors for n=1.
- Grandis on Collared Cobordisms and TQFT (May 2, 2007)
- Marco Grandis discusses the arrow-theory of collared cobordisms and topological quantum field theory.
- Symposium on "Higher Gauge Theory" in Golm (May 2, 2007)
- A workshop on abelian gerbes, Deligne cohomology and strings.
- n-Curvature (Apr 25, 2007)
- The n-curvature canonically associated with a transport n-functor.
- Report-Back on BMC (Apr 22, 2007)
- Bruce Bartlett reports from the British Mathematics Colloquium 2007.
- Some Conferences (Apr 19, 2007)
- A conference on bundles and gerbes, another one on topology, and comments on associated 2-vector bundles and String connections.
- Oberwolfach CFT, Tuesday Morning (Apr 3, 2007)
- On Q-systems, on the Drinfeld Double and its modular tensor representation category, and on John Roberts ideas on nonabelian cohomology and QFT.
- Oberwolfach CFT, Monday Evening (Apr 3, 2007)
- Some random notes concerning, bundles, functorial quantum field theory and algebraic QFT.
- Oberwolfach CFT, Monday Morning (Apr 2, 2007)
- Some basic concepts and facts concerning local representations of nets of local algebras on the real line.
- Oberwolfach CFT, Arrival Night (Apr 1, 2007)
- Some musings on the relation of AQFT to functorial QFT.
- Some Notes on Local QFT (Mar 31, 2007)
- Some aspects of the AQFT description of 2d CFT.
- History of Understanding Bundles with Connection using Parallel Transport around Loops (Mar 23, 2007)
- A list of some papers involved in the historical development of the idea of expressing bundles with connection in terms of their parallel transport around loops.
- Branes, Bi-Branes, 2-Vectors, 2-Linear Maps (Mar 22, 2007)
- In which sense D-branes generalize to “bi-branes”.
- Recent Developments in QFT in Leipzig (Mar 21, 2007)
- A conference on new developments in Quantum Field Theory at the Max Planck Institute in Leipzig.
- QFT of Charged n-Particle: The Canonical 1-Particle (Mar 19, 2007)
- On the category of paths whose canonical Leinster measure reproduces the path integral measure appearing in the quantization of the charged particle.
- Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna (Mar 16, 2007)
- Announcement of ESI Workshop on Lie Algebroids in Summer 2007.
- Star-Structures and Daggers (Mar 15, 2007)
- Question on the compatibility of daggers and stars in monoidal 2-categories with duals.
- Differentiating Lie Groupoids to Lie Algebroids (Mar 14, 2007)
- On an attempt to find a nice way to formulate the definition of the Lie algebroid obtained from a Lie groupoid.
- Canonical Measures on Configuration Spaces (Mar 8, 2007)
- On how the Leinster weighting on a category might provide path integral measures in physics.
- QFT of Charged n-Particle: Sheaves of Observables (Mar 6, 2007)
- On the concepts of sheaves and nets of algebras of observables in quantum field theory.
- QFT of Charged n-Particle: Disk Path Integral for String in trivial KR Field (Mar 5, 2007)
- The arrow-theoretic perspective on the path integral for the disk diagram of the open string.
- QFT of Charged n-Particle: Gauge Theory Kinematics (Feb 28, 2007)
- A review of Fleischhack’s discussion of a Weyl algebra on spaces of generalized connections.
- QFT of Charged n-Particle: Algebra of Observables (Feb 28, 2007)
- The algebra of observables as certain endomorphisms of the n-category of sections.
- Amplimorphisms and Quantum Symmetry, II (Feb 25, 2007)
- A remark on the appearance of iterated module
*n*-categories in quantum field theory. - QFT of Charged n-Particle: T-Duality (Feb 16, 2007)
- Topological T-duality as a pull-push transformation of sections of the 2-particle.
- Higher Morphisms of Lie n-Algebras and L-infinity Algebras (Feb 15, 2007)
- On higher morphisms of Lie n-algebras, and higher homotopies between L_oo algebras.
- Slides for Freed's Andrejewski Lecture (Feb 13, 2007)
- Lecture by Freed on Freed-Hopkins-Teleman.
- QFT of Charged n-Particle: Dynamics (Feb 12, 2007)
- Definition of the dynamics of the charged quantum particle by pull-push along correspondences of path spaces.
- Day on RCFTs (Feb 9, 2007)
- Brian Day on a relation between fusion rings, braided tensor categories and “realisation” in enriched category theory.
- Isham on Arrow Fields (Feb 8, 2007)
- On Chris Isham’s notion of an “arrow field” on a category.
- QFT of Charged n-particle: Chan-Paton Bundles (Feb 7, 2007)
- Chan-Paton bundles from the pull-push quantization of the open 2-particle.
- Amplimorphisms and Quantum Symmetry, I (Feb 6, 2007)
- Localized endomorphisms of quantum observables in arrow-theoretic terms.
- Amplimorphisms (Feb 5, 2007)
- A certain notion of twisted morphisms of algebras – and how to think about it.
- Higher Structure in Geometry and Physics -- and in Paris (Feb 2, 2007)
- Slides of talks for a conference on higher structures in geometry and physics
- Huisken on Uniformization, II (Feb 2, 2007)
- Something about Ricci flow and the proof of the Poincare conjecture.
- Huisken on Uniformization, I (Feb 2, 2007)
- Some ideas behind the proof of the Poincare conjecture by means of Ricci flow.
- Towards the FFRS Description of 2dCFT (B) (Feb 1, 2007)
- “2-processes”: 2-morphisms, adjunctions, the exchange law and the Frobenius property
- CFT in Oberwolfach (Jan 29, 2007)
- An Oberwolfach meeting on conformal field theory.
- Globular Extended QFT of the Charged n-Particle: String on BG (Jan 26, 2007)
- The string on the classifying space of a strict 2-group.
- The Globular Extended QFT of the Charged n-Particle: Definition (Jan 24, 2007)
- Turning a classical parallel transport functor on target space into a quantum propagation functor on parameter space.
- Cocycle Category (Jan 24, 2007)
- Bruce Bartlett reports on Rick Jardine’s concept of ‘cocycle categories’ and their relation to anafunctors.
- Fusion and String Field Star Product (Jan 21, 2007)
- A description of the string field star product and of fusion of loop group representations from the point of view of functorial transport.
- D-Branes from Tin Cans, III: Homs of Homs (Jan 18, 2007)
- Sections of sections, their pairing and n-disk correlators.
- Towards the FFRS Description of 2dCFT (A) (Jan 16, 2007)
- 2-dimensional cobordisms, topological quantum field theory and Frobenius algebras
- Aaronson on the Nature of Quantum Mechanics (Jan 16, 2007)
- Scott Aaronson on the nature of quantum mechanics.
- Khovanov Homology (Jan 14, 2007)
- Khovanov homology and its generalization from links to tangles.
- The First Part of the Story of Quantizing by Pushing to a Point... (Jan 13, 2007)
- Taking sections of transport functors by pushing them to a point.
- FFRS on Uniqueness of CFT: Sewing as Natural Transformation (Jan 4, 2007)
- On FFRS’s formulation of sewing constraints in terms of natural transformations.
- FFRS on Uniqueness of CFT: Morphisms into Transport Functors (Jan 3, 2007)
- On morphisms into functors and states and sections in the FFRS description of conformal field theory.
- FFRS on Uniqueness of Conformal Field Theory (Jan 3, 2007)
- A strengthening of the FFRS theorem on 2-dimensional rational conformal field theory.
- Conference: Lie Algebroids and Lie Groupoids in Differential Geometry (Dec 21, 2006)
- Conference in Sheffield on Lie algebroids and Lie groupoids in Differential Geometry
- A Little Bit of Geometric Langlands: Relation to Integrable Systems (Dec 21, 2006)
- On Hitchin integrable systems and their role in geometric Langlands duality.
- Excellent Math in Bonn: Opening Colloquium in January (Dec 20, 2006)
- Opening colloquium of the new “cluster of excellence” of mathematics in Bonn.
- Research Blogging (Dec 20, 2006)
- On research blogging.
- Universal Gerbes (Dec 18, 2006)
- What is known about universal gerbes?
- Frobenius Algebroids with Invertible Products (Dec 15, 2006)
- Thinking of algebroids with invertible products as Frobenius algebroids.
- Communicating Thoughts on the Web (Dec 13, 2006)
- Thinking, communicating and having math on the web.
- Navigating Geometric Langlands by Analogies (Dec 12, 2006)
- Some basic analogies that help us navigate the geometric Langlands duality.
- Local Transition of Transport, Anafunctors and Descent of n-Functors (Dec 8, 2006)
- Concepts and examples of what would be called transition data or descent data for n-functors.
- Talks at "Higher Categories and their Applications" (Dec 5, 2006)
- Talks on 2-functorial TFT and CFT.
- Postdoctoral Position at the Interface of Algebra, Conformal Field Theory and String Theory (Dec 5, 2006)
- Postdoc position in algebra, CFT and strings.
- What Does the Classifying Space of a 2-Category Classify? (Dec 4, 2006)
- Notes by Baas, Boekstedt and Kro on classifying spaces for 2-vector bundles.
- Nicolai on E10 and Supergravity (Nov 29, 2006)
- H. Nicolai on further progress in checking the hypothesis that the dynamics of supergravity is encoded in geodesic motion on a Kac-Moody group coset.
- D-Branes from Tin Cans, II (Nov 28, 2006)
- Gerbe modules from 2-sections.
- 2-Monoid of Observables on String-G (Nov 24, 2006)
- Rep(L G) from 2-sections.
- The Baby Version of Freed-Hopkins-Teleman (Nov 23, 2006)
- The Freed-Hopkins-Teleman result and its baby version for finite groups, as explained by Simon Willerton.
- The 1-Dimensional 3-Vector Space (Nov 23, 2006)
- Alg(C) as the 3-category of canonical 1-dimensional 3-vector spaces.
- Basic Question on Homs in 2-Cat (Nov 21, 2006)
- A basic question on internal homs in 2-categories.
- Derived Categories in Utah (Nov 20, 2006)
- A workshop on derived categories and their application in string theory.
- Categorical Trace and Sections of 2-Transport (Nov 17, 2006)
- A general concept of extended QFT and its relation to the Kapranov-Ganter 2-character.
- Flat Sections and Twisted Groupoid Reps (Nov 8, 2006)
- A comment on Willerton’s explanation of twisted groupoid reps in terms of flat sections of n-bundles.
- Chern-Simons Lie-3-Algebra Inside Derivations of String Lie-2-Algebra (Nov 7, 2006)
- The Chern-Simons Lie 3-algebra sits inside that of inner derivations of the string Lie 2-algebra.
- Dijkgraaf-Witten Theory and its Structure 3-Group (Nov 6, 2006)
- The idea of Dijkgraaf-Witten theory and its reformulation in terms of parallel volume transport with respect to a structure 3-group.
- A 3-Category of Twisted Bimodules (Nov 3, 2006)
- A 3-category of twisted bimodules.
- Bakovic on 2-Groupoid 2-Torsors (Oct 31, 2006)
- Igor Bakovic defines and classifies categorified groupoid bundles.
- Markl on Natural Differential Operators (Oct 31, 2006)
- M. Markl explains how to think about “naturality” of differential operators.
- WZW as Transition 1-Gerbe of Chern-Simons 2-Gerbe (Oct 29, 2006)
- How the WZW 1-gerbe arises as the transition 1-gerbe of the Chern-Simons 2-gerbe.
- Hopkins Lecture on TFT: Chern-Simons (Oct 27, 2006)
- Basic and advanced concepts in Chern-Simons theory.
- Hopkins Lecture on TFT: Infinity-Category Definition (Oct 25, 2006)
- A suggestion for a definition of (extended) TFT in terms of morphisms of omega-categories.
- Hopkins Lecture on TFT: Introduction and Outlook (Oct 25, 2006)
- Introductory lecture by M. Hopkins on topological field theory.
- Algebras as 2-Categories and its Effect on Algebraic Geometry (Oct 19, 2006)
- A question by Bruce Bartlett about categories of algebras, algebras as categories and the possible implications for non-commutative algebraic geometry.
- Topology in Trondheim and Kro, Baas & Bökstedt on 2-Vector Bundles (Oct 18, 2006)
- Baas, Dundas and Kro with new insights into 2-vector bundles.
- D-Branes from Tin Cans: Arrow Theory of Disks (Oct 18, 2006)
- On disk holonomy and boundary conditions.
- Adjunctions and String Composition (Oct 16, 2006)
- A remark on describing string composition and string field products in terms of adjunctions in categories of paths.
- Bundle Gerbes: Connections and Surface Transport (Oct 13, 2006)
- Definition of connection on a bundle gerbe and of the surface transport computed from it.
- Bundle Gerbes: General Idea and Definition (Oct 13, 2006)
- The general idea of bundle gerbes and the basic definition.
- What is the Categorified Gelfand-Naimark Theorem? (Oct 11, 2006)
- A lightning review of the categorified Gelfand-Naimark theorem.
- Talks by Hopkins and Willerton (Oct 10, 2006)
- Talk by Hopkins of TFT and by Willerton on Dijkgraaf-Witten.
- Kosmann-Schwarzbach & Weinstein on Lie Algebroid Classes (Oct 10, 2006)
- Kosmann-Schwarzbach on classes of Lie algebroids generalizing the character of a Lie algebra.
- On n-Transport: Descent of the Universal Transition (Oct 9, 2006)
- How the universal transition mediates descent from a surjection down to the original space.
- On n-Transport: Universal Transition (Oct 6, 2006)
- Paths in categories from universal transitions.
- Puzzle Pieces Falling Into Place (Sep 28, 2006)
- On the 3-group which should be underlying Chern-Simons theory.
- 2-Groups and Algebras (Sep 28, 2006)
- Bundles of algebras from principal 2-group transitions.
- Bulk Fields and Induced Bimodules (Sep 27, 2006)
- Bulk field insertions in 2D CFT in terms of 2-transport: endomorphisms of 2-monoids.
- Fahrenberg and Raussen on Continuous Paths (Sep 26, 2006)
- A theory of continuous n-paths modulo continuous reparameterization.
- Differential n-Geometry (Sep 20, 2006)
- A quest for arrow-theoretic differential geometry.
- Quantum n-Transport (Sep 14, 2006)
- An attempt to understand the path integral for an n-dimensional field theory as a coproduct operation over transport n-functors.
- Freed on Higher Structures in QFT, I (Sep 12, 2006)
- Freed’s old observation that n-dimensional QFT assigns (n-d)-Hilbert spaces to d-dimensional volumes.
- Wirth and Stasheff on Homotopy Transition Cocycles (Sep 11, 2006)
- Stasheff recalls an old result by Wirth on passing between fibrations and their homotopy transition cocycles.
- Kock on 1-Transport (Sep 8, 2006)
- A new preprint by Anders Kock on the synthetic formulation of the notion of parallel transport.
- Connes on Spectral Geometry of the Standard Model, IV (Sep 8, 2006)
- The details of the spectral triple which describes the standard model.
- Connes on Spectral Geometry of the Standard Model, III (Sep 7, 2006)
- First technical details for spectral action theory.
- On n-Transport: 2-Vector Transport and Line Bundle Gerbes (Sep 7, 2006)
- Associated 2-transport, 2-representations and bundle gerbes with connection.
- Connes on Spectral Geometry of the Standard Model, II (Sep 6, 2006)
- On the nature and implication of Connes’ identification of the spectral triple of the standard model coupled to gravity.
- Connes on Spectral Geometry of the Standard Model, I (Sep 6, 2006)
- Connes is getting closer to the spectral triple encoding the standard model coupled to gravity. Part I: some background material.
- n-Transport and Higher Schreier Theory (Sep 5, 2006)
- Understanding n-transport in terms of Schreier theory for groupoids.
- 10D SuGra 2-Connection (Aug 28, 2006)
- On the Lie 2-algebra governing 10-dimensional supergravity.
- Picturing Morphisms of 3-Functors (Aug 25, 2006)
- Diagrams governing morphisms of 3-functors.
- n-Curvature (Aug 21, 2006)
- Definition of n-curvature and the nature of “fake curvature”.
- On n-Transport, Part II (Aug 21, 2006)
- Smooth transport, differentials of transport, and nonabelian differential cocycles.
- On n-Transport, Part I (Aug 18, 2006)
- The concept of n-transport and its local trivialization and transition.
- SuGra 3-Connection Reloaded (Aug 17, 2006)
- Discussion of n-category description of supergravity continued.

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