# The Hedgehog Fund

Established: October 2010
Founder and CEO: Oleg Pikhurko
Hedgehog Consultant: Oksana Trushkevych
PR Officer: John Mackey

## Hedgehog Awards

The Fund makes awards, of various size and prickliness, for finding a substantially nicer or simpler proof of any result that I present during my lectures. The proof need not be new (eg it may come from a book or another course). But it has to be more "interesting" than the one I presented in the class, and/or introduce a novel point of view, etc (so that next time I lecture on this material, I'll present it differently).

Nominations can be made any time, ideally as soon as possible, so that I can present the new hedgehog-approved proof immediately in the same course.
-OP

Note to Instructors: We do franchise the Hedgehog Fund, subject to preserving the spirit of the Hedgehog Awards and including a link to the original webpage of the fund  (http://homepages.warwick.ac.uk/~maskat/hedgehog/).

## Laureats (chronologically)

• Jonathan Adams
• Alex Woolf
• Sang Tian
• Hui Han Chin
• Tim Wilson
• Sam McCardal-Kilby
• Kamel Alchikh Kasem

## Why Hedgehogs?

Thoughtful and careful, hedgehogs have made essential contributions to various areas of mathematics and mathematical physics. Here are some highlights. (See also some hedgehog-inspired creativity by students.)

 MR1088326 (92c:83013) Williams, J. G. Combed hedgehog kink metric in (2+1) $(2+1)$ dimensions. Gen. Relativity Gravitation 23 (1991), no. 2, 181–187. Also, the famous theorem of Poincare from 1885 states that it is impossible to comb a hedgehog. Unfortunately, to the great annoyance of hedgehogs, this prominent result became known under the vulgar name of the Hairy Ball Theorem (uffa!...) so it does not qualify. Pat Cladis, Liquid Crystals and the Drunken Hedgehog, Physics World, 5 (1992) 22. Apparently, the LC monitor you are probably looking at right now can be a home to a whole universe of hedgehogs:  Hedgehogs Radial and Hyperbolic and less orderly Metastable and Drunken ones... :-) MR1218832 (93m:83075) Guendelman, E. I.; Rabinowitz, A. I. Hedgehog compactification. Phys. Rev. D (3) 47 (1993), no. 8, 3474–3475, MR1696588 (2000d:54033) Simon, Petr A hedgehog in a product. Acta Univ. Carolin. Math. Phys. 39 (1998), no. 1-2, 147–153. MR1922133 (2003i:54004) Simon, Petr; Tironi, Gino No hedgehog in the product? Comment. Math. Univ. Carolin. 43 (2002), no. 2, 349–361. And no product left! :-P MR2003552 Cladis, P. E.; Brand, Helmut R. Hedgehog-antihedgehog pair annihilation to a static soliton. Phys. A 326 (2003), no. 3-4, 322–332. MR2039432 (2004k:83019) Delice, Ozgur Gravitational hedgehog, stringy hedgehog and stringy sphere. J. High Energy Phys. 2003, no. 11, 058, 11 pp. MR2242680 (2007b:81147) Belavin, V. A.; Chernodub, M. N.; Kozlov, I. E. Hedgehogs in Wilson loops and phase transition in SU(2) ${\rm SU}(2$ Yang-Mills theory. Nuclear Phys. B 748 (2006), no. 3, 524–539. MR2443582 (2009j:83050) Headrick, Matthew Hedgehog black holes and the Polyakov loop at strong coupling. Phys. Rev. D 77 (2008), no. 10, 105017, 13 pp. MR2477418 (2010b:37136) Childers, Douglas K. Are there critical points on the boundaries of mother hedgehogs? Holomorphic dynamics and renormalization, 75–87, Fields Inst. Commun., 53, Amer. Math. Soc., Providence, RI, 2008. MR2465597 (2010e:37061) Biswas, Kingshook Hedgehogs of Hausdorff dimension one. Ergodic Theory Dynam. Systems 28 (2008), no. 6, 1713–1727. Hyperbolic hedgehog steers active droplets in a liquid crystal, a intriguingly titled review in Physics World of this paper in Nature. The recent discovery was warmly received by the hedgehog community: David Conlon, Jacob Fox and Vojtech Rodl Hedgehogs are not colour blind, Journal of Combinatorics 8 (2017) 475 - 485