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28 Nov 2012: Theorem 1.20. If the smooth map f : X Y is transversal to a submanifoldZ Y , then f1(Z) is submanifold of X. ... Definition 2.20. The determinant of dNp is the Gaussian curvature K(p) ofS at p.

27 Nov 2012: 20. For Riemannian geometers, on the other hand, the objects of study are fromthe beginning Riemannian manifolds.

27 Nov 2012: Dodecahedron 20 3 60Icosahedron 12 5 60. These give finite groups of orientation preserving symmetries. ... Lecture 5 19. Lecture 5 20. 5.2 Regularity. The Platonic solids are the only regular, convex polyhedra.

26 Apr 2012: 1 20 1. ). defines a representation (check). The representation R2 breaks up as 〈e1〉 〈e1 e2〉 as subreps even though thematrix is upper triangular but not diagonal. ... χρ,χρ〉G = 1|G|. gG χρ(g)χρ(g) =|N||G|. gNG/N χρ(gN)χρ(gN) =

9 Nov 2012: Use these to reconstruct thecharacter table of S5. Then repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of S5 of order 20.

28 Nov 2012: 1 20 1. ). defines a representation (check). The representation R2 breaks up as 〈e1〉 〈e1 e2〉 as subreps even though thematrix is upper triangular but not diagonal. ... Lecture 9. Recall the character table of S3. Example. S3. 20 SIMON WADSLEY.

27 Nov 2012: 20. Let G be the graph obtained by subdividing a single edge of Kn,n by a new vertex.

2 Mar 2012: 20 is smooth ifchar(k) 6= 2, 3. Find the degree and ramification degrees for (i) the projection φ = (X0 : X1) : V P1 (ii) theprojectionφ = (X0 : X2) : V P1.

14 May 2012: arX. iv:1. 102. 2606. v3 [. mat. h.R. T]. 11. May. 201. 2. ON IRREDUCIBLE REPRESENTATIONS OF COMPACT p-ADIC. ANALYTIC GROUPS. KONSTANTIN ARDAKOV AND SIMON WADSLEY. Abstract. We prove that the canonical dimension of a coadmissible repre-sentation of

23 Jun 2012: 20) Suppose p 6= 2 is prime number. Choose a Z which is not a square and notdivisible by p.