Archive for January, 2011

IV.9 Representation Theory by Ian Grojnowski, Why Vector Spaces?: Page 423.

Monday, January 24th, 2011

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

Theorem: Let G be a finite group.  then the characters of the irreducible representations form an orthonormal basis of K-sub-G, the vector space of all complex valued functions on G that are constant functions on each conjugacy class.  This means the character table is square.

IV.9 Representation Theory by Ian Grojnowski, Why Vector Spaces?: Page 422.

Friday, January 21st, 2011

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

The analogy to Fourier transform decomposition.

Introduction to Nanoscience by S. M. Lindsay ISBN: 9780199544219

Thursday, January 20th, 2011

Read 1. What is Nanoscience?: Pages 5 – 15.

Completed reading chapter 1.

Reversible and Chemically Programmable Micelle Assembly with DNA Block-Copolymer Amphiphiles by Zhi Li, Yi Zhang, Paige Fullhart and Chad Mirkin, NANO Letters 2004, Vol. 4, No. 6, 1055 – 1058.

Thursday, January 20th, 2011

Discusses how to create Nano size objects which can be joined and separated by temperature.

IV.9 Representation Theory by Ian Grojnowski, Why Vector Spaces?: Page 421.

Thursday, January 20th, 2011

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

Definition: A representation of a group G on a vector space V is a homomorphism from G to GL(V).  GL(V) is the set of linear maps from V to V.

If G is the dihedral group D8 acting on the set X of ordered pairs of vertices of the square, of which there are 16, then there are three orbits of G on X.

Reading Introduction to Nanoscience by S. M. Lindsay ISBN: 9780199544219

Tuesday, January 18th, 2011

Read 1. What is Nanoscience? Pages 1 – 4.

Read Appendix B: There’s plenty of room at the bottom by Richard P. Feynman.

IV.8 Moduli Spaces by David. D. Ben-Zvi, Invariants from Moduli Spaces, Modular Forms and Further Reading, IV.9 Representation Theory by Ian Grojnowski, Introduction and Why Vector Spaces?: Pages 418 – 420.

Monday, January 17th, 2011

IV.8 Moduli Spaces by David. D. Ben-Zvi.

Invariants from moduli spaces.

Modular forms.

Further reading.

IV.9 Representation Theory by Ian Grojnowski.

Introduction.

Why vector spaces?

IV.8 Moduli Spaces by David. D. Ben-Zvi, Moduli Spaces and Jacobians, Further Directions and Deformations and Degenerations: Page 418.

Friday, January 14th, 2011

IV.8 Moduli Spaces by David. D. Ben-Zvi.

Moduli spaces and Jacobians.

Further directions.

Deformations and degenerations.

IV.8 Moduli Spaces by David. D. Ben-Zvi, Digression “Abstract Nonsense” and Moduli Spaces and Representations: Page 417.

Thursday, January 13th, 2011

Moduli Spaces by David. D. Ben-Zvi.

Digression “Abstract Nonsense”.

Moduli spaces and representations.

IV.8 Moduli Spaces by David. D. Ben-Zvi, From Teichmuller Spaces to Moduli Spaces, Higher-Genus Moduli Spaces and Teichmuller Spaces, and the Characteristic Property of Teichmuller g-Space: Pages 415 – 416.

Wednesday, January 12th, 2011

Moduli Spaces by David. D. Ben-Zvi.

From Teichmuller spaces to moduli spaces.

Higher-genus moduli spaces and Teichmuller spaces.

The characteristic property of Teichmuller g-space.