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6 Mar 2023: Logarithmic Gromov-Witten theory defines the notion of a logarithmic stable mapto such targets X B; more generally, this morphism just needs to be toroidal ratherthan normal crossings, i.e., log ... The type of such a family consistsof the data τ := (G,

24 Oct 2023: Vn such that V ' V1 Vn. Theorem 4.12. Suppose that G is finite and |G| 6= 0 in F. ... central character, such that z v = λ(z) v forall z Z(G) and v V.

23 Jan 2023: Suppose there exists a class [b] B(G,{µ}) such that ν[b] = µ(such a class is necessarily unique if it exists by the above remark). ... When G is quasi-split,this class is just [b]µ. However if G is not quasi-split, there may be no [b] B(G,{µ})such

24 Nov 2023: Let a,b K such that the polynomials f = Xm a, g = Xm b are irreducible. ... Use asuitable Lagrange resolvent to find a Q(ζ3) such that K = Q(ζ3, 3.

7 Feb 2023: b) We say that a measurable 𝑓 : R𝑛 C is in weak-𝐿𝑝(R𝑛), written 𝑓 𝐿𝑝,𝑤 (R𝑛) if there exists aconstant 𝐶 such that. |{ ... Deduce 𝑁𝑖=1. 𝐵𝑖. 6 3𝑛 𝑘︁𝑗=1. 𝐵𝑖𝑗. b) () Suppose {𝐵 𝑗 : 𝑗

27 Nov 2023: X̃1, that is, β̃1 = (X̃T1 X̃1). 1X̃T1 Ỹ. (c) Find a condition on X0 and X1 such that β̃0 = β̂0. ... b) The model is to be reparametrised in such a way that it can be specialised to (i) two parallellines for the two groups, (ii) two lines with

10 Feb 2023: g :(D2,S1. ) (M,B). such that[g|S1. ]6 N. We first explain why the Loop Theorem implies Dehn’s Lemma:. ... g :(D2,S1. ) (M,B). such that[g|S1. ]6= 1. Set c =. [g|S1. ] π1B, and write c = ka b, with. k, Z.

25 Nov 2023: Let θ : A B be a -homomorphism from a Banach -algebra A to a C-algebraB. ... H) such thatz(T) = T, where z(λ) = λ for all λ K.

9 Nov 2023: SC =2π. κ. C. [Q[ξ] ξ BH]. However, it is not possible for θ to be of the form of a totalvariation δBH on H in general because such a ... M =. [Q[t] t B]. and there is no difficulty in obtaining an M that satisfies thedesired relation.

5 Oct 2023: Theleast such n is called the order of g.). (b) Show from first principles that there is a positive integer N such that gN = e for all g G. ... 9. Let H and G be groups and let X G such that 〈X〉 = G.

13 Mar 2023: E,E′) such that Hom(π,π′)s = IdX gives for each x X. ... Choose vectors en1,. ,eN FN such that. s1(x),. ,sn(x),en1,. ,eN FN.

1 Feb 2023: problem. To describe such a problem, let (M,g) be a compact Rieman-. ... function on R2 such that |x|kf L(R2) for any k 0.