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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 21st 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a quote > _only poetry and mathematics are capable of speaking meaningfully about such things_ _Mathematics as Metaphor_: Selected Essays of Yuri I. Manin (ed. 2007) ([libquotes](https://libquotes.com/yuri-manin/quote/lbj0h0e)) <a href="https://ncatlab.org/nlab/revision/diff/Yuri+Manin/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/Yuri+Manin/12">v12</a>, <a href="https://ncatlab.org/nlab/show/Yuri+Manin">current</a>

   added a quote

   only poetry and mathematics are capable of speaking meaningfully about such things

   Mathematics as Metaphor: Selected Essays of Yuri I. Manin (ed. 2007) (libquotes)

   diff, v12, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added pointer to the [MPI obituary](https://www.mpim-bonn.mpg.de/node/11864). <a href="https://ncatlab.org/nlab/revision/diff/Yuri+Manin/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Yuri+Manin/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Yuri+Manin">current</a>

   have added pointer to the MPI obituary.

   diff, v16, current

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2023
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIntroduced [[quantum linear group]]s as universal coacting bialgebras (and their quotient Hopf algebras) in * [[Yu. I. Manin]], _Quantum groups and non-commutative geometry_, CRM, Montreal 1988. <a href="https://ncatlab.org/nlab/revision/diff/Yuri+Manin/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/Yuri+Manin/19">v19</a>, <a href="https://ncatlab.org/nlab/show/Yuri+Manin">current</a>

   Introduced quantum linear groups as universal coacting bialgebras (and their quotient Hopf algebras) in

   • Yu. I. Manin, Quantum groups and non-commutative geometry, CRM, Montreal 1988.

   diff, v19, current

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 15th 2023
   • PermaLink
   Author: zskoda
   Format: MarkdownItexOn [[quantum cohomology]] and [[Gromov-Witten invariants]] * [[Maxim Kontsevich]], [[Yuri Manin]], _Gromov-Witten classes, quantum cohomology, and enumerative geometry_, Commun. Math. Physics __164__ (1994) 525-562 [doi](https://doi.org/10.1007/BF02101490) arXiv:[hep-th/9402147](https://arxiv.org/pdf/hep-th/9402147) * [[Yuri Manin]], _Frobenius manifolds, quantum cohomology, and moduli spaces_, Amer. Math. Soc. Colloqium Publications __47__, 1999 * [[Maxim Kontsevich]], [[Yuri Manin]], [[Ralph Kaufmann]], _Quantum cohomology of a product_, Invent. Math. __124__ (1996) 313-339 [doi](https://doi.org/10.1007/s002220050055) arXiv:[q-alg/9502009](https://arxiv.org/abs/q-alg/9502009) <a href="https://ncatlab.org/nlab/revision/diff/Yuri+Manin/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/Yuri+Manin/21">v21</a>, <a href="https://ncatlab.org/nlab/show/Yuri+Manin">current</a>

   On quantum cohomology and Gromov-Witten invariants

   • Maxim Kontsevich, Yuri Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Commun. Math. Physics 164 (1994) 525-562 doi arXiv:hep-th/9402147

   • Yuri Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Amer. Math. Soc. Colloqium Publications 47, 1999

   • Maxim Kontsevich, Yuri Manin, Ralph Kaufmann, Quantum cohomology of a product, Invent. Math. 124 (1996) 313-339 doi arXiv:q-alg/9502009

   diff, v21, current