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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

2 votes
Accepted

Reference request: SGA7

Maybe the following book will be helpful: http://www.springer.com/birkhauser/mathematics/book/978-3-7643-7535-5 (The Monodromy Group, by Henryk Zoladek).
5 votes

Physicist trying to understand modern mathematics

On this website http://www.theorie.physik.uni-muenchen.de/activities/schools/archiv/2011_asc_school/index.html there are videos of the lectures given at the 2011 Arnold Sommerfeld PhD School ''Algebra …
Zurab Silagadze's user avatar
1 vote

Reference request for the relation of Ext groups and bar construction

Maybe the following lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991, will be useful: http://www.ams.org/bookstore-getitem/item=pspum-55.s
Zurab Silagadze's user avatar
6 votes

Schubert calculus, as lowbrow as possible

Although this is certainly a too late answer on this question, maybe this paper http://arxiv.org/abs/math/0608784 (Schubert Calculus according to Schubert, by Felice Ronga) is worth to be mentioned. I …
Zurab Silagadze's user avatar
10 votes
2 answers
1k views

Kummer's quartic surface and the Dirac operator

(source) The picture shows 1936 photograph by Man Ray of a Kummer surface plaster model in the collection of the Institute Henri Poincaré (from Mathematics, Art and Science of the Pseudosphere by K …
Zurab Silagadze's user avatar
6 votes

Yang-Mills equations are not elliptic

In fact Yang-Mills equations are elliptic modulo gauge transformations. In simple terms this can be explained as follows (credit: Jonathan Evans, http://www.homepages.ucl.ac.uk/~ucahjde/yangmills.htm) …
Zurab Silagadze's user avatar
13 votes

Algebra and cancer research

Here are some examples: http://arxiv.org/abs/1004.1341 (Algebraic Comparison of Partial Lists in Bioinformatics) http://arxiv.org/abs/1303.5569 (An algebraic framework to sample the rearrangement hi …
Zurab Silagadze's user avatar
2 votes

Why can the general quintic be transformed to $v^5-5\beta v^3+10\beta^2v-\beta^2 = 0$?

Geometry behind the Brioschi quintic is explained in Jerry Shurman book "Geometry of the Quintic" (available from his website http://people.reed.edu/~jerry/ ). However, it seems no explanation of (2) …
Zurab Silagadze's user avatar
10 votes

H. Cartan's "Variétés analytiques complexes et cohomologie"?

In addition to the Myshkin's answer. An electronic version of the paper can be found here: http://www.inp.nsk.su/~silagadz/Cartan.pdf
Zurab Silagadze's user avatar