ar X iv : m at h / 06 07 06 1 v 2 [ m at h . A G ] 1 7 N ov 2 00 7 POISSON GEOMETRY OF PARABOLIC BUNDLES ON ELLIPTIC CURVES

ar X iv : m at h / 06 10 30 1 v 1 [ m at h . A G ] 9 O ct 2 00 6 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P

— In this paper, we give a completely algebraic description of Nahm transform for parabolic Higgs bundles on P. 2 KÜRŞAT AKER & SZILÁRD SZABÓ

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 06 02 50 8 v 2 [ m at h . G R ] 1 9 N ov 2 00 7 PRESENTATIONS OF FINITE SIMPLE GROUPS : A QUANTITATIVE APPROACH

There is a constant C 0 such that all nonabelian finite simple groups of rank n over Fq, with the possible exception of the Ree groups 2 G 2 (3 2e+1), have presentations with at most C 0 generators and relations and total length at most C 0 (log n + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dim H 2 (G, M) ≤ C dim M for every finite simple group G, e...

ar X iv : m at h / 06 11 62 6 v 1 [ m at h . C O ] 2 1 N ov 2 00 6 COUNTING LINKS IN COMPLETE GRAPHS

We find the minimal number of links in an embedding of any complete k-partite graph on 7 vertices (including K 7 , which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete k-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with min...