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3 Feb 2006: f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C. ... 1 < |z| < 2}, {0 < |z| < 1}, {0 < |z| < }. 8. (i) Let R and S be some Riemann surfaces, f : R S a continuous map, and p a pointin R.

10 Oct 2006: n}.How large can we make a family A of subsets of [n] subject to thecondition that for all A, A′ A, there is some B B with B A A′? ... n}.How large can we make a family A of subsets of [n] subject to thecondition that for all A, A′ A, there is some

8 Oct 2006: GEOMETRY AND GROUPS. These notes are to remind you of the results from earlier courses that we will need at some pointin this course. ... d(xn, ) 0 as n. A subsequence of the sequence (xn) is given by taking only some of the terms in the sequence.

13 Oct 2006: ON SOME -ADIC REPRESENTATIONS OF Gal(Q/Q)ATTACHED TO NONCONGRUENCE SUBGROUPS. A. J. ... Therefore for some a, b Z, azHT b is asemisimple element of g with exactly 2 eigenvalues.

10 May 2006: Earlierproofs of Theorem B for some geodesic and magnetic flows using Fourier analysis canbe found in [12, 18]. ... Systems. 4 (1984) 67–80.[12] V. Guillemin, D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds,.

13 May 2006: for some a b. If a > b then the first binary quartic has singularreduction above (x : z) = (0 : 1). ... ]for some a b c. If b > c then the first ternary cubic has singularreduction at (x : y : z) = (0 : 0 : 1).

21 Oct 2006: f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C. ... 1 < |z| < 2}, {0 < |z| < 1}, {0 < |z| < }. 8. (i) Let R and S be some Riemann surfaces, f : R S a continuous map, and p a pointin R.

22 Oct 2006: The proof has three stages. First, we briefly review some facts about quasirandom. ... As promised, let us briefly review some of the standard theory of quasirandomness,.

20 Nov 2006: The trouble is that we donot know if v consists entirely of a’s, or entirely of b’s, or of some a’s followed bysome b’s. ... Because w is minimalwith this bad property we know that u belongs to (b|ab)n for some n.

8 Nov 2006: J : z 7 az bcz d. for some complex numbers a, b, c, d with ad bc = 1. ... For which choices of a, b, c, d is this map J aninvolution, that is J 2 = I?