New PDF release: Algebraic Geometry and Number Theory: In Honor of Vladimir

By Alex Eskin, Andrei Okounkov (auth.), Victor Ginzburg (eds.)

ISBN-10: 0817644717

ISBN-13: 9780817644710

ISBN-10: 0817645322

ISBN-13: 9780817645328

One of the main artistic mathematicians of our occasions, Vladimir Drinfeld got the Fields Medal in 1990 for his groundbreaking contributions to the Langlands software and to the idea of quantum groups.

These ten unique articles via famous mathematicians, devoted to Drinfeld at the social gathering of his fiftieth birthday, extensively mirror the variety of Drinfeld's personal pursuits in algebra, algebraic geometry, and quantity theory.

Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman.

Show description

Read or Download Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld’s 50th Birthday PDF

Similar geometry and topology books

Sharipov R.A.'s Course of Linear Algebra and Multidimensional Geometry PDF

This e-book is written as a textbook for the process multidimensional geometryand linear algebra. At Mathematical division of Bashkir country college thiscourse is taught to the 1st 12 months scholars within the Spring semester. it's a half ofthe uncomplicated mathematical schooling. consequently, this direction is taught at actual andMathematical Departments in all Universities of Russia.

New PDF release: The Penguin dictionary of curious and interesting geometry

A significant other quantity to the author's "Dictionary of Curious and engaging Numbers", which makes a speciality of mathematics and quantity idea. The entries during this ebook disguise curves, topology, tilings and all branches of aircraft and third-dimensional geometry, from Euclid to fractals.

Additional info for Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld’s 50th Birthday

Sample text

Let µk be the kth letter of D and let sgn(k) be +1 if µk ∈ and −1 otherwise. Let finally |µk | = sgn(µk )µk ∈ . 3. Let D be a word of W; then • • the multipliers are given by the rule d(αi ) (D) = d α ; the integers ε(α )(β ) are defined by the formula i j ε(α )(β ) β j i (αi )(j ) = 1 2 ∂ ∂ ∧ ∂ log xiα ∂ log x β j l(D) sgn(µk )Cµ(k)α k=1 α ⎛ ∧⎝ ∂ |µ | ∂ log xn|µkk | (k)−1 − ∂ ∂ log xnαα (k) ∂ |µ | ∂ log xn|µkk | (k) ⎞ ⎠. 42 V. V. Fock and A. B. Goncharov Remark. One can check that in the case when D is reduced, our function εij is related to the cluster function bij defined in [BFZ3] for the corresponding double Bruhat cell as follows.

4) We would like to stress that the multiplication m is a projection with fibers of nonzero dimension. 6 Cluster X -varieties related to the Hecke semigroup Let π : B → H be the canonical projection of semigroups. Considered as a projection of sets it has a canonical splitting s : H → B. Namely, for every H ∈ H there is a unique reduced element s(H ) in π −1 (H ), the reduced representative of H in B. So given an element H ∈ H there is a cluster variety Xs(H ) . Abusing notation, we will denote it by XH .

Let us elaborate on this point. 2 Amalgamation We introduce operations of amalgamation and defrosting of seeds. The amalgamation of a collection of seeds I(s), parametrised by a set S, is a new seed K = (K, K0 , εij , d). The set K is defined by gluing some of the frozen vertices of the sets I (s). The frozen subset K0 is obtained by gluing the frozen subsets I0 (s). The rest of the data of K is also inherited from those of I(s). Defrosting simply shrinks the subset of the frozen vertices of K, without changing the set K.

Download PDF sample

Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld’s 50th Birthday by Alex Eskin, Andrei Okounkov (auth.), Victor Ginzburg (eds.)


by John
4.0

Rated 4.24 of 5 – based on 14 votes