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22 Jan 2024: ρp(k,2k 1) =. aQp/(Qp)2P2k1(d(Q) = (1)ka,c(Q) = (1,a)k);. ρp(k,2k 2) = 1P2k2(d(Q) = (1)k1,c(Q) = 1). ... This gives four Qp-equivalence classes of forms, with invariants d(Q) = (1)ka andc(Q) = (1,a)k.

9 Nov 2023: cross-sections C1 and C2 yieldsκ. 2π[δSC2 δSC1 ] =. ξaδCa =. δTabξ. akbhdV dn2x. where ka is the tangent to the affinely parametrized generatorsof the horizon. ... Since. ka =1. κVξa. this is equivalent to. V2SvNV 2. 2πκ.

29 Sep 2008: jA : I [A,A],– eA : [I,A] A natural in A,– kA = kA,B,C : [B,C] [[A,B], [A,C]] natural in A, B and C,. ... 1. IjB - [B,B]. [[A,B], [A,B]]. kA? j[A. ,B] -. 2.

29 Jan 2010: FJ;KA_y3M,5GF¤/¥Ì :¿Í6{ @ 63A0Aa3Q:A638:WY8:WY8,O]L263JPK]WYK5¤M,C A0a3AK]5_OJPCAaM,KpH¢8:9P9;8>}'KG58:3KXJ;a3AGOsF63A0a3JPKXFJ;3Q:c3JPK]63AaF]OJ;M,3Q:9;A ... Æ Î Ñ E- Æ' 1 O Æ Î Ó m ÆßÈ@

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31 Jan 2024: Algebraic TopologyOscar Randal-Williams. https://www.dpmms.cam.ac.uk/or257/teaching/notes/at.pdf. 1 Introduction 11.1 Some recollections and conventions. 21.2 Cell complexes. 3. 2 Homotopy and the fundamental group 42.1 Homotopy. 42.2 Paths. 72.3

22 Nov 2010: Let t = a! and d = t. By Ramsey’s theorem, there exists a positive integer b such that whenever[b](t) is ka-coloured, there exists a monochromatic subset of order ... We next induce a ka-colouring c5 of [b](t) by colouring the set R [b](t).

6 Mar 2008: N QoKA][a@sGYbªicmFWGIyXjGIG» iyGIX2NpVWiTHjVsa>H2A{H2dYiyvH¢a>AvW]UHjVWGsGYbN?à ÌyCpá VWiTHjVsa>HuâRãä)å A]KWA{kA]jAgWbGhgzæT2VWGIvWGIcGYXFæ.A] x XjAtwGacvW.ç@è%é¡èæpFêÛmJëA]asGYbicmod¢VsacXjacdIHjGYXZA]ZHjAdKæ¡?BH_V4A]KtuG)a

15 Jun 2000: How to discover a proof of the fundamental theorem of arithmetic. The usual proof. Here is a brief sketch of the proof of the fundamental theorem of arithmetic that is most commonly presented in textbooks. 1. First one introduces Euclid's algorithm,

20 Dec 2023: GLOBAL SECTIONS OF EQUIVARIANT LINE BUNDLES ON. THE p-ADIC UPPER HALF PLANE. KONSTANTIN ARDAKOV AND SIMON WADSLEY. Abstract. Let F be a finite extension of Qp, let F be Drinfeld’s upper half-plane over F and let G0 the subgroup of GL2(F )