Math 7310 Fall 2010: Introduction to Geometric Representation Theory

Advanced Topics in Discrete Math : Graph Theory Fall 2010

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

Quantum Computing - From Linear Algebra to Physical Realizations

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On Third Geometric-Arithmetic Index of Graphs

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric−arithmetic index of graphs, Iran. J. Math Chem., 1 (2010) 17−27, in this paper we present lower and upper bounds on the third geometric−arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus−Gaddum−type result for GA3.

F2015 Topics Perverse Sheaves and Fundamental Lemmas

[1] A. Arabia, Faisceaux pervers sur les varie?te?s alge?briques complexes. Correspondance de Springer, [2] A. Arabia, Introduction a‘ l?homologie d?intersection [3] A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, in: Analyse et topologie sur les espaces singuliers, Aste?risque 100, 1982. [4] A. Borel et. al., Intersection Cohomology, Birka?user Progress in Math. 50, 1984, SB 2083. [...