- Arun Ram: Notes
- Lectures In Geometry: Linear Algebra And Differential Geometry (semester Ii)
- Journal of Geometry and Symmetry in Physics
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The exercises of the non-graded sheets will be used during the final exam, the first question of every exam will be taken from there. We will communicate the date of the final exam as soon as possible. The oral exam will be half an hour long for every student, and the first question of every exam will be an exercise from the non-graded exercise sheets.

The final exam will be in English. In this lecture course we will discuss symmetric and locally symmetric spaces.

## Arun Ram: Notes

Symmetric spaces are Riemannian manifolds in which the geodesic symmetry, at any point, is induced by an isometry. In particular the group of isometries acts transitively on the space. We will study the Riemannian geometry of symmetric spaces as well as their connection to the theory of semisimple Lie groups. An outline of the material covered in the lecture is the following:.

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This course is aimed at students who are interested in differential geometry. Students are expected to have a certain familiarity with Riemannian geometry, ideally they have followed Differential Geometry I or a similar course. The course will be taught in English. Contact JProf. Beatrice Pozzetti Dr. Beatrice Pozzetti tba INF , Iberoamericana, Rev. Iberoamericana, Madrid, , 87— Cayley degrees of simple algebraic groups.

Faddeev St. Petersburg, September 24—29, , St. Petersburg State University, St.

Petersburg Department of the V. Losik, P. Michor, V. Lecture Notes, 35 , Amer. A'Campo, V. Popov ed. Carrell, W. McGovern, Algebraic quotients. Torus actions and cohomology.

News in Foreign Science, 50 , Mir, Moscow, Katsylo, V. Popov, Generators and relations of the affine coordinate rings of connected semisimple algebraic groups , preprint ESI, no. Cox, J.

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Little, D. O'Shea, Ideals, Varieties, and Algorithms. Popov, Mir, Moscow, , 6. Sukhotsky, Analytic Geometry. Hilbert, Selected Works , Factorial Publ. Einh"ullende Algebren und Darstellungstheorie. Alekseevskii, V. Bugaenko, G. Olshanskii, V. Popov, O. Algebra , :3 , — Popov, Predislovie k russkomu perevodu knigi: V. Kats, Beskonechnomernye algebry Li , eds. Popov, Mir, M. Conference commemorating A.

### Lectures In Geometry: Linear Algebra And Differential Geometry (semester Ii)

Mal'cev Novosibirsk , Math. Branch Acad. Sovet Filos. USSR, Moscow, , Popov, Editor's preface to the Russian translation of the book: H. Kraft, Geometrische Methoden in der Invariantentheorie , eds.

### Journal of Geometry and Symmetry in Physics

Popov, Mir, Moscow, , 5—7. Kraft, V. Weyl, Selected Works , Nauka, Moscow, , —; — Reine Angew. Sci, , — Grigor'ev, V. Popov, D. France, Paris, , — News in Foreign Science, 24 , eds. Popov, Mir, Moscow, , — Popov, Preface to the Russian translation of: T. Springer, Invariant theory , Mir, Moscow, , 5—8. Nauk , 32 :1 , — A-B , , A—A Vinberg, V. Andreev, V. Istitute Mold. Simple algebras and invariants of linear actions V. Algebraic group actions and Zariski's cancellation problem V. Jordan groups V. On the canonical form of one-parameter groups of rational transformations V.

Around Zariski cancellation problem V. Algebraic structure of the Cremona groups and other automorphism groups V. Compressing finite subgroups of Cremona groups Vladimir Popov Workshop on birational geometry October 30, Affine algebraic groups and Cremona groups V. Cremona groups vs. Variations on the theme of Zariski's Cancellation Problem V.

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Discrete groups generated by complex reflections. Lecture 3 V. Popov Sixth school-conference on algebraic geometry and complex analysis for young russian mathematicians August 26, Lecture 2 V. Popov Sixth school-conference on algebraic geometry and complex analysis for young russian mathematicians August 25, Lecture 1 V.

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What are the equations defining linear algebraic groups? Popov "Algebra, algebraic geometry, and number theory". Memorial conference for academician Igor Rostislavovich Shafarevich June 5, On Borel subgroups in the Cremona groups V. Around the Bass' Triangulability Problem V. Triangulable subgroups of the Cremona groups V. Popov International conference on algebraic geometry, complex analysis and computer algebra August 7, Coordinate algebras of connected affine algebraic groups: generators and relations V.

On the equations defining affine algebraic groups V. Popov The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics May 14, The equations defining algebraic groups V. Popov Talk delivered at the Chebyshev Laboratory, St. Petersburg State University December 24, Simple algebras and algebraic groups V. Popov September 16, Bass' problem on triangulable subgroups of the Cremona group V.

Popov May 22, Invariant Theory V. Popov May 21, Algebraic subgroups of the Cremona groups V. About Grothendieck V. Popov General Mathematics Seminar of the St. Closures of orbits V. Popov St. Orbit closures of algebraic group actions V. Orbit closures V. Infinite dimensional automorphism groups of algebraic varieties, multiple transitivity, and unirationality V.

Popov July 17, Popov July 10, Automorphism groups of algebraic varieties V.

Quotients by conjugation action, cross-sections, singularities, and representation rings V. Popov January 20, Grothendieck's questions on conjugating actions of semisimple groups V.