De Morgan Association Newsletter 2019/20 Contents

Letter from the Editor ...... 3 Letter from the Head of Department ...... 3 British Society Of Rheology Annual Award 2019 ...... 5 De Morgan Association Dinner ...... 6 What Biology Can Do For Maths ...... 8 4th Floor Opening ...... 14 ICDEA 2019 ...... 16 Inaugural Lecture – Professor Yiannis Petridis ...... 18 Susan Brown Day – International Women’s Day ...... 20 STEM for Britain ...... 22 April Colloquium 2019 ...... 24 Wikithon ...... 25 Thomas Harriot - England's leading mathematical scientist before Newton .... 26 Chalkdust ...... 30 Scaling, PDEs and Iceberg Melting ...... 32 Institute for Mathematical and Statistical Sciences (IMSS) Events 2019 ...... 38 The Michael Singers ...... 39 Awards ...... 40 Staff and Graduate Student Awards ...... 41 Undergraduate and MSc Prizes ...... 42 PhD Scholarships and Prizes ...... 43 PhD Awards ...... 44 New Academic Staff ...... 45 Alumni Careers ...... 47 In Memoriam - Professor Yaroslav Kurylev ...... 48

2 LETTERS FROM THE EDITOR AND THE HEAD OF DEPARTMENT

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^^Ăŵ,ŽƉŬŝŶƐŚĂƐŵŽǀĞĚƚŽĂŶŽƚŚĞƌĂŵ,ŽƉŬŝŶƐŚĂƐŵŽǀĞĚƚŽĂŶŽƚŚĞƌ h>ĞdžĂŵŝŶĂƟŽŶƐĂƌĞƵƐƵĂůůLJƌƵŶŝŶƚŚĞ ƌƌŽůĞŝŶƚŚĞĚĞƉĂƌƚŵĞŶƚĂŶĚƐŽǁĞŚĂǀĞŽůĞŝŶƚŚĞĚĞƉĂƌƚŵĞŶƚĂŶĚƐŽǁĞŚĂǀĞ džĞ>ĐĞŶƚƌĞŝŶĂƐƚ>ŽŶĚŽŶ͘dŚŝƐLJĞĂƌ͕ŽĨ uunfortunatelynfortunately onceonce againagain lostlost anan excellentexcellent ĐŽƵƌƐĞ͕ŝƚďĞĐĂŵĞE,^EŝŐŚƟŶŐĂůĞĂŶĚƐƉĞŶƚ ƐƐŽĐŝĂƚĞĚŝƚŽƌŽĨƚŚĞEĞǁƐůĞƩĞƌ͘ƐƐŽĐŝĂƚĞĚŝƚŽƌŽĨƚŚĞEĞǁƐůĞƩĞƌ͘ ƚŚĞƐƵŵŵĞƌďƵƐLJǁŝƚŚƐŽŵĞƚŚŝŶŐƌĂƚŚĞƌ ŵŽƌĞŝŵƉŽƌƚĂŶƚƚŚĂŶƵŶŝǀĞƌƐŝƚLJĞdžĂŵƐ͘KƵƌ KKƵƌŶĞǁƐƐŽĐŝĂƚĞĚŝƚŽƌŝƐĚƌŝĂŶŶĂƵƌŶĞǁƐƐŽĐŝĂƚĞĚŝƚŽƌŝƐĚƌŝĂŶŶĂ ƐƚĂīŚĂĚƚŽĚĞǀŝƐĞĂƐƐĞƐƐŵĞŶƚŵĞƚŚŽĚƐƚŚĂƚ DDŝĐŬŝĞǁŝĐnj͕ǁŚŽũŽŝŶĞĚƚŚĞĚĞƉĂƌƚŵĞŶƚŝŶŝĐŬŝĞǁŝĐnj͕ǁŚŽũŽŝŶĞĚƚŚĞĚĞƉĂƌƚŵĞŶƚŝŶ ĚŝĚŶ͛ƚƌĞƋƵŝƌĞƚŚĞƐƚƵĚĞŶƚƐƚŽďĞƉƌĞƐĞŶƚ͕ ϮϮϬϭϵ͘ĚƌŝĂŶŶĂŚĂƐƌĂƉŝĚůLJŵĂƐƚĞƌĞĚƚŚĞϬϭϵ͘ĚƌŝĂŶŶĂŚĂƐƌĂƉŝĚůLJŵĂƐƚĞƌĞĚƚŚĞ ĂŶĚƚŚĂƚĂůůŽǁĞĚƐƵŝƚĂďůLJĨŽƌƐƚƵĚĞŶƚƐŝŶ ďďƌŝĞĨĂŶĚĐŽŵƉĞƚĞŶƚůLJŐƵŝĚĞĚƚŚŝƐĞĚŝƟŽŶ͕ƌŝĞĨĂŶĚĐŽŵƉĞƚĞŶƚůLJŐƵŝĚĞĚƚŚŝƐĞĚŝƟŽŶ͕ ĚŝīĞƌĞŶƚƟŵĞnjŽŶĞƐ;ƐŝŶĐĞƐŽŵĂŶLJĐŽƵŶƚƌŝĞƐ ƐƐŵŽŽƚŚůLJĐŽƉŝŶŐǁŝƚŚƚŚĞĚŝƐƌƵƉƟŽŶĨƌŽŵƚŚĞŵŽŽƚŚůLJĐŽƉŝŶŐǁŝƚŚƚŚĞĚŝƐƌƵƉƟŽŶĨƌŽŵƚŚĞ ŚĂĚůŽĐŬĞĚĚŽǁŶŝŶƚĞƌŶĂƟŽŶĂůƚƌĂǀĞůͿĂŶĚ ŵŵŽǀĞƚŽƌĞŵŽƚĞǁŽƌŬŝŶŐ͘ŽǀĞƚŽƌĞŵŽƚĞǁŽƌŬŝŶŐ͘ ƚŚŽƐĞǁŝƚŚƌĞůĂƟǀĞůLJůŝŵŝƚĞĚŝŶƚĞƌŶĞƚĂĐĐĞƐƐ͘ tĞĐĂŵĞƵƉǁŝƚŚĂƐĞƚŽĨŶĞǁ͞ŽƉĞŶŬ͟ ttĞŚŽƉĞLJŽƵĞŶũŽLJŝƚ͕ĂŶĚĞŶĐŽƵƌĂŐĞLJŽƵƚŽĞŚŽƉĞLJŽƵĞŶũŽLJŝƚ͕ĂŶĚĞŶĐŽƵƌĂŐĞLJŽƵƚŽ ĂƐƐĞƐƐŵĞŶƚƐ͕ƐŽŵĞƚŽďĞƚĂŬĞŶŝŶϮϰŚŽƵƌƐ ƐƐĞŶĚƵƐĂƌƟĐůĞƐĂŶĚƉŚŽƚŽŐƌĂƉŚƐĨŽƌĨƵƚƵƌĞĞŶĚƵƐĂƌƟĐůĞƐĂŶĚƉŚŽƚŽŐƌĂƉŚƐĨŽƌĨƵƚƵƌĞ ĂŶĚŽƚŚĞƌƐĂǁĞĞŬŝŶĚƵƌĂƟŽŶ͕ĂůůƚŽďĞ ĞĞĚŝƟŽŶƐ͘ĚŝƟŽŶƐ͘ ƚĂŬĞŶƌĞŵŽƚĞůLJ͘tĞŚĂĚƚŽǁƌŝƚĞƋƵĞƐƟŽŶƐ ƚŚĂƚǁŽƵůĚƐƟůůĚŝƐƟŶŐƵŝƐŚĚŝīĞƌĞŶƚƐƚƵĚĞŶƚƐ //ƐƐƵĞϮϳƐƐƵĞϮϳ even though they had access to their notes, ::ƵůLJϮϬϮϬƵůLJϮϬϮϬ ĂŶĚƚĞdžƚŬƐ͕ǁŚŝůĞƐŽůǀŝŶŐƚŚĞŵʹĂŶĚ LJĞƚƌĞŵĂŝŶĨĂŝƌƐŽƚŚĂƚĂůůƐƚƵĚĞŶƚƐĐŽƵůĚ ĚŝƚŽƌ͗WƌŽĨĞƐƐŽƌdĞĚ:ŽŚŶƐŽŶ ĚĞŵŽŶƐƚƌĂƚĞǁŚĂƚƚŚĞLJŚĂǀĞůĞĂƌŶƚ͘dŚŝƐǁĂƐ ƐƐŽĐŝĂƚĞĚŝƚŽƌ͗ĚƌŝĂŶŶĂDŝĐŬŝĞǁŝĐnj ĂƐƵďƐƚĂŶƟĂůĐŚĂůůĞŶŐĞĨŽƌƵƐ͕ĂŶĚ/͛ŵƌĞĂůůLJ ƉƌŽƵĚŽĨƚŚĞǁĂLJŵLJĐŽůůĞĂŐƵĞƐƌŽƐĞƚŽŝƚ͘ ĞĚŝƚŽƌͺŶĞǁƐůĞƩĞƌΛŵĂƚŚ͘ƵĐů͘ĂĐ͘ƵŬ tĞĂůƐŽďƌŽƵŐŚƚŝŶĂ͞ŶŽĚĞƚƌŝŵĞŶƚ͟ƉŽůŝĐLJʹ ĂƐĚŝĚŵĂŶLJŽƚŚĞƌŝŶƐƟƚƵƟŽŶƐʹĞŶƐƵƌŝŶŐƚŚĂƚ ΛDĂƚŚĞŵĂƟĐƐh> ĂŶLJĮŶĂůLJĞĂƌƐƚƵĚĞŶƚǁŚŽǁŽƵůĚŚĂǀĞďĞĞŶ ŝŶĂĚǀĞƌƚĞŶƚůLJĚŝƐĂĚǀĂŶƚĂŐĞĚďLJŽƵƌŶĞǁ͕ ƵŶƚƌŝĞĚĂƐƐĞƐƐŵĞŶƚƐǁŽƵůĚďĞĂǁĂƌĚĞĚƚŚĞ

3 LETTER FROM THE HEAD OF DEPARTMENT

ĚĞŐƌĞĞƚŚĂƚƚŚĞŝƌƉƌĞǀŝŽƵƐĨŽƌŵƐƵŐŐĞƐƚĞĚ Ăƚ/ŵƉĞƌŝĂůŽůůĞŐĞ͖ƚŚĞŶĞdžƚĂƉƉŽŝŶƚĞĞ;Ă ƚŚĞLJǁŽƵůĚŐĞƚ͘ ƉƵƌĞŵĂƚŚĞŵĂƟĐŝĂŶƚŚŝƐƟŵĞͿŝƐƌEŝŬŽŶ <ƵƌŶŽƐŽǀ͘&ŝŶĂůůLJ͕ǁĞůĂƵŶĐŚĞĚĂŶĞǁƐĞŶŝŽƌ KĨĐŽƵƌƐĞ͕ŽƵƌƌĞƐƉŽŶƐĞƚŽŽǀŝĚͲϭϵŚĂƐŶŽƚ ƌĞƐĞĂƌĐŚĨĞůůŽǁƐŚŝƉƐĐŚĞŵĞ͕ƚŚĞ/D^^ ũƵƐƚďĞĞŶƚŽĞŶƐƵƌĞƚŚĂƚŽƵƌŽǁŶĂĐƟǀŝƟĞƐ &ĞůůŽǁƐŚŝƉƐʹŝŶƚĞŶĚĞĚƚŽŚĞůƉĚƌĂǁƚŚĞƚǁŽ ĐĂŶĐŽŶƟŶƵĞĂƐĨĂƌĂƐƉŽƐƐŝďůĞ͘tĞŚĂǀĞ ĚĞƉĂƌƚŵĞŶƚƐŽĨDĂƚŚĞŵĂƟĐƐĂŶĚ^ƚĂƟƐƟĐĂů ǁŽƌůĚĐůĂƐƐŵĂƚŚĞŵĂƟĐĂůŵŽĚĞůůŝŶŐĞdžƉĞƌƚƐ ^ĐŝĞŶĐĞĐůŽƐĞƌƚŽŐĞƚŚĞƌĂƐǁĞƉůĂŶĨŽƌƚŚĞ ŝŶƚŚŝƐĚĞƉĂƌƚŵĞŶƚ͕ǁŚŽŝŵŵĞĚŝĂƚĞůLJƚƵƌŶĞĚ ũŽŝŶƚ/ŶƐƟƚƵƚĞ͘dǁŽ/D^^&ĞůůŽǁƐ͕ƌůĞŶĂ ƚŚĞŝƌĞdžƉĞƌƟƐĞƚŽƚŚĞƉƌŽďůĞŵĂƚŚĂŶĚ͘ >ƵĐĂĂŶĚƌ:ŽŽŶŬLJƵŶŐ>ĞĞĂƌĞĂůƐŽũŽŝŶŝŶŐƵƐ ŽǀĞƌƚŚĞƐƵŵŵĞƌ͘ WƌŽĨĞƐƐŽƌŚƌŝƐƟŶĂWĂŐĞů;ŝƌĞĐƚŽƌŽĨKZhͿ ŝƐŽŶƚŚĞůĞĂĚĞƌƐŚŝƉƚĞĂŵŽĨKs/͕ƚŚĞ dŚŝƐLJĞĂƌŚĂƐďĞĞŶĨĂƌĨƌŽŵŽƌĚŝŶĂƌLJ͘tĞ ŶĞǁŶĂƟŽŶĂůĚĂƚĂĞīŽƌƚŽĨǁŚŝĐŚh>ŝƐĂ ŚĂĚƚŽĐĂŶĐĞůŽƵƌĞdžĂŵƐ͕ƚŚĞĞDŽƌŐĂŶ ĨŽƵŶĚŝŶŐƉĂƌƚŶĞƌ͘dŚĞKZhƚĞĂŵ;ǁŚŽƐĞ ŝŶŶĞƌ͕ĂŶĚŐƌĂĚƵĂƟŽŶ͖ĂƐ/ǁƌŝƚĞ͕ǁĞĂƌĞ ĞdžƉĞƌƟƐĞŝŶůŝŶŝĐĂůKƉĞƌĂƟŽŶĂůZĞƐĞĂƌĐŚ ůŽŽŬŝŶŐŝŶƚŽƚŚĞƉƌĂĐƟĐĂůŝƟĞƐŽĨĚĞůŝǀĞƌŝŶŐ ŝƐŽƵƌŐƌĞĂƚĞƐƚĂƐƐĞƚĂƚƚŚŝƐƟŵĞͿŚĂǀĞ ŽƵƌĂƵƚƵŵŶƚĞƌŵůĞĐƚƵƌĞƐƌĞŵŽƚĞůLJŝĨŶĞĞĚ ĂůƐŽďĞĞŶǁŽƌŬŝŶŐǁŝƚŚƚŚĞEŝŐŚƟŶŐĂůĞƚŽ ďĞ͖ĂŶĚŶŽĚŽƵďƚďLJƚŚĞƟŵĞLJŽƵƌĞĂĚƚŚŝƐ ĚĞƐŝŐŶƚŚĞŝƌĚĂƐŚďŽĂƌĚƐĂŶĚĚĂƚĂƉƌŽĐĞƐƐĞƐ͖ ǁĞǁŝůůďĞĂǁĂƌĞŽĨŵĂŶLJŵĞŵďĞƌƐŽĨƚŚĞ ǁŝƚŚh>,͕ƚŚĞZŽLJĂů&ƌĞĞĂŶĚ^ƚdŚŽŵĂƐ͛Ɛ h>DĂƚŚĞŵĂƟĐƐĐŽŵŵƵŶŝƚLJǁŚŽŚĂǀĞďĞĞŶ ŚĞůƉŝŶŐĂŶĂůLJƐĞƚŚĞŝƌƌĞĂůͲƟŵĞĚĂƚĂƚŽ ďĂĚůLJĂīĞĐƚĞĚďLJŽǀŝĚͲϭϵ͘ƵƚǁĞŚĂǀĞƚŽ ƵŶĚĞƌƐƚĂŶĚƉƌĂĐƟĐĞ͖ĂŶĚǁŝƚŚE,^^ĐŽƚůĂŶĚ ůŽŽŬƚŽƚŚĞĨƵƚƵƌĞ͕ĂŶĚ/ŚŽƉĞǁĞǁŝůůĐŽŵĞ ƚŽŚĞůƉĚĞƐŝŐŶĐŽŶƚĂĐƚƚƌĂĐŝŶŐĨŽƌƚŚĞƉŽƐƚͲ ŽƵƚŽĨƚŚŝƐŶŽƚũƵƐƚǁŝƚŚŶĞǁƚĞĐŚŶŝĐĂůƐŬŝůůƐ͕ ůŽĐŬĚŽǁŶƉĞƌŝŽĚ͘DĂŶLJŽƚŚĞƌŵĞŵďĞƌƐŽĨ ďƵƚĂůƐŽĂĚŝīĞƌĞŶƚǀŝĞǁŽŶǁĂLJƐŽĨǁŽƌŬŝŶŐ͕ ƚŚĞĚĞƉĂƌƚŵĞŶƚƐŝŐŶĞĚƵƉĨŽƌƚŚĞŶĂƟŽŶĂů ĂĚĞĞƉĞƌĂƉƉƌĞĐŝĂƟŽŶŽĨƚŚĞƚĞĂĐŚŝŶŐ ŵŽĚĞůůŝŶŐĞīŽƌƚ͕ZDW͕ĐŽŽƌĚŝŶĂƚĞĚďLJƚŚĞ ƉƌŽĨĞƐƐŝŽŶ;ĨŽƌƚŚŽƐĞŽĨƵƐǁŚŽĂƌĞƉĂƌĞŶƚƐͿ ZŽLJĂů^ŽĐŝĞƚLJ͘ ĂŶĚʹũƵƐƚƉĞƌŚĂƉƐʹǁŝƚŚƚŚĞƐĂƟƐĨĂĐƟŽŶŽĨĂ ũŽďǁĞůůĚŽŶĞ͘ ďƐŽůƵƚĞůLJƚŚĞůĂƐƚƚŚŝŶŐ/ĚŝĚďĞĨŽƌĞůĞĂǀŝŶŐ ƚŚĞĚĞƉĂƌƚŵĞŶƚĨŽƌŵĂŶLJŵŽŶƚŚƐǁĂƐƚŽ ŚŽůĚŝŶƚĞƌǀŝĞǁƐĨŽƌůĞĐƚƵƌĞƐŚŝƉƐŝŶƉƵƌĞ ŵĂƚŚĞŵĂƟĐƐ͘dŚĞƐĞǁĞƌĞƉŽƐƐŝďůLJƚŚĞ ůĂƐƚƉŽƐƚƐƚŽďĞĂƉƉƌŽǀĞĚŝŶƚŚĞǁŚŽůĞŽĨ h>ďĞĨŽƌĞƚŚĞŽǀŝĚƐŚƵƚĚŽǁŶ͕ĂŶĚ/͛ŵ ĚĞůŝŐŚƚĞĚƚŚĂƚƌĂƌŝŽĞƌĂůĚŽ͕ƌ^ŚŽŚĂŵ >ĞƚnjƚĞƌĂŶĚƌůĞdžĞLJWŽŬƌŽǀƐŬŝLJǁŝůůĂůůũŽŝŶ ƵƐŽǀĞƌƚŚĞƐƵŵŵĞƌ͘tĞǁĞůĐŽŵĞĂůůƚŚƌĞĞŽĨ ƚŚĞŵĂƐŽƵƌĐŽůůĞĂŐƵĞƐ͘

We had a good year for research ĂƉƉŽŝŶƚŵĞŶƚƐƚŽŽ͘KƵƌůŝīŽƌĚ&ĞůůŽǁ͕ ĂƉƉůŝĞĚŵĂƚŚĞŵĂƟĐŝĂŶƌZƵďĠŶWĠƌĞnj ĂƌƌĂƐĐŽ͕ŵŽǀĞĚŽŶƚŽĂƉĞƌŵĂŶĞŶƚƉŽƐƚ

4 BRITISH SOCIETY OF RHEOLOGY ANNUAL AWARD 2019

ƌŝƟƐŚ^ŽĐŝĞƚLJŽĨZŚĞŽůŽŐLJŶŶƵĂů ŇƵŝĚƐǁŚŝĐŚŝƐƚŚĞĮƌƐƚƚŽďĞĂďůĞƚŽĐĂƉƚƵƌĞ ǁĂƌĚϮϬϭϵ ƵŶƐƚĞĂĚLJĞīĞĐƚƐĂƐǁĞůůĂƐƚŚĞďĞŚĂǀŝŽƵƌ ƵŶĚĞƌŐĞŶĞƌĂůŇŽǁĐŽŶĚŝƟŽŶƐ͘ dŚĞƌŝƟƐŚ^ŽĐŝĞƚLJŽĨZŚĞŽůŽŐLJ;^ZͿ ǀĞƌLJƌĞĐŝƉŝĞŶƚŽĨƚŚĞ^ZŶŶƵĂůǁĂƌĚ ŐĂǀĞŝƚƐŶŶƵĂůǁĂƌĚϮϬϭϵƚŽŽƵƌ,ĞĂĚ ǁƌŝƚĞƐĂƐƵŵŵĂƌLJŽĨƚŚĞŝƌĂǁĂƌĚůĞĐƚƵƌĞ ŽĨĞƉĂƌƚŵĞŶƚ͕WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ͘ ĨŽƌƚŚŽƐĞ^ZŵĞŵďĞƌƐǁŚŽĐŽƵůĚŶ͛ƚďĞ dŚŝƐĂǁĂƌĚƌĞĐŽŐŶŝƐĞƐƚŚĞĐŽŶƚƌŝďƵƟŽŶ ƚŚĞƌĞ͕ǁŚŝĐŚŝƐƉƵďůŝƐŚĞĚŝŶƚŚĞ^ZƵůůĞƟŶ͘ of a UK researcher to rheology, either dŚŝƐLJĞĂƌƚŚĞƐƉƌŝŶŐĞĚŝƟŽŶŽĨƚŚĞƵůůĞƟŶ͕ directly through their research or through ĐŽŶƚĂŝŶŝŶŐ,ĞůĞŶ͛ƐĂƌƟĐůĞ͕ǁĂƐŵĂĚĞĨƌĞĞůLJ ĚŝƐƟŶŐƵŝƐŚĞĚƐĞƌǀŝĐĞƚŽƚŚĞ^ZŝƚƐĞůĨ͘/Ŷ ĂǀĂŝůĂďůĞƚŽĂůů;ŶŽƚũƵƐƚ^ZŵĞŵďĞƌƐͿʹƐŽŝĨ ,ĞůĞŶ͛ƐĐĂƐĞŝƚǁĂƐĂĐŽŵďŝŶĂƟŽŶŽĨƚŚĞƚǁŽ͘ LJŽƵǁĂŶƚƚŽƌĞĂĚŵŽƌĞ͕ŝƚ͛ƐŚĞƌĞ͗ ,ĞƌƌĞƐĞĂƌĐŚŽǀĞƌƚŚĞůĂƐƚϮϱLJĞĂƌƐŚĂƐďĞĞŶ ŚƩƉƐ͗ͬͬǁǁǁ͘ďƐƌ͘ŽƌŐ͘ƵŬͬĂƌƟĐůĞͬĨƌĞĞͲ ŽŶĂƌĂŶŐĞŽĨĚŝīĞƌĞŶƚƚŽƉŝĐƐǁŝƚŚŝŶƌŚĞŽůŽŐLJ ďƵůůĞƟŶͲϮϱͬ;ƉĂŐĞϱͿ͘ ;ĚĞĮŶĞĚĂƐƚŚĞĚĞĨŽƌŵĂƟŽŶĂŶĚŇŽǁŽĨ ŵĂƩĞƌ͕ĂŶĚŶŽǁŐĞŶĞƌĂůůLJǀŝĞǁĞĚĂƐƚŚĞ WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ ƐĐŝĞŶĐĞŽĨŚŽǁĐŽŵƉůĞdžŵĂƚĞƌŝĂůƐďĞŚĂǀĞͿ͖ ĨƌŽŵϮϬϭϱͲϮϬϭϳƐŚĞǁĂƐWƌĞƐŝĚĞŶƚŽĨƚŚĞ^Z ĂŶĚƐŚĞŚĂƐĐŽͲŽƌŐĂŶŝƐĞĚĂůĂƌŐĞŶƵŵďĞƌŽĨ ŵĞĞƟŶŐƐŽŶďĞŚĂůĨŽĨƚŚĞ^Z͘

WƌŽĨĞƐƐŽƌtŝůƐŽŶƚŚĞŶŐĂǀĞŚĞƌĂǁĂƌĚ ůĞĐƚƵƌĞ͕ĞŶƟƚůĞĚ͞DŽĚĞůůŝŶŐŽŵƉůĞdž ^ƵƐƉĞŶƐŝŽŶƐ͕͟ĚĞƐĐƌŝďŝŶŐƚŚĞŽƌLJƐŚĞŚĂƐ ĚĞǀĞůŽƉĞĚŝŶĐŽůůĂďŽƌĂƟŽŶǁŝƚŚƉŽƐƚĚŽĐƌ :ƵƌƌŝĂĂŶ'ŝůůŝƐƐĞŶĨŽƌƚǁŽĚŝīĞƌĞŶƚŬŝŶĚƐŽĨ ĐŽŵƉůĞdžƐƵƐƉĞŶƐŝŽŶƐ͘/ŶƚŚĞĮƌƐƚĐĂƚĞŐŽƌLJ͕ ƚŚĞƉĂƌƟĐůĞƐĂƌĞĂƩƌĂĐƚĞĚƚŽŽŶĞĂŶŽƚŚĞƌĂŶĚ ŝŶƚŚĞĂďƐĞŶĐĞŽĨŇŽǁƚŚĞLJǁŽƵůĚĐŽĂŐƵůĂƚĞ͘ Gillissen and Wilson have developed a scaling ůĂǁƚŚĂƚĂůůŽǁƐĞdžƉĞƌŝŵĞŶƚĂůƌĞƐĞĂƌĐŚĞƌƐ ƚŽĞdžƚƌĂĐƚŝŶĨŽƌŵĂƟŽŶĂďŽƵƚƚŚĞƐŝnjĞŽĨ ƚŚĞĂƩƌĂĐƟǀĞĨŽƌĐĞďĞƚǁĞĞŶƚŚĞƉĂƌƟĐůĞƐ͕ ĨƌŽŵƚŚĞǀŝƐĐŽƐŝƚLJŽĨƚŚĞǁŚŽůĞƐƵƐƉĞŶƐŝŽŶ ĂƚĂƌĂŶŐĞŽĨĨĂƐƚŇŽǁƌĂƚĞƐ͘/ŶƚŚĞƐĞĐŽŶĚ ĐĂƚĞŐŽƌLJ͕ƚŚĞƉĂƌƟĐůĞƐƌĞƉĞůĞĂĐŚŽƚŚĞƌĂŶĚ͕ ĂƚŚŝŐŚĐŽŶĐĞŶƚƌĂƟŽŶƐ͕ƚŚĞƐLJƐƚĞŵĐĂŶũĂŵ ;ƚŚŝƐŝƐǁŚĂƚ͛ƐŐŽŝŶŐŽŶŝŶĂĚĞŶƐĞĐŽƌŶŇŽƵƌͲ The award was presented at the BSR Midwinter ĂŶĚͲǁĂƚĞƌŵŝdžƚƵƌĞǁŚĞŶLJŽƵƐƟƌƚŽŽĨĂƐƚĂŶĚ DĞĞƟŶŐŝŶŝƌŵŝŶŐŚĂŵŝŶĞĐĞŵďĞƌϮϬϭϵ͕ďLJ ƚŚĞ͞ůŝƋƵŝĚ͟ƐƵĚĚĞŶůLJƐŚĂƩĞƌƐůŝŬĞĐŚŝŶĂͿ͘ ƚŚĞĐƵƌƌĞŶƚ^ZWƌĞƐŝĚĞŶƚ͕ŶĚƌĞǁ,ŽǁĞ 'ŝůůŝƐƐĞŶĂŶĚtŝůƐŽŶ͕ŝŶĐŽůůĂďŽƌĂƟŽŶǁŝƚŚ ƌĞƐĞĂƌĐŚĞƌƐĨƌŽŵĂŵďƌŝĚŐĞĂŶĚĚŝŶďƵƌŐŚ͕ ŚĂǀĞĐŽŵĞƵƉǁŝƚŚĂŶĞǁŵŽĚĞůĨŽƌƚŚĞƐĞ /ŵĂŐĞƌĞĚŝƚͲWƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ

5 DE MORGAN ASSOCIATION DINNER

ĞDŽƌŐĂŶƐƐŽĐŝĂƟŽŶŝŶŶĞƌϮϬϭϵ

dŚŝƐLJĞĂƌΖƐƐƉĞĂŬĞƌǁĂƐZŽďĂƐƚĂǁĂLJ͘ZŽď ŚĂƐǁƌŝƩĞŶŽƌĐŽͲǁƌŝƩĞŶĞůĞǀĞŶŬƐ͕ƐŽŵĞ ŽĨǁŚŝĐŚŚĂǀĞĂƉƉĞĂƌĞĚŝŶƐĞǀĞƌĂůůĂŶŐƵĂŐĞƐ͘ dŚĞŵĂũŽƌŝƚLJĂƌĞĂďŽƵƚƚŚĞŵĂƚŚĞŵĂƟĐƐŽĨ ĞǀĞƌLJĚĂLJůŝĨĞ͕ďƵƚŚĞŚĂƐĂůƐŽǁƌŝƩĞŶŬƐ ŽŶĐƌŝĐŬĞƚ͕ŵĞŵŽƌLJĂŶĚĐƌĞĂƟǀĞƚŚŝŶŬŝŶŐ͘ ,ĞŝƐƚŚĞŝƌĞĐƚŽƌŽĨΖΖDĂƚŚƐ/ŶƐƉŝƌĂƟŽŶΖΖ͕Ă ŶĂƟŽŶĂůƉƌŽŐƌĂŵŵĞŽĨŝŶƚĞƌĂĐƟǀĞůĞĐƚƵƌĞ ƐŚŽǁƐŝŶƚŚĞĂƚƌĞƐƚŚĂƚŚĂƐƌĞĂĐŚĞĚŽǀĞƌ ϭϬϬ͕ϬϬϬƚĞĞŶĂŐĞƌƐŝŶƚŚĞůĂƐƚƚĞŶLJĞĂƌƐ͘ ZŽďŝƐĂůƐŽĐůŽƐĞůLJŝŶǀŽůǀĞĚǁŝƚŚƚŚĞh< ŵĂƚŚĞŵĂƟĐƐĐŽŵŵƵŶŝƚLJ͕ĨƌŽŵƉƌŝŵĂƌLJ ƐĐŚŽŽůƐƚŽƵŶŝǀĞƌƐŝƟĞƐ͕ĂŶĚŐŝǀĞƐƚĂůŬƐƚŽ adults, teenagers and children that range ĨƌŽŵƐŵĂůůŝŶƚĞƌĂĐƟǀĞǁŽƌŬƐŚŽƉƐƚŽŬĞLJŶŽƚĞ lectures in front of several hundred people. ,ĞŚĂƐĂůƐŽĚŽŶĞůŽƚƐŽĨƌĂĚŝŽ;ŝŶĐůƵĚŝŶŐ ŶƵŵĞƌŽƵƐĂƉƉĞĂƌĂŶĐĞƐŽŶZĂĚŝŽϰΖƐ DŽƌĞKƌ>ĞƐƐͿĂŶĚŵĂŶLJƉŽĚĐĂƐƚƐ͘ZŽďŐĂǀĞ ĂŶĞŶƚĞƌƚĂŝŶŝŶŐĂŌĞƌͲĚŝŶŶĞƌƚĂůŬĨĂƐĐŝŶĂƟŶŐ ƵƐǁŝƚŚĂŶƵŵďĞƌŽĨƉƵnjnjůĞƐŝŶĐůƵĚŝŶŐŚŝƐ ŽǁŶǀĂƌŝĂƟŽŶŽŶƚŚĞĨĂŵŽƵƐDŽŶƚLJ,Ăůů ƉƌŽďůĞŵ͘

'ƵĞƐƚƐĂƚƚŚĞĞDŽƌŐĂŶŝŶŶĞƌ

ZŽďĂƐƚĂǁĂLJ͕ƐƉĞĂŬĞƌ

6 DE MORGAN ASSOCIATION DINNER

dĂďůĞƐĞƚƵƉĂƚƚŚĞĚŝŶŶĞƌ   dŚĞDŝĐŚĂĞů^ŝŶŐĞƌƐŚŽŝƌƉĞƌĨŽƌŵŝŶŐ

WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ ŵŝůLJDĂǁƉĂƌƟĐŝƉĂƟŶŐŝŶĂĚĞŵŽŶƐƚƌĂƟŽŶ /ŵĂŐĞƌĞĚŝƚͲ^ŽŚĞŶŝ&ƌĂŶĐŝƐ

7 WHAT BIOLOGY CAN DO FOR MATHS

ĐƵƌŝŽƵƐŶŽŶͲůŝŶĞĂƌǁĂǀĞƉĂƩĞƌŶʹ tŚĂƚďŝŽůŽŐLJĐĂŶĚŽĨŽƌŵĂƚŚƐ

ďLJƌŶŐĞůŝŬĂDĂŶŚĂƌƚ

/ĂŵĐƵƌƌĞŶƚůLJƚĞĂĐŚŝŶŐƚŚĞĨŝƌƐƚLJĞĂƌƉƉůŝĞĚDĂƚŚƐĐŽƵƌƐĞĂƚh>͘/ƚƚĂŬĞƐ ŵĞďĂĐŬƚŽŵLJŽǁŶĨŝƌƐƚLJĞĂƌŽĨƐƚƵĚLJŝŶŐDĂƚŚĞŵĂƚŝĐƐŝŶsŝĞŶŶĂ͘ dŚĞ ĞdžĐŝƚĞŵĞŶƚŽĨƐŝƚƚŝŶŐŝŶĂŶĂĐƚƵĂůƵŶŝǀĞƌƐŝƚLJůĞĐƚƵƌĞŚĂůů͕ƚŚĞũŽLJŽĨďĞŝŶŐ ƐƵƌƌŽƵŶĚĞĚďLJĨĞůůŽǁƐƚƵĚĞŶƚƐƚŚĂƚƐŚĂƌĞŵLJĞŶƚŚƵƐŝĂƐŵĨŽƌŵĂƚŚĞŵĂƚŝĐƐ͕ĂŶĚ ƚŚĞĚĞĞƉĐŽŶǀŝĐƚŝŽŶƚŚĂƚƚŚĞƌĞǁŽŶ͛ƚďĞĂŶLJƚŚŝŶŐƵŶŝǀĞƌƐŝƚLJŵĂƚŚƐĐĂŶƚŚƌŽǁĂƚ ŵĞ͕ƚŚĂƚ/ǁŽŶ͛ƚďĞĂďůĞƚŽƵŶĚĞƌƐƚĂŶĚ͘/ǁĂƐƉƌŽǀĞŶǁƌŽŶŐĂďŽƵƚƚŚĂƚ͘KĨ ĐŽƵƌƐĞ͘

/ŶƚŚĞh>ƉƉůŝĞĚDĂƚŚƐĐŽƵƌƐĞ͕ǁĞƌĞĐĞŶƚůLJĐŽǀĞƌĞĚŽŶĞŽĨƚŚĞŵŽƐƚ ∂2u ĨĂŵŽƵƐůŝŶĞĂƌƉĂƌƚŝĂůĚŝĨĨĞƌĞŶƚŝĂůĞƋƵĂƚŝŽŶƐ;WƐͿ͕ƚŚĞǁĂǀĞĞƋƵĂƚŝŽŶ t
=
c2∂2u x ͕ĂďĞĂƵƚŝĨƵůŵŽĚĞůĞ͘Ő͘ĨŽƌǀŝďƌĂƚŝŶŐƐƚƌŝŶŐƐ͘^ŚŽƌƚůLJĂĨƚĞƌǁĞŚĂĚĚŝƐĐƵƐƐĞĚ ŚŽǁƚŽƐŽůǀĞŝƚ͕ĂƐƚƵĚĞŶƚĂƉƉƌŽĂĐŚĞĚŵĞĂĨƚĞƌĐůĂƐƐĂŶĚĂƐŬĞĚ͕ǁŚLJĂĨƵŶĐƚŝŽŶ ŽĨƚŚĞĨŽƌŵ

u(x,
t)
=
f(x
−
ct)

ǁŽƵůĚĚĞĨŝŶĞĂƚƌĂǀĞůůŝŶŐǁĂǀĞ͘/ǁĂƐƐƵƌƉƌŝƐĞĚĂƚĨŝƌƐƚʹŝƐŶ͛ƚŝƚŽďǀŝŽƵƐ͍KĨ ĐŽƵƌƐĞŝƚŝƐŶ͛ƚ͕ĂŶĚĂĨĞǁŵƵůƚŝͲĐŽůŽƵƌĞĚƐŬĞƚĐŚĞƐůĂƚĞƌ͕/ŚĂĚŚĞƌĐŽŶǀŝŶĐĞĚƚŚĂƚ ŵĂLJďĞ͕ũƵƐƚŵĂLJďĞ͕ƚŚŝƐĞdžƉƌĞƐƐŝŽŶŝƐŝŶĨĂĐƚƌĞĂƐŽŶĂďůĞ͘ ƚůĞĂƐƚ/ŚŽƉĞ/ĚŝĚ͘ dƌĂǀĞůůŝŶŐǁĂǀĞƐĐĂŵĞƵƉŽĨĐŽƵƌƐĞ͕ďĞĐĂƵƐĞŵĂŶLJƐŽůƵƚŝŽŶƐƚŽƚŚĞǁĂǀĞ ĞƋƵĂƚŝŽŶĐĂŶďĞǁƌŝƚƚĞŶĂƐƐƵŵƐŽĨƚƌĂǀĞůůŝŶŐǁĂǀĞƐŵŽǀŝŶŐŝŶŽƉƉŽƐŝƚĞ ĚŝƌĞĐƚŝŽŶƐ

u(x,
t)
=
f(x
−
ct)
+
f(x
+
ct).

,ĞƌĞ͕/ǁĂŶƚƚŽǁƌŝƚĞĂďŽƵƚĂŵĂƚŚĞŵĂƚŝĐĂůĐƵƌŝŽƐŝƚLJ͕ƐŽůƵƚŝŽŶƐƚŽŶŽŶͲůŝŶĞĂƌ WƐƚŚĂƚĂƌĞƚŚĞƉƌŽĚƵĐƚŽĨƚǁŽƚƌĂǀĞůůŝŶŐǁĂǀĞƐ

u(x,
t)
=
A(x
−
ct)B(x
+
ct).

/ƐƚƵŵďůĞĚĂĐƌŽƐƐƚŚĞƐLJƐƚĞŵĂŶĚŝƚƐƐŽůƵƚŝŽŶǁŚŝůĞǁŽƌŬŝŶŐŽŶŵŽĚĞůůŝŶŐƚŚĞ ƐǁĂƌŵŝŶŐďĞŚĂǀŝŽƵƌŽĨŵLJdžŽďĂĐƚĞƌŝĂ͘ƚƚŚŝƐƉŽŝŶƚ/ƐŚŽƵůĚŵĞŶƚŝŽŶƚŚĂƚďĞƐŝĚĞƐ DĂƚŚĞŵĂƚŝĐƐ͕DŽůĞĐƵůĂƌŝŽůŽŐLJŝƐŵLJƐĞĐŽŶĚďŝŐƐĐŝĞŶƚŝĨŝĐƉĂƐƐŝŽŶ͘ /ǁƌŽƚĞŵLJ ĂĐŚĞůŽƌ͛Ɛ ƚŚĞƐŝƐ ŽŶ ƚŚĞ ŵŽǀĞŵĞŶƚ ŽĨ ĐĞůůƐ ĐĂůůĞĚ ŬĞƌĂƚŽĐLJƚĞƐ͘

8 DR ANGELIKA MANHART

&ŝŐƵƌĞ ϭ͗ >ĞĨƚ͗ZŝƉƉůĞƐĐĂƵƐĞĚďLJƌĂŝŶĚƌŽƉƐŝŶĂ ůĂŬĞ͘ZŝŐŚƚ͗ZŝƉƉůĞƐŝŶĐŽůŽŶŝĞƐŽĨ ŵLJdžŽďĂĐƚĞƌŝĂ͘

KŶĞƉůĂĐĞǁŚĞƌĞƚŚĞLJůŝǀĞŝƐŽŶĨŝƐŚƐĐĂůĞƐ͕ƐŽŽŶĐĞĂǁĞĞŬ͕ĂĨŝƐŚĚĞůŝǀĞƌLJŐƵLJ ǁŽƵůĚƉƵůůƵƉŝŶĨƌŽŶƚŽĨƚŚĞůĂďŽƌĂƚŽƌLJĂŶĚĚĞůŝǀĞƌĨƌĞƐŚůLJŬŝůůĞĚĨŝƐŚ͕ĨƌŽŵǁŚŝĐŚ ǁĞǁŽƵůĚŚĂƌǀĞƐƚƚŚĞĐĞůůƐƚŽĂŶĂůLJƐĞƚŚĞŵůĂƚĞƌ͘ŶŝŶƚĞƌĞƐƚŝŶŐƐŝĚĞĞĨĨĞĐƚŽĨƚŚŝƐ ǁĂƐƚŚĂƚŽŶĞŽĨƚŚŝŶŐƐ/ůĞĂƌŶĞĚĚƵƌŝŶŐƚŚĞĂĐŚĞůŽƌ͛ƐƚŚĞƐŝƐ͕ǁĂƐŚŽǁƚŽ ĚŝƐĞŵďŽǁĞůĨŝƐŚ͘tŚŽǁŽƵůĚŚĂǀĞƚŚŽƵŐŚƚ͍

,ŽǁĞǀĞƌ͕ŵLJdžŽďĂĐƚĞƌŝĂĐĞůůƐĂƌĞǀĞƌLJĚŝĨĨĞƌĞŶƚĨƌŽŵŬĞƌĂƚŽĐLJƚĞƐ͘ dŚĞLJ ĚǁĞůůŝŶƚŚĞĞĂƌƚŚĂŶĚƉƌŽĚƵĐĞƐůŝŵĞƚŽŚĞůƉŵŽǀĞĂƌŽƵŶĚ͘dŚĞŶŝĐĞ͕ĞĂƌƚŚLJ ƐŵĞůůĂĨƚĞƌĂƌĂŝŶŝƐŝŶĨĂĐƚƚŚĞƐůŝŵĞƚŚĞLJƉƌŽĚƵĐĞ͘ĂĐŚĐĞůůŝƐŝƚƐŽǁŶŽƌŐĂŶŝƐŵ͕ ŚŽǁĞǀĞƌƚŚĞLJŚƵŶƚƚŚĞŝƌƉƌĞLJĐŽůůĞĐƚŝǀĞůLJʹũƵƐƚůŝŬĞĂƉĂĐŬŽĨǁŽůǀĞƐ͘tŚĞŶƚŚĞLJ ĞŶĐŽƵŶƚĞƌƉƌĞLJ͕ƚŚĞLJŽĨƚĞŶĨŽƌŵĂŶŝŶƚƌŝŐƵŝŶŐƉĂƚƚĞƌŶ͗ hŶĚĞƌƚŚĞŵŝĐƌŽƐĐŽƉĞ ƚŚĞǁŚŽůĞĐŽůŽŶLJ;ƚŚŝŶŬŚƵŶĚƌĞĚƐŽĨƚŚŽƵƐĂŶĚƐŽĨďĂĐƚĞƌŝĂͿůŽŽŬƐůŝŬĞƚŚĞ ƐƵƌĨĂĐĞŽĨĂůĂŬĞǁŚĞƌĞƐŽŵĞŽŶĞŚĂƐƚŚƌŽǁŶŝŶƐŽŵĞƉĞďďůĞƐ͕&ŝŐ͘ϭ͗&ĂŵŝůŝĞƐŽĨ ƚƌĂǀĞůůŝŶŐĚĞŶƐŝƚLJǁĂǀĞƐŵŽǀŝŶŐŝŶĚŝĨĨĞƌĞŶƚĚŝƌĞĐƚŝŽŶƐ͘tŚĞŶƚŚĞǁĂǀĞĨĂŵŝůŝĞƐ ŵĞĞƚ͕ƚŚĞLJƐĞĞŵƚŽƉĞŶĞƚƌĂƚĞĞĂĐŚŽƚŚĞƌƐĞĞŵŝŶŐůLJǁŝƚŚŽƵƚĂĨĨĞĐƚŝŶŐĞĂĐŚ ŽƚŚĞƌ͘ůŽƐĞƌŝŶƐƉĞĐƚŝŽŶƐŚŽǁƐƚŚĂƚŝŶĨĂĐƚ͕ ƵƉŽŶĐŽůůŝƐŝŽŶŵĂŶLJŽĨƚŚĞ ŝŶĚŝǀŝĚƵĂůďĂĐƚĞƌŝĂŝŶĨĂĐƚƌĞǀĞƌƐĞƚŚĞŝƌĚŝƌĞĐƚŝŽŶ͕ƐŽǁŚŝůĞŵŝĐƌŽƐĐŽƉŝĐĂůůLJƚŚĞ ǁĂǀĞƚŚĂƚĐŽŶƚŝŶƵĞƐĂĨƚĞƌƚŚĞĐŽůůŝƐŝŽŶĐŽŶƚĂŝŶƐĐŽŵƉůĞƚĞůLJĚŝĨĨĞƌĞŶƚďĂĐƚĞƌŝĂ ƚŚĂŶďĞĨŽƌĞƚŚĞĐŽůůŝƐŝŽŶ͕ŵĂĐƌŽƐĐŽƉŝĐĂůůLJ͕ƚŚĞǁĂǀĞůŽŽŬƐƚŚĞƐĂŵĞ͘

DLJĨĂǀŽƵƌŝƚĞǁĂLJƚŽĂƉƉƌŽĂĐŚƐƵĐŚƉƌŽďůĞŵƐŵĂƚŚĞŵĂƚŝĐĂůůLJŝƐƚŽƐƚĂƌƚďLJ ǁƌŝƚŝŶŐĂŶŐĞŶƚͲďĂƐĞĚŵŽĚĞů͕ǁŚĞƌĞĞĂĐŚďĂĐƚĞƌŝƵŵŐĞƚƐŝƚƐŽǁŶĞƋƵĂƚŝŽŶ ;ƚLJƉŝĐĂůůLJƐƚŽĐŚĂƐƚŝĐ͕ŽƌĚŝŶĂƌLJĚŝĨĨĞƌĞŶƚŝĂůĞƋƵĂƚŝŽŶƐ;KƐͿͿĂŶĚƚŚĞŶĚĞƌŝǀĞĂ ĐŽŶƚŝŶƵƵŵWĚĞƐĐƌŝƉƚŝŽŶĨŽƌƚŚĞĚĞŶƐŝƚŝĞƐďLJĐŽĂƌƐĞͲŐƌĂŝŶŝŶŐ͕ŝ͘Ğ͘ ĂƐƐƵŵŝŶŐ ƚŚĂƚƚŚĞŶƵŵďĞƌŽĨďĂĐƚĞƌŝĂŝƐǀĞƌLJŚŝŐŚĂŶĚƚŚĂƚƚŚĞŝƌŝŶƚĞƌĂĐƚŝŽŶůĞŶŐƚŚƐĐĂůĞƐĂƌĞ ŵƵĐŚƐŵĂůůĞƌƚŚĂŶƚŚĞƌĞƐƵůƚŝŶŐ;ǁĂǀĞͿƉŚĞŶŽŵĞŶĂ͘

9 WHAT BIOLOGY CAN DO FOR MATHS

&ŝŐ͘ϮƐŚŽǁƐƐŝŵƵůĂƚŝŽŶƐŶĂƉƐŚŽƚƐĨŽƌƚŚĞŐĞŶƚͲďĂƐĞĚĂŶĚƚŚĞWͲďĂƐĞĚ ŵŽĚĞů͘

&ŝŐƵƌĞϮ͗ >ĞĨƚ͗^ŝŵƵůĂƚŝŽŶƐŶĂƉƐŚŽƚĨƌŽŵƚŚĞϮŐĞŶƚͲďĂƐĞĚŵŽĚĞů;ĐŽůŽƵƌŝŶĚŝĐĂƚĞƐ ĚŝͲƌĞĐƚŝŽŶͿ͘ZŝŐŚƚ͗^ŝŵƵůĂƚŝŽŶƐŶĂƉƐŚŽƚĨƌŽŵƚŚĞϮWŵŽĚĞůƐŚŽǁŝŶŐu0
+
u1
+
v0
+
v1͘

>ĞƚŵĞƐŚŽǁLJŽƵƚŚĞϭǀĞƌƐŝŽŶŽĨƚŚĞWƐLJƐƚĞŵƚŚŝƐĞdžĞƌĐŝƐĞLJŝĞůĚĞĚ͘/ƚŝƐ ĂƐLJƐƚĞŵĨŽƌĨŽƵƌĚĞŶƐŝƚŝĞƐ͕ƚǁŽƌŝŐŚƚŵŽǀŝŶŐu0(x,
t)
ĂŶĚu1(x,
t)
ĂŶĚƚǁŽůĞŌ ŵŽǀŝŶŐŽŶĞƐ͕v0(x,
t)
ĂŶĚv1(x,
t)͘dŚĞŝŶĚĞdž0
ĂŶĚ1
ŝŶĚŝĐĂƚĞƐǁŚĞƚŚĞƌďĂĐƚĞƌŝĂ ŝŶƚŚĂƚŐƌŽƵƉĐĂŶƌĞǀĞƌƐĞ;ŝŶĚĞdž1ͿŽƌŶŽƚ;ŝŶĚĞdž0Ϳ͘dŚŝƐĐŽŵĞƐĨƌŽŵĂŵŽĚĞůůŝŶŐ ŝŶŐƌĞĚŝĞŶƚƚŚĂƚƐĂLJƐĂďĂĐƚĞƌŝĂŚĂƐƚŽǁĂŝƚĂĐĞƌƚĂŝŶƚŝŵĞ1/γ
ĂĨƚĞƌĂƌĞǀĞƌƐĂů͕ ďĞĨŽƌĞŝƚĐĂŶƌĞǀĞƌƐĞĂŐĂŝŶ͘EŽǁ͕ŝĨŝƚĐĂŶƌĞǀĞƌƐĞ͕ŝƚǁŝůůĚŽƐŽǁŝƚŚĂƌĂƚĞρ
→
λ(ρ)
ƚŚĂƚĚĞƉĞŶĚƐŽŶƚŚĞĚĞŶƐŝƚLJŽĨŽŶĐŽŵŝŶŐďĂĐƚĞƌŝĂ͘zŽƵĐĂŶŝŵĂŐŝŶĞLJŽƵƌƐĞůĨ ǁĂůŬŝŶŐƚŽǁĂƌĚƐƵƐƚŽŶƐƚĂƚŝŽŶĨƌŽŵh>ǁŝƚŚƐƉĞĞĚc
ĂŶĚůŽƚƐŽĨƉĞŽƉůĞŐŽŝŶŐ ƚŚĞŽƉƉŽƐŝƚĞǁĂLJ͘dŚĞŵŽƌĞƉĞŽƉůĞLJŽƵŵĞĞƚ͕ƚŚĞŵŽƌĞůŝŬĞůLJLJŽƵĂƌĞƚŽƚƵƌŶ ĂƌŽƵŶĚĂŶĚŐŽďĂĐŬƚŽh>ƚŽǁŽƌŬĂďŝƚŵŽƌĞ͘

,ĞƌĞĂƌĞƚŚĞĞƋƵĂƚŝŽŶƐŝŶϭ͗ ;ϭͿ ∂tu0 + c∂xu0 = −γu0 + λ(u0 + u1)v1,

∂tu1 + c∂xu1 = γu0 − λ(v0 + v1)u1,

∂tv0 − c∂xv0 = −γv0 + λ(v0 + v1)u1,

∂tv1 − c∂xv1 = γv0 − λ(u0 + u1)v1.

dŚĞƌĞĂĐƚŝŽŶƚĞƌŵƐŽŶƚŚĞƌŝŐŚƚĐĂŶďĞƵŶĚĞƌƐƚŽŽĚĂƐĐLJĐůŝĐƚƌĂŶƐŝƚŝŽŶƐ͗u0
→
u1
→
v0
→
v1
→
u0͗/ŵĂŐŝŶĞĂďĂĐƚĞƌŝĂƐƚĂƌƚŝŶŐĞ͘Ő͘ŝŶƚŚĞu0
ŐƌŽƵƉĂŶĚĐLJĐůŝŶŐ

10 DR ANGELIKA MANHART

ƚŚƌŽƵŐŚƚŚĞĨŽƵƌŐƌŽƵƉƐďLJϭ͘,ĂǀŝŶŐǁĂŝƚĞĚůŽŶŐĞŶŽƵŐŚƚŽũŽŝŶƚŚĞƌĞǀĞƌƐŝďůĞ͕ ƌŝŐŚƚͲŵŽǀŝŶŐŐƌŽƵƉu0
→
u1͕Ϯ͘ZĞǀĞƌƐŝŶŐĂŶĚƚŚĞƌĞĨŽƌĞƐƚĂƌƚŝŶŐƚŽŵŽǀĞůĞĨƚ͕ďƵƚ

ŶŽƚďĞŝŶŐƌĞǀĞƌƐŝďůĞu1
→
v0͕ϯ͘tĂŝƚŝŶŐůŽŶŐĞŶŽƵŐŚƚŽďĞĂďůĞƚŽƌĞǀĞƌƐĞv0
→
v1͕ϰ͘ŶĚƚŚĞŶĨŝŶĂůůLJƌĞǀĞƌƐŝŶŐĂŐĂŝŶv1
→
u0͘

&ƌŽŵĂWƉŽŝŶƚŽĨǀŝĞǁƚŚŝƐĚŽĞƐŶ͛ƚůŽŽŬƐŽďĂĚ͗ůůƚŚĞŶŽŶͲůŝŶĞĂƌŝƚLJŝƐĐŽŶͲ ƚĂŝŶĞĚŽŶƚŚĞƌĞĂĐƚŝŽŶƐŝĚĞ͕ŝŶƚŚĞĨƵŶĐƚŝŽŶλ(ρ)͕ǁŚŝĐŚĐŽƵůĚĞ͘Ő͘ŚĂǀĞĂƐŝŐŵŽŝĚ ƐŚĂƉĞ͘,ŽǁĚŽǁĞĨŝŶĚƚŚĞƚƌĂǀĞůůŝŶŐǁĂǀĞƐ͍dŚĞƵƐƵĂůƚŚŝŶŐƚŽĚŽŝƐƚŽƵƐĞĂ ƚƌĂǀĞůůŝŶŐǁĂǀĞĂŶƐĂƚnj͕ŝ͘Ğ͘ƐĞĂƌĐŚĨŽƌƐŽůƵƚŝŽŶƐŽĨƚŚĞĨŽƌŵf(x
−
vt)͕ƚŚĞŶ ĐŚĂŶŐĞŝŶƚŽƚŚĞƚƌĂǀĞůůŝŶŐǁĂǀĞĨƌĂŵĞξ
=
x
−
vt
ǁŚĞƌĞĞǀĞƌLJƚŚŝŶŐƌĞĚƵĐĞƐƚŽĂŶ KĨŽƌf(ξ)͘dŚĞƉƌŽďůĞŵŝƐƚŚĂƚƚŚŝƐĚŽĞƐŶ͛ƚǁŽƌŬŚĞƌĞ͘ĨƚĞƌĂůů͕ƚŚĞĞƋƵĂƚŝŽŶ ŝƐŶŽƚůŝŶĞĂƌ͕ƐŽǁĞĐĂŶŶŽƚũƵƐƚĂĚĚƵƉƚǁŽƚƌĂǀĞůůŝŶŐǁĂǀĞƐŽůƵƚŝŽŶƐ;ŝĨƚŚĞLJĞdžŝƐƚͿ ƚŚĂƚĨŽƌĂƌŝŐŚƚͲŵŽǀŝŶŐǁĂǀĞĂŶĚƚŚĂƚĨŽƌĂůĞŌŵŽǀŝŶŐǁĂǀĞ͕ĂŶĚĞdžƉĞĐƚƚŽŐĞƚĂ ŶĞǁƐŽůƵƚŝŽŶďĂĐŬ͘ǀĞŶŵŽƌĞƉƌŽďůĞŵĂƚŝĐ͕ǁŚLJǁŽƵůĚƚŚĞůĞĨƚͲŵŽǀŝŶŐĚĞŶƐŝƚŝĞƐ v0
ĂŶĚv1
ĨŽƌŵĂƚƌĂǀĞůůŝŶŐǁĂǀĞƚŽƚŚĞƌŝŐŚƚĂƚĂůů͍/ƚƐĞĞŵƐŵŽƌĞůŝŬĞůLJƚŚĂƚƚŚĞƌĞ ĂƌĞƚǁŽƚƌĂǀĞůůŝŶŐǁĂǀĞĨƌĂŵĞƐĂƚǁŽƌŬĂƚƚŚĞƐĂŵĞƚŝŵĞ͕ŽŶĞƚŽƚŚĞƌŝŐŚƚĂŶĚ ŽŶĞƚŽƚŚĞůĞĨƚ͘ /ƚ ƚƵƌŶƐ ŽƵƚ ƚŚĞ ƌŝŐŚƚ ĂŶƐĂƚnj ;ĂƐ ŝŶ ƚŚĞ ƐƵĐĐĞƐƐĨƵů ŽŶĞͿ͕ ŝƐ ƚŚĞ ĨŽůůŽǁŝŶŐ

u0(x, t)=P (x − ct)[1 − A(x + ct)],u1(x, t)=P (x − ct)A(x + ct) ;ϮͿ

v0(x, t)=M(x − ct)[1 − B(x + ct)],v1(x, t)=M(x − ct)B(x + ct).

,ĞƌĞǁĞĨŝŶĂůůLJŚĂǀĞƚŚĞƉƌŽĚƵĐƚƐŽĨƚƌĂǀĞůůŝŶŐǁĂǀĞ/ƉƌŽŵŝƐĞĚĞĂƌůŝĞƌ͘EŽƚĞŚŽǁ ƚŚŝƐĂŶƐĂƚnjŝŵƉůŝĞƐƚŚĂƚ

u0(x,
t)
+
u1(x,
t)
=
P
(x
−
ct),
v0(x,
t)
+
v1(x,
t)
=
M(x
+
ct),

ŝ͘Ğ͘ƚŚĞƌŝŐŚƚͲŵŽǀŝŶŐďĂĐƚĞƌŝĂĨŽƌŵĂƚƌƵĞƚƌĂǀĞůůŝŶŐǁĂǀĞƚŽƚŚĞƌŝŐŚƚĂŶĚƚŚĞ ůĞĨƚͲŵŽǀŝŶŐďĂĐƚĞƌŝĂĨŽƌŵĂƚƌƵĞƚƌĂǀĞůůŝŶŐǁĂǀĞƚŽƚŚĞůĞĨƚ͕ũƵƐƚůŝŬĞǁŚĂƚǁĞ ŽďƐĞƌǀĞƵŶĚĞƌƚŚĞŵŝĐƌŽƐĐŽƉĞ͊;ƐĞĞ&ŝŐ͘ϯŵŝĚĚůĞͿ

EŽǁǁŚĂƚĚŽĞƐƚŚŝƐĂŶƐĂƚnjLJŝĞůĚ͍>Ğƚ͛ƐŐŝǀĞŶĂŵĞƐƚŽƚŚĞƚƌĂǀĞůůŝŶŐǁĂǀĞ ĨƌĂŵĞƐξ
=
x
−
ct
ĂŶĚη
=
x
+
ct͘^ƵďƐƟƚƵƟŶŐ;ϮͿŝŶƚŽ;ϭͿŐŝǀĞƐ

−2cP
(ξ)A (η)
=
−γP
(ξ)[1
−
A(η)]
+
λ(P
(ξ))M(η)B(ξ), ;ϯͿ 2cP
(ξ)A (η)
=
γP
(ξ)[1
−
A(η)]
−
λ(M(η))P
(ξ)A(η), 2cM(η)B (ξ)
=
−γM(η)[1
−
B(ξ)]
+
λ(M(η))P
(ξ)A(η), −2cM(η)B (ξ)
=
γM(η)[1
−
B(ξ)]
−
λ(P
(ξ))M(η)B(ξ).

11 WHAT BIOLOGY CAN DO FOR MATHS

&ŝŐƵƌĞϯ͗dŚƌĞĞǀŝĞǁƐŽĨƚŚĞƐĂŵĞƐŝŵƵůĂƚŝŽŶĂƚĂŶĞĂƌůŝĞƌ;ƉĂůĞĐŽůŽƵƌƐͿĂŶĚĂůĂƚĞƌ;ĨƵůů ĐŽůŽƵƌƐͿƚŝŵĞƐƚĞƉ͘>ĞĨƚ͗dŚĞŝŶĚŝǀŝĚƵĂůĚĞŶƐŝƚŝĞƐu0͕u1͕v0͕v1͘DŝĚĚůĞ͗dŚĞĚĞŶƐŝƚLJƚŽƚĂůƐ

u =
u0
+u1
ĂŶĚv
=
v0
+v1͘ZŝŐŚƚ͗dŚĞĚĞŶƐŝƚLJĨƌĂĐƚŝŽŶƐu1/(u0
+u1)
ĂŶĚv1/(u0
+u1)͘

ƚ ƚŚŝƐ ƉŽŝŶƚ ǁĞ ŚĂǀĞŶ͛ƚ ǁŽŶ ŵƵĐŚ͕ ďƵƚ ŶŽǁ Ă ŵŝƌĂĐůĞ ŚĂƉƉĞŶƐ͗ /Ŷ ƚŚĞ ƐĞĐŽŶĚ ĂŶĚ ĨŽƵƌƚŚ ĞƋƵĂƟŽŶ͕ ǁĞ ĐĂŶ ĐĂŶĐĞů P (ξ) ĂŶĚ M(η) ƌĞƐƉĞĐƟǀĞůLJ͕ ŐŝǀŝŶŐ 2cA (η)=γ[1 − A(η)] − λ(M(η))A(η), ;ϰͿ −2cB(ξ)=γ[1 − B(ξ)] − λ(P (ξ))B(ξ), ďĞĂƵƚŝĨƵůůLJĚĞĐŽƵƉůĞĚĞƋƵĂƚŝŽŶƐĨŽƌƚŚĞƚǁŽǁĂǀĞĨƌĂŵĞƐ͘ /ĨǁĞƚŚĞŶĂĚĚƵƉƚŚĞ ĨŝƌƐƚĂŶĚƚŚĞƐĞĐŽŶĚ͕ĂŶĚƚŚĞƚŚŝƌĚĂŶĚƚŚĞĨŽƵƌƚŚĞƋƵĂƚŝŽŶŝŶ;ϯͿ͕ǁĞŐĞƚĨƌŽŵ ďŽƚŚ 0
=
λ(P
(ξ))M(η)B(ξ)
−
λ(M(η))P
(ξ)A(η) P (ξ) M(η) ⇐⇒ = ≡ k, λ(P (ξ))B(ξ) λ(M(η))A(η) ƐŽĂŐĂŝŶƚŚĞξ
ĂŶĚƚŚĞη
ĨƌĂŵĞƐĂƌĞĚĞĐŽƵƉůĞĚ͘^ŽŝŶƚŽƚĂůǁĞŚĂǀĞƚŽƐŽůǀĞƐĞƉĂͲ ƌĂƚĞůLJĨŽƌƚŚĞξ
ĂŶĚη
ĨƌĂŵĞĂŶKĐŽƵƉůĞĚƚŽĂŶĂůŐĞďƌĂŝĐĞƋƵĂƚŝŽŶ͕ǁŚĞƌĞƚŚĞ ŽŶůLJĐŽŶŶĞĐƚŝŽŶďĞƚǁĞĞŶƚŚĞŵŝƐƚŚĞĐŽŶƐƚĂŶƚk͘EŽƚĞƚŚĂƚƚŚĞƌĞŝƐĂŐĂŝŶƐŽŵĞ ƐŝŵŝůĂƌŝƚLJƚŽƚŚĞƐĞƉĂƌĂƚŝŽŶŽĨǀĂƌŝĂďůĞƐĂŶƐĂƚnjŽŶĞƵƐĞƐƚŽƐŽůǀĞƚŚĞǁĂǀĞĞƋƵĂͲ ƚŝŽŶ͘

tŚĂƚŝƐƌĞĂůůLJƐƵƌƉƌŝƐŝŶŐŝƐƚŚĂƚǁĞĚŝĚŶŽƚĚĞĐŽƵƉůĞƚŚĞƌŝŐŚƚĨƌŽŵƚŚĞůĞŌ ŵŽǀŝŶŐĚĞŶƐŝƚŝĞƐ͊/ĨǁĞŝŶƐƉĞĐƚĞ͘Ő͘;ϰͿǁĞƐĞĞƚŚĂƚǁĞŚĂǀĞĐŽƵƉůŝŶŐďĞƚǁĞĞŶ ƚŚĞƐƵŵŽĨƚŚĞůĞĨƚͲŵŽǀŝŶŐďĂĐƚĞƌŝĂM(η)
ĂŶĚƚŚĞĨƌĂĐƚŝŽŶŽĨƚŚĞƌŝŐŚƚͲŵŽǀŝŶŐ ďĂĐƚĞƌŝĂƚŚĂƚĐĂŶƌĞǀĞƌƐĞA(η)
ĂŶĚǀŝĐĞǀĞƌƐĂ;ƐĞĞ&ŝŐ͘ϯͿ͘tĞĐŽƵůĚŶŽǁĐŽŶƚŝŶƵĞ ĂŶĂůLJƐŝŶŐƚŚĞƌĞƐƵůƚŝŶŐĞƋƵĂƚŝŽŶƐ͕ǁŚŝĐŚůĞĂĚƐƚŽƐŽŵĞďĞĂƵƚŝĨƵůŐĞŽŵĞƚƌŝĐ ĂƌŐƵŵĞŶƚƐ͕ďƵƚ/ǁŝůůůĞĂǀĞƚŚĂƚƐƚŽƌLJĨŽƌĂŶŽƚŚĞƌĚĂLJ͘

ŝŽůŽŐŝĐĂůůLJƚŚĞŵŽĚĞůŝƐƵƐĞĨƵů͕ďĞĐĂƵƐĞŝƚĐĂŶƌĞĐĂƉŝƚƵůĂƚĞƚŚĞďĞŚĂǀŝŽƵƌŝŶƚŚĞ ďĂĐƚĞƌŝĂůƐǁĂƌŵƐ͘/ƚƐĂLJƐƚŚĂƚǁŚĞŶƚŚĞǁĂǀĞƐĐŽůůŝĚĞƚŚĞLJĚŽŶ͛ƚĐŚĂŶŐĞĞĂĐŚ

12 DR ANGELIKA MANHART

ŽƚŚĞƌ͛ƐƐŚĂƉĞ͕ďƵƚƚŚĞLJŵŽĚŝĨLJĞĂĐŚŽƚŚĞƌ͛ƐĐŽŵƉŽƐŝƚŝŽŶŝŶƚĞƌŵƐŽĨƌĞǀĞƌƐŝďůĞĂŶĚ ŶŽŶͲƌĞǀĞƌƐŝďůĞďĂĐƚĞƌŝĂ͘

DĂƚŚĞŵĂƚŝĐĂůůLJ͕ƚŚŝƐŵŽĚĞůůĞĚƚŽƚŚĞĚŝƐĐŽǀĞƌLJŽĨƚŚĞƐĞƋƵŝƚĞƵŶƵƐƵĂů͕ďƵƚ ǀĞƌLJŝŶƚĞƌĞƐƚŝŶŐǁĂǀĞƉĂƚƚĞƌŶƐ͘ dŽŵĞƚŚŝƐĚĞŵŽŶƐƚƌĂƚĞƐƌĞĂůůLJǁĞůůŚŽǁ͕ƐŽŵĞͲ ƚŝŵĞƐƵŶĞdžƉĞĐƚĞĚůLJ͕ŵŽĚĞůůŝŶŐďŝŽůŽŐLJĐĂŶůĞĂĚƚŽŶĞǁĂŶĚŝŶƚĞƌĞƐƚŝŶŐŵĂƚŚƐ͘

ZĞĨĞƌĞŶĐĞƐ

΀ϭ΁ ͘ DĂŶŚĂƌƚ͕ ŽƵŶƚĞƌͲƉƌŽƉĂŐĂƟŶŐ ǁĂǀĞƐ ŝŶ Ă ƐǁĂƌŵ ŵŽĚĞů ǁŝƚŚ ŵĞŵŽƌLJ͘ :ŽƵƌͲ ŶĂů ŽĨ DĂƚŚĞŵĂƟĐĂů ŝŽůŽŐLJ ;ϮϬϭϴͿ ŚƩƉƐ͗ͬͬĚŽŝ͘ŽƌŐͬϭϬ͘ϭϬϬϳͬƐϬϬϮϴϱͲϬϭϴͲϭϮϴϳͲ dž

΀Ϯ΁ W͘ ĞŐŽŶĚ͕ ͘ DĂŶŚĂƌƚ͕ ,͘ zƵ͕ Ŷ ĂŐĞͲƐƚƌƵĐƚƵƌĞĚ ĐŽŶƟŶƵƵŵ ŵŽĚĞů ĨŽƌ ŵLJdžŽďĂĐƚĞƌŝĂ͘ DĂƚŚĞŵĂƟĐĂů DŽĚĞůƐ Θ DĞƚŚŽĚƐ ŝŶ ƉƉůŝĞĚ ^ĐŝĞŶĐĞƐ ;ϮϬϭϴͿ Ϯϴ;ϵͿ͗ϭϳϯϳʹϭϳϳϬ

13 4th FLOOR OPENING

ϰƚŚ&ůŽŽƌKƉĞŶŝŶŐ dŚĞŶĞǁϰƚŚŇŽŽƌƉƌŽǀŝĚĞƐŽĸĐĞƐĨŽƌϭϲ ƐƚĂī͕ĂƚƵƚŽƌŝĂůͬŵĞĞƟnŐƌŽŽŵǁŝƚŚĂƵĚŝŽͲ ϯϬƚŚKĐƚŽďĞƌϮϬϭϵ ǀŝƐƵĂůĨĂĐŝůŝƟĞƐ͕ĂƐƚĂīĂŶĚWŚƐƚƵĚĞŶƚƐŽĐŝĂů ƚĂƉĂƌƚLJŽŶϯϬƚŚKĐƚŽďĞƌϮϬϭϵĂƩĞŶĚĞĚ ƌŽŽŵ͕ĂŶĚƐƉĂĐĞĨŽƌϮϬWŚƐƚƵĚĞŶƚƐ͘ƚƚŚĞ ďLJƚŚĞWƌŽǀŽƐƚWƌŽĨĞƐƐŽƌDŝĐŚĂĞůƌƚŚƵƌ͕ĂŶĚ ƐĂŵĞƟŵĞ͕ƚŚĞƵƉƉĞƌŇŽŽƌƐǁĞƌĞŝŵƉƌŽǀĞĚ ĞĂŶŽĨƚŚĞ&ĂĐƵůƚLJŽĨDĂƚŚĞŵĂƟĐĂůĂŶĚWŚLJƐͲ ǁŝƚŚŶĞǁŇŽŽƌŝŶŐ͕ƐŝŐŶĂŐĞ͕ƌĞͲƉĂŝŶƟŶŐĂŶĚ ŝĐĂů^ĐŝĞŶĐĞƐWƌŽĨĞƐƐŽƌ/ǀĂŶWĂƌŬŝŶ͕ƚŚĞĞƉĂƌƚͲ ĚŝƐƉůĂLJŽĨƉƌŽŵŝŶĞŶƚŵĂƚŚĞŵĂƟĐĂů͚ĂƌƚǁŽƌŬ͛ ŵĞŶƚĐĞůĞďƌĂƚĞĚƚŚĞŽĸĐŝĂůŽƉĞŶŝŶŐŽĨƚŚĞϰth ĂĚŽƌŶŝŶŐƚŚĞǁĂůůƐĂŶĚƐƚĂŝƌĐĂƐĞƐ͘ &ůŽŽƌŽĨϮϱ'ŽƌĚŽŶ^ƚƌĞĞƚ͘ůŝnjĂďĞƚŚƌŝƚĐŚůĞLJ͕ ĂŶĂůƵŵŶĂŽĨh>DĂƚŚĞŵĂƟĐƐ͕ŐĂǀĞĂƐŚŽƌƚ dŚĞ,ĞĂĚŽĨĞƉĂƌƚŵĞŶƚWƌŽĨĞƐƐŽƌ,ĞůĞŶ ƚĂůŬĂŶĚĐƵƚƚŚĞƌŝďďŽŶƚŽĨŽƌŵĂůůLJŽƉĞŶƚŚĞ tŝůƐŽŶ͕ĞƉĂƌƚŵĞŶƚĂůDĂŶĂŐĞƌ,ĞůĞŶ,ŝŐŐŝŶƐ ŶĞǁƐƉĂĐĞ͘dŚĞƉƌŽǀŝƐŝŽŶŽĨƚŚŝƐŶĞǁĂŶĚ ĂŶĚĞƉƵƚLJĞƉĂƌƚŵĞŶƚĂůDĂŶĂŐĞƌ^ŽŚĞŶŝ ŝĚĞĂůůLJůŽĐĂƚĞĚƐƉĂĐĞƐƵŝƚĂďůĞĨŽƌƚĞĂĐŚŝŶŐ͕ &ƌĂŶĐŝƐĂůŽŶŐǁŝƚŚĐŽůůĞĂŐƵĞƐŝŶh>ƐƚĂƚĞƐ ƌĞƐĞĂƌĐŚĂŶĚĐŽůůĂďŽƌĂƟŽŶŝŶŵĂƚŚĞŵĂƟĐƐŝŵͲ ĐĂŶƚĂŬĞŐƌĞĂƚĐƌĞĚŝƚŝŶƚŚĞŝƌůĞĂĚĞƌƐŚŝƉ͕ ŵĞĚŝĂƚĞůLJďĞůŽǁƚŚĞĞƉĂƌƚŵĞŶƚ͛ƐůŽŶŐͲƚĞƌŵ ĚĞƐŝŐŶĂŶĚŵĂŶĂŐĞŵĞŶƚŽĨƚŚŝƐƚƌĂŶƐĨŽƌŵĂƟǀĞ ŽĐĐƵƉĂŶĐLJŽĨŇŽŽƌƐϱͲϴƌĞĂůŝƐĞƐĂůŽŶŐͲŚĞůĚ ƉƌŽũĞĐƚ͘dŚĞŝƌĞīŽƌƚƐŚĂǀĞůĞĚƚŽĂƐƉĂĐĞ ĚƌĞĂŵ͘^ŽŵĞƐĞŶŝŽƌĐŽůůĞĂŐƵĞƐĞǀĞŶĐůĂŝŵƚŚĞ ǁŝƚŚĂŐĞŶƵŝŶĞƐĞŶƐĞŽĨŝĚĞŶƟƚLJ͕ƐƵƉƉŽƌƟǀĞ ŝĚĞĂŽĨĞdžƉĂŶĚŝŶŐƚŽŽƚŚĞƌŇŽŽƌƐŽĨϮϱ'ŽƌĚŽŶ ŽĨƚĞĂĐŚŝŶŐ͕ƌĞƐĞĂƌĐŚĂŶĚĐŽůůĂďŽƌĂƟŽŶĂŶĚ ^ƚƌĞĞƚǁĂƐŵŽŽƚĞĚĂƐĞĂƌůLJƚŚĞϭϵϲϬƐ͊ ǁŚŝĐŚĞŶŚĂŶĐĞƐƚŚĞĞdžƉĞƌŝĞŶĐĞŽĨƐƚƵĚĞŶƚƐ͕ dŚĞŶĞĂƌĚŽƵďůŝŶŐŽĨƐƚĂīĂŶĚƌĞƐĞĂƌĐŚĞƌƐ ƐƚĂīĂŶĚǀŝƐŝƚŽƌƐ͘ ƐŝŶĐĞϮϬϭϬ͕ďƵŝůƚŽŶƐƵĐĐĞƐƐĨƵůƌĞĐƌƵŝƚŵĞŶƚŽĨ ŚŝŐŚůLJƋƵĂůŝĮĞĚƵŶĚĞƌŐƌĂĚƵĂƚĞƐĂŶĚƌĞƐĞĂƌĐŚ ZŽďďDĐŽŶĂůĚ͕DĂƌĐŚϮϬϮϬ ŐƌĂŶƚƐƵĐĐĞƐƐĞƐ͕ŵĂĚĞƚŚĞƉƌĞǀŝŽƵƐĂĐĐŽŵŵŽͲ ĚĂƟŽŶƵŶƐƵƐƚĂŝŶĂďůĞ͘^ĞǀĞƌĂůďƵƐŝŶĞƐƐĐĂƐĞƐ ůĂƚĞƌĂŶĚǁŝƚŚƚŚĞƐƚƌŽŶŐƐƵƉƉŽƌƚŽĨWƌŽĨĞƐƐŽƌ WĂƌŬŝŶĂŶĚ͕ĐƌƵĐŝĂůůLJ͕ǁŝƚŚƚŚĞŐŽŽĚǁŝůůŽĨƚŚĞ h>^ƚƵĚĞŶƚƐ͛hŶŝŽŶ͕ƚŚĞƉƌĞǀŝŽƵƐŽĐĐƵƉŝĞƌƐ ŽĨƚŚĞϰthŇŽŽƌ͕ǁŚŽŚĂĚƚŚĞŝƌŶĞŝŐŚďŽƵƌŝŶŐ ƐƉĂĐĞƐŝŵƉƌŽǀĞĚĂƐƉĂƌƚŽĨƚŚĞƐĂŵĞƉƌŽũĞĐƚ͕ ƚŚĞƉƌŽũĞĐƚďĞĐĂŵĞƌĞĂůŝƚLJ͘ tŽƌŬƐŝŶǀŽůǀŝŶŐƌĞĨƵƌďŝƐŚŵĞŶƚĂŶĚƌĞďƵŝůĚŝŶŐ ŽĨƚŚĞϰƚŚŇŽŽƌĐŽŵŵĞŶĐĞĚŝŶƐƉƌŝŶŐϮϬϭϵ ĂŶĚǁĞƌĞĐŽŵƉůĞƚĞĚďĞĨŽƌĞƚŚĞƐƚĂƌƚŽĨƚŚĞ ϮϬϭϵͲϮϬĂĐĂĚĞŵŝĐLJĞĂƌ͘ &ƌŽŵ>ĞŌ͗WƌŽǀŽƐƚWƌŽĨĞƐƐŽƌDŝĐŚĂĞůƌƚŚƵƌ͕ WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ͕ůŝnjĂďĞƚŚƌŝƚĐŚůĞLJĂŶĚ ĞĂŶŽĨƚŚĞDW^&ĂĐƵůƚLJWƌŽĨĞƐƐŽƌ/ǀĂŶWĂƌŬŝŶ

14 4th FLOOR OPENING

KĸĐŝĂůĐƵƫŶŐŽĨƚŚĞƌŝďďŽŶŽŶƚŚĞϰƚŚŇŽŽƌ

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WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶĂŶĚŐƵĞƐƚƐďĞĨŽƌĞƚŚĞƌŝďďŽŶĐƵƫŶŐ

/ŵĂŐĞƌĞĚŝƚͲůĞũĂŶĚƌŽ^ĂůŝŶĂƐ>ŽƉĞnjĨƌŽŵh>ŝŐŝƚĂůDĞĚŝĂ

15 ICDEA 2019

25th International Conference for Difference Equations and Applications

UCL, June 24 – 28, 2019.

Over 120 researchers from over 35 countries participated in the 2019 International Conference for Difference Equations and Applications, hosted by the UCL Mathematics Department.

This was the 25th anniversary of the meeting of the International Society of Difference Equations (ISDE). Since its conception at Trinity University in Texas in 1994, the annual event has been hosted worldwide, including in Germany, Romania, Japan, Poland, China, Oman, Spain, Latvia, Canada, Chile, and many other countries.

There was a very busy program with 8 plenary talks and over 90 contributed talks spread over 4½ days. The plenary speakers were Paul Glendinning (UK), Horst Thieme (USA), Adina Luminiԑa Sasu (Romania), Andrey Shilnikov (USA), Ewa Schmeidel (Poland), Patricia Wong (Singapore), Mats Gyllenberg (Finland) and Mihály Pituk (Hungary).

In addition to the plenary and contributed talks, for the first time in the history of the conference we ran a series of tutorial style lectures, including from our own Prof Rod Halburd who spoke on Discrete Integrable Systems, and Prof Steven Bishop who spoke on Agent-based Modelling.

There was a huge variety of topics covered at the conference. Difference equations pervade Mathematics and we covered Mihály Pituk presenting his plenary lecture Asymptotic Behavior of the chaos, bifurcation theory, renormalization theory, exponential Solutions of Linear Difference dichotomies, dynamical systems on timescales, monotone Equations. systems theory, and many other areas.

Applications ranged from ecology, neuroscience and epidemiology to economics and control theory. Thanks to Rod there were also special sessions of more of a pure flavour

16 ICDEA 2019

organized for Nevanlinna Theory and Discrete Integrable Dynamics.

Several prizes were awarded at the conference. The best student presentation was awarded to Tim Russell (Royal Holloway, UK) for his talk `Difference equations in population genetics’, and best student poster was awarded to Mauricio Diaz (Bio-Bio, Chile) for his `Relation between Sensitive systems and MDS using Furstenberg family’. The 2018 prize for the best paper in Journal of Difference Equations and Applications was awarded to R. Bouyekhf & L. T. Gruyitch for their paper `An alternative approach for stability analysis of discrete time nonlinear dynamical systems’, JDEA Vol 24(1) (2018).

The society’s prestigious prize, the Bernd Aulbach Prize, which is bestowed biennially by the ISDE for significant contributions to the areas of difference equations and/or discrete dynamical systems, was presented to Professor Allan Peterson from Nebraska University.

As is traditional for the ICDEA, there was a conference Professor Allan Peterson (Nebraska) receiving the Bernd Aulbach Prize from excursion. Delegates took a Thames Clipper trip to Professors Elaydi and Bohner. Greenwich, where through a guided tour they visited well- known attractions such as the National Maritime Museum, the Royal Observatory, and the Cutty Sark.

The weather was kind to us, and we finished the day with a trip across the Thames on the Emirates Air Line and enjoyed dinner of stone-baked pizzas in a converted Double Decker bus in Docklands, before taking the River Cruiser back to the Embankment.

On the penultimate night, the conference dinner was held at the Imperial Hotel in Russell Square. Professor Saber Elaydi, who organised the first ICDEA meeting in Trinity University, and who is now President of ISDE, treated diners to a special powerpoint presentation to celebrate 25 years of the conference. The ICDEA2019 Dinner at the Imperial Hotel Any international conference of this size takes a fair amount of organization. So, it is entirely appropriate to wrap up with thanks to all those that contributed to the success of ƚŚĞŵĞĞƚŝŶŐ͘dŚĂƚŝŶĐůƵĚĞƐZŽĚĂŶĚ^ƚĞǀĞŶĂƐĨĞůůŽǁŽƌŐĂŶŝƐĞƌƐ͕ĂŶĚĞůŐŝŶ^ĞLJŵĞŶŽŒůƵ͕ Jason Vittis and Jordan Hofmann who helped with the day-to-day running of the conference, and finally Soheni Francis who patiently watched over the whole event, booked and orchestrated all the refreshments, and much more, and prompted or rescued us where necessary.

Finally, we would like to acknowledge the generous support of our sponsors, the UCL Mathematics Department and the Taylor & Francis group.

Steve Baigent, Chair of Organising Committee

17 INAUGURAL LECTURE - PROFESSOR YIANNIS PETRIDIS

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ůŽŐ10 d ͘ dŚŝƐǁĂƐĂůůĚŝƐĐƵƐƐĞĚƚŽŵŽƚŝǀĂƚĞĂƌĞƐƵůƚŽĨzŝĂŶŶŝƐƚŽŐĞƚŚĞƌǁŝƚŚŚŝƐ ůŽŶŐͲƚŝŵĞĐŽůůĂďŽƌĂƚŽƌDŽƌƚĞŶ^͘ZŝƐĂŐĞƌ͖ŝŶƐƚĞĂĚŽĨƐƚƵĚLJŝŶŐůŽŐĂƌŝƚŚŵƐ ŽĨƉŽƐŝƟǀĞƌĞĂůŶƵŵďĞƌƐ͕ƚŚĞLJƐƚƵĚLJƚŚĞĚŝƐĐƌĞƚĞůŽŐĂƌŝƚŚŵŽŶĨƌĞĞŐƌŽƵƉƐ͘ &ƌŽŵĂƉĂŝƌŽĨŐĞŶĞƌĂƚŽƌƐA,
B
ƚŽŐĞƚŚĞƌǁŝƚŚƚŚĞŝƌŝŶǀĞƌƐĞƐA−1,
B−1͕ŽŶĞ ĨŽƌŵƐǁŽƌĚƐƐƵĐŚĂƐg
=
A−1BA2B2A3͘dŚĞǁŽƌĚůĞŶŐƚŚǁů(g)
ŽĨƐƵĐŚĂ ǁŽƌĚŝƐƚŚĞƐƵŵŽĨĂďƐŽůƵƚĞǀĂůƵĞƐŽĨƚŚĞĞdžƉŽŶĞŶƚƐ͖ŝŶƚŚŝƐĐĂƐĞ͕ǁů(g)
=
1 + 1 + 2 + 2 + 3 = 9 ( )









͘dŚĞĚŝƐĐƌĞƚĞůŽŐĂƌŝƚŚŵůŽŐA g
ǁŝƚŚƌĞƐƉĞĐƚƚŽƚŚĞ ( ) = ŐĞŶĞƌĂƚŽƌA
ŝƐƚŚĞƐƵŵŽĨƚŚĞĞdžƉŽŶĞŶƚƐŝŶǀŽůǀŝŶŐA͖ŝŶƚŚŝƐĐĂƐĞ͕ůŽŐA g
−1+2+3 = 4͘ dŚĞ ƌĞƐƵůƚ ŽĨ WĞƚƌŝĚŝƐʹZŝƐĂŐĞƌ ŝƐ ƚŚĂƚ ƚŚĞ ĚŝƐĐƌĞƚĞ ůŽŐĂƌŝƚŚŵ ŽďĞLJ Ă ŶŽƌŵĂů ĚŝƐƚƌŝďƵƟŽŶ͗   g : (g) ≤ x, √ 1 (g) ∈ [a, b]  η ǁů ůŽŐA b 2 ǁů(g) 1 − u ůŝŵ = √ e 2 du. →∞ { : ( ) ≤ } x η g ǁů g x 2π a ƚƚŚŝƐƉŽŝŶƚ͕zŝĂŶŶŝƐ͛ƐƚĂůŬĚĞǀŝĂƚĞĚƐŚĂƌƉůLJŝŶĂǁŝůĚůLJĚŝĨĨĞƌĞŶƚ ĚŝƌĞĐƚŝŽŶ͗ŚLJƉĞƌďŽůŝĐŐĞŽŵĞƚƌLJ͘ dŚŝƐŝƐĂŐĞŽŵĞƚƌŝĐƐĞƚƚŝŶŐŝŶǁŚŝĐŚ ƵĐůŝĚ͛ƐƉĂƌĂůůĞůƉŽƐƚƵůĂƚĞĨĂŝůƐ͕ƐŽƚŚĂƚŐŝǀĞŶĂůŝŶĞĂŶĚĂƉŽŝŶƚ͕ƚŚĞƌĞ ĞdžŝƐƚĂŶŝŶĨŝŶŝƚƵĚĞŽĨ͞ƉĂƌĂůůĞů͟ůŝŶĞƐƉĂƐƐŝŶŐƚŚƌŽƵŐŚƚŚĂƚƉŽŝŶƚ͘  ƉĂƌƚŝĐƵůĂƌŵŽĚĞůŽĨƚŚŝƐŐĞŽŵĞƚƌŝĐƐĞƚƚŝŶŐŝƐƚŚĞƵƉƉĞƌŚĂůĨͲƉůĂŶĞŝŶƚŚĞ ĐŽŵƉůĞdžƉůĂŶĞ͕ŝŶǁŚŝĐŚ͞ƐƚƌĂŝŐŚƚůŝŶĞƐ͟ĂƌĞĞŝƚŚĞƌǀĞƌƚŝĐĂůůŝŶĞƐŽƌŐƌĞĂƚ ƐĞŵŝĐŝƌĐůĞƐǁŚŽƐĞĐĞŶƚƌĞƐůŝĞ ŽŶ ƚŚĞ ƌĞĂů ůŝŶĞ͘ dŚŝƐ ŝƐ ƚŚĞ ǁŽƌůĚ ŝŶ ǁŚŝĐŚ ŵŽĚƵůĂƌ ƐLJŵďŽůƐ ůŝǀĞ͕ ĂƌĞƐĞĂƌĐŚƚŽƉŝĐƚŚĂƚzŝĂŶŶŝƐŚĂƐǁŽƌŬĞĚ ŽŶĨŽƌƚŚĞƉĂƐƚĨŝĨƚĞĞŶLJĞĂƌƐ͘

18 INAUGURAL LECTURE - PROFESSOR YIANNIS PETRIDIS

DŽĚƵůĂƌƐLJŵďŽůƐĐĂŶďĞƚŚŽƵŐŚƚŽĨĂƐŝŶƚĞŐƌĂůƐĂůŽŶŐĐĞƌƚĂŝŶǀĞƌƚŝĐĂů ůŝŶĞƐŝŶƚŚĞƵƉƉĞƌŚĂůĨͲƉůĂŶĞŽĨĂƉĂƌƚŝĐƵůĂƌƚLJƉĞŽĨĨƵŶĐƚŝŽŶĐĂůůĞĚĂ ŵŽĚƵůĂƌĨŽƌŵ͖ƚŚĞƐĞƐƉĞĐŝĂůĨƵŶĐƚŝŽŶƐĨĞĂƚƵƌĞƉƌŽŵŝŶĞŶƚůLJŝŶŶĚƌĞǁ tŝůĞƐ͛ƐƉƌŽŽĨŽĨ&ĞƌŵĂƚ͛ƐůĂƐƚƚŚĞŽƌĞŵ͘ dŚĞǀĞƌƚŝĐĂůůŝŶĞƐŝŶǀŽůǀĞĚĂƌĞ ƚŚŽƐĞƚŚĂƚŝŶƚĞƌƐĞĐƚƚŚĞƌĞĂůůŝŶĞĂƚƌĂƚŝŽŶĂůƉŽŝŶƚƐa/c͘ /ŶĐĞůĞďƌĂƚĞĚ ũŽŝŶƚǁŽƌŬǁŝƚŚDŽƌƚĞŶ^͘ZŝƐĂŐĞƌ͕zŝĂŶŶŝƐƐƚƵĚŝĞĚƚŚĞďĞŚĂǀŝŽƵƌŽĨ ŵŽĚƵůĂƌƐLJŵďŽůƐǁŚĞŶĂǀĞƌĂŐĞĚŽǀĞƌƚŚĞĚĞŶŽŵŝŶĂƚŽƌƐc͖ƚŚĞLJƐŚŽǁĞĚ ƚŚĂƚƚŚĞƐĞŵŽĚƵůĂƌƐLJŵďŽůƐ͕ũƵƐƚůŝŬĞƚŚĞĚŝƐĐƌĞƚĞůŽŐĂƌŝƚŚŵ͕ŽďĞLJĂ ŶŽƌŵĂůĚŝƐƚƌŝďƵƚŝŽŶ͘

 WƌŽĨĞƐƐŽƌzŝĂŶŶŝƐWĞƚƌŝĚŝƐ

tƌŝƚĞͲƵƉƉƌŽǀŝĚĞĚďLJWĞƚĞƌ,ƵŵƉŚƌŝĞƐ /ŵĂŐĞƌĞĚŝƚͲDĂƌLJ,ŝŶŬůĞLJĨƌŽŵh>ŝŐŝƚĂůDĞĚŝĂ

19 SUSAN BROWN DAY - INTERNATIONAL WOMEN'S DAY

^ƵƐĂŶƌŽǁŶĂLJʹ/ŶƚĞƌŶĂƟŽŶĂů tŽŵĞŶ͛ƐĂLJ

ϴƚŚDĂƌĐŚϮϬϭϵ

KŶ/ŶƚĞƌŶĂƟŽŶĂůtŽŵĞŶ͛ƐĂLJ͕ƚŚĞ ĞƉĂƌƚŵĞŶƚŽĨDĂƚŚĞŵĂƟĐƐůĂƵŶĐŚĞĚ^ƵƐĂŶ ƌŽǁŶĂLJ͕ŶĂŵĞĚŝŶŚŽŶŽƵƌŽĨƚŚĞĮƌƐƚ ĨĞŵĂůĞWƌŽĨĞƐƐŽƌĂƉƉŽŝŶƚĞĚŚĞƌĞ͘dŚĞƌĞǁĞƌĞ ĮǀĞƐƉĞĂŬĞƌƐůŝŶĞĚƵƉ͕ĨƌŽŵǀĂƌŝŽƵƐĂƌĞĂƐ ŽĨƚŚĞĚĞƉĂƌƚŵĞŶƚ͕ĞĂĐŚƉƌĞƐĞŶƟŶŐŽŶƚŚĞ ƚŚĞŵĞŽĨ͚tŽŵĞŶtŚŽ/ŶƐƉŝƌĞhƐ͛͘ ƌ<ŝŵDŽŽƌĞ

dŚĞĮƌƐƚƐƉĞĂŬĞƌǁĂƐ<ĂƚĞ&ƌĂƐĞƌ͕^ĞŶŝŽƌ hŶĚĞƌŐƌĂĚƵĂƚĞƐƚƵĚĞŶƚsŝǀŝĞŶŶĞ>ĞĞĐŚ ^ƚĂĸŶŐKĸĐĞƌ͕ǁŚŽƚĂůŬĞĚĂďŽƵƚdŝŶĂ&ĞLJ ƐƉŽŬĞĂďŽƵƚŶŶŝůďĞƌƐ͕ĂƚĞdžƟůĞĂƌƟƐƚǁŚŽ ĂƐĂŶĞdžĂŵƉůĞŽĨƚŚĞĞdžƉĞƌŝĞŶĐĞŽĨďĞŝŶŐĂ ƌĞĂƉƉƌŽƉƌŝĂƚĞĚĂƚƌĂĚŝƟŽŶĂůůLJĨĞŵŝŶŝŶĞĐƌĂŌ ǁŽŵĂŶŝŶĂƉĂƌƟĐƵůĂƌůLJŝŶĂŵĂůĞͲĚŽŵŝŶĂƚĞĚ ĂƐĂƌĂĚŝĐĂůĞdžƉƌĞƐƐŝŽŶŽĨŵŽĚĞƌŶĂƌƚĂŶĚ ǁŽƌŬƉůĂĐĞ͘ ĚĞƐŝŐŶ͘WĂƌĂůůĞůƐǁĞƌĞĚƌĂǁŶďĞƚǁĞĞŶŚĞƌ ŐĞŽŵĞƚƌŝĐĚĞƐŝŐŶƐĂŶĚƚŚĞŵĂƚŚĞŵĂƟĐĂů ƉĂƩĞƌŶƐƚŚĂƚƵŶĚĞƌƉŝŶƚŚĞŵ͘

ƌ<ŝŵDŽŽƌĞ͕ƉŽƐƚĚŽĐƚŽƌĂůƌĞƐĞĂƌĐŚĞƌ͕ƚŚĞŶ ĚĞůŝǀĞƌĞĚĂƉƌĞƐĞŶƚĂƟŽŶŽŶůĞŐĞŶĚĂƌLJĂƵƚŚŽƌ sŝǀŝĞŶŶĞ>ĞĞĐŚ ŐĂƚŚĂŚƌŝƐƟĞĂŶĚŚĞƌĞdžƚƌĂŽƌĚŝŶĂƌLJůŝĨĞ͘ <ŝŵŶŽƚĞĚƚŚĂƚĚĞƐƉŝƚĞŐĂƚŚĂ͛ƐƐĞŶƐĂƟŽŶĂů WŽƐƚŐƌĂĚƵĂƚĞƐƚƵĚĞŶƚĂǀŝĚ^ŚĞĂƌĚĨŽůůŽǁĞĚ͕ ƐƵĐĐĞƐƐĂƐĂŶĂƵƚŚŽƌ͕ďĞŝŶŐƚŚŝƌĚďĞŚŝŶĚ ƚĞůůŝŶŐƚŚĞƐƚŽƌLJŽĨDĂƌLJůůŝƐ͕ĂƉŝŽŶĞĞƌŝŶŐ ŽŶůLJ^ŚĂŬĞƐƉĞĂƌĞĂŶĚƚŚĞŝďůĞŝŶƚĞƌŵƐŽĨ ĂǀŝĂƚŽƌǁŝƚŚƚŚĞŝƌdƌĂŶƐƉŽƌƚƵdžŝůŝĂƌLJʹ ƉƵďůŝƐŚŝŶŐŶƵŵďĞƌƐ͕ƐŚĞĂůƐŽĞdžƉĞƌŝĞŶĐĞĚ ǁŚŽĂůƐŽŚĂƉƉĞŶĞĚƚŽďĞŚŝƐŐƌĞĂƚĂƵŶƚ͘ ǁŚĂƚǁĞŵŝŐŚƚƌĞĐŽŐŶŝƐĞĂƐŝŵƉŽƐƚĞƌ dŚĞĨĂŵŝůŝĂůĐŽŶŶĞĐƟŽŶĂůůŽǁĞĚŚŝŵƚŽƚĞůů ƐLJŶĚƌŽŵĞ͕ĂƉŚĞŶŽŵĞŶŽŶƚŚĂƚƉĞƌŵĞĂƚĞƐ ĂĐĂƉƟǀĂƟŶŐƐĞƌŝĞƐŽĨĂŶĞĐĚŽƚĞƐŽŶƚŚĞ ĂĐĂĚĞŵŝĂǁŝƚŚŚĞŝŐŚƚĞŶĞĚƉƌĞǀĂůĞŶĐĞŝŶ astonishing role that Mary played in the ǁŽŵĞŶ͘ ^ĞĐŽŶĚtŽƌůĚtĂƌ͕ĂŶĚŚŽǁƐŚĞĐŽŶƟŶƵĞĚƚŽ ůŝǀĞǁŝƚŚƚŚĞƐĂŵĞŝŶƚƌĞƉŝĚƉĂƐƐŝŽŶĨŽƌŇLJŝŶŐ

20 SUSAN BROWN DAY – INTERNATIONAL WOMEN'S DAY

into her centennial years.

ĂǀŝĚ^ŚĞĂƌĚ

ůŽƐŝŶŐŽīƚŚĞĚĂLJ͕WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ ƉĂŝĚƚƌŝďƵƚĞƚŽWƌŽĨĞƐƐŽƌ^ƵƐĂŶƌŽǁŶ͘^ŚĞ ƐƉŽŬĞŽĨ^ƵƐĂŶ͛ƐƌĞƉƵƚĂƟŽŶĂƐĂůĞĂĚŝŶŐ ĂĐĂĚĞŵŝĐ͕ďƵƚĂůƐŽŽĨŚĞƌŽƵƚƐƚĂŶĚŝŶŐ ĐŽŵŵŝƚŵĞŶƚƚŽƚĞĂĐŚŝŶŐ͕ďĞŝŶŐĂŶ &ƌŽŵƚŚĞůĞŌ͗<ĂƚĞ&ƌĂƐĞƌ͕WƌŽĨĞƐƐŽƌ,ĞůĞŶ ŝŶƐƉŝƌĂƟŽŶĂůĮŐƵƌĞĨŽƌďŽƚŚƐƚƵĚĞŶƚƐĂŶĚ tŝůƐŽŶ͕ƌ<ŝŵDŽŽƌĞ͕sŝǀŝĞŶŶĞ>ĞĞĐŚ͕ĂǀŝĚ ĨĞůůŽǁƐƚĂī͘,ĞůĞŶĂůƐŽƌĞĐĂůůĞĚŵĞĞƟŶŐ Sheard ^ƵƐĂŶĂƚŚĞƌŝŶƚĞƌǀŝĞǁ͕ĂŶĚƚŚĞĨĂĐƚƚŚĂƚ ĂǁŽŵĂŶǁĂƐĂďůĞƚŽŚŽůĚƐƵĐŚĂƐĞŶŝŽƌ ƉŽƐŝƟŽŶĚĞǀĞůŽƉĞĚĂƐĞŶƐĞƚŚĂƚǁĞŚŽƉĞ ĐŽŶƟŶƵĞƐĨŽƌĂůůǁŽŵĞŶŝŶŵĂƚŚĞŵĂƟĐƐʹ ͞/ďĞůŽŶŐŚĞƌĞ͘͟

tŽŵĞŶŝŶĞƉĂƌƚŵĞŶƚŽĨDĂƚŚĞŵĂƟĐƐ

WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ

/ŵĂŐĞĐƌĞĚŝƚͲ^Ăŵ,ŽƉŬŝŶƐ

21 STEM for BRITAIN

^dDĨŽƌZ/d/E ŚŝŐŚůŝŐŚƚĞĚĂŶĚƐŚŽǁĐĂƐĞĚƚŚĞďƌĞĂĚƚŚ ŽĨĐƵƌƌĞŶƚǁŽƌůĚĐŚĂŶŐŝŶŐ^dDƌĞƐĞĂƌĐŚ ϭϯƚŚDĂƌĐŚϮϬϭϵ ;^ĐŝĞŶƟĮĐ͕dĞĐŚŶŽůŽŐŝĐĂů͕ŶŐŝŶĞĞƌŝŶŐ͕ DĂƚŚĞŵĂƟĐĂůͿ͘/ƚǁĂƐĂŶĞǀĞŶƚƚŚĂƚĂĚĚĞĚ ƐŽŵĞĨƵƚƵƌĞŚŽƉĞĂŶĚƉĞƌƐƉĞĐƟǀĞƚŽƚŚĞ /ƚǁĂƐĂŚŝƐƚŽƌŝĐĚĂLJƚŽďĞŝŶtĞƐƚŵŝŶƐƚĞƌ͘ ĐƵƌƌĞŶƚĐůŝŵĂƚĞĂǁĂLJĨƌŽŵƚŚĞƉŽůŝƟĐĂů dŚĞĂŝƌƚŚŝĐŬǁŝƚŚĞdžƉĞĐƚĂŶĐLJ͕ƚŚĞƌŽŽŵ ƐƉŚĞƌĞ͘ŽŶƐŝƐƟŶŐŽĨƉĂƌƟĐŝƉĂŶƚƐĨƌŽŵ ƐƚƵīĞĚƚŽƚŚĞƌĂŌĞƌƐǁŝƚŚƉĞŽƉůĞƌĞĂĚLJƚŽ ĂůůŽǀĞƌƚŚĞǁŽƌůĚ͕ǁŽƌŬŝŶŐŝŶƌĞƐĞĂƌĐŚ ƐĂLJƚŚĞŝƌďŝƚ͘ZĞƉƌĞƐĞŶƚĂƟǀĞƐĨƌŽŵĂůůŽǀĞƌ ŝŶƐƟƚƵƟŽŶƐƚŚƌŽƵŐŚŽƵƚƚŚĞh<͕ƚŚĞƌĞǁĞƌĞĂůů ƚŚĞĐŽƵŶƚƌLJũŽŝŶŝŶŐŝŶƚŚĞĚŝƐĐƵƐƐŝŽŶĂďŽƵƚ ƐŽƌƚƐŽĨƉƌŽďůĞŵƐŽŶĚŝƐƉůĂLJĨƌŽŵĂůůƐŽƌƚƐŽĨ ƚŚĞĨƵƚƵƌĞ͕ƚŚĞĨŽƌĞƐĞĞĂďůĞƉƌŽďůĞŵƐĂŶĚ ĮĞůĚƐ͘^ƉĂŶŶŝŶŐŵĂƚŚĞŵĂƟĐƐ͕ĞŶŐŝŶĞĞƌŝŶŐ͕ ƚŚĞŵĂŶLJƉŽƐƐŝďůĞƐŽůƵƟŽŶƐ͘dŚŝƐďĞŝŶŐŵŝĚͲ ďŝŽůŽŐLJ͕ƉŚLJƐŝĐƐ͕ĐŚĞŵŝƐƚƌLJ͖ĂŶĚƌĂŶŐŝŶŐĨƌŽŵ DĂƌĐŚ͕ƚŚƌŽƵŐŚŽƵƚƚŚĞĚĂLJƚŚĞƌĞǁĂƐĂŶ ƚŚĞƚŚĞŽƌĞƟĐĂůƚŽƚŚĞƉƌĂĐƟĐĂů͕ƚŚĞŝŶĚƵƐƚƌŝĂů ĂŝƌŽĨĂŶƟĐŝƉĂƟŽŶĨŽƌƚŚĞĮŶĂůƌĞdžŝƚǀŽƚĞƐ͕ ƚŽƚŚĞĂĐĂĚĞŵŝĐͲŝƚǁĂƐĂƌĞĂůĐĞůĞďƌĂƟŽŶŽĨ ĂƚĞŶƐŝŽŶĂƐĞĂĐŚǁŽŶĚĞƌĞĚǁŚŝĐŚǁĂLJ ƚŚĞŝŶŇƵĞŶƟĂůǁŽƌŬŐŽŝŶŐŽŶďLJĞĂƌůLJĐĂƌĞĞƌ ƚŚĞLJǁŽƵůĚƵůƟŵĂƚĞůLJŐŽ͘^dDĨŽƌZ/d/E researchers. ŚĂĚĂůůƚŚĞĚƌĂŵĂĞdžƉĞĐƚĞĚĨƌŽŵĂĚĂLJŝŶ ƉĂƌůŝĂŵĞŶƚ͘ ƵƚŝƚǁĂƐŶ͛ƚũƵƐƚĂĐŚĂŶĐĞĨŽƌƵƉĂŶĚĐŽŵŝŶŐ ƌĞƐĞĂƌĐŚĞƌƐƚŽƐŚŝŶĞĂŵŽŶŐƐƚŽŶĞĂŶŽƚŚĞƌ͕ ŝƚǁĂƐĂůƐŽĂŬĞLJŽƉƉŽƌƚƵŶŝƚLJƚŽŚŝŐŚůŝŐŚƚ ƚŽDWƐƚŚĞƐƚƌĞŶŐƚŚĂŶĚŝŵƉŽƌƚĂŶĐĞŽĨh< ƌĞƐĞĂƌĐŚ͘dŚĞŵĞƐƐĂŐĞǁĂƐĐůĞĂƌ͗ƚŚĂƚƚŚĞ h<ŚĂƐĂŶŝŵƉŽƌƚĂŶƚƌŽůĞŝŶǁŽƌůĚǁŝĚĞ͕ ĐŽůůĂďŽƌĂƟǀĞƌĞƐĞĂƌĐŚĂŶĚƚŚĂƚƚŚŝƐƌŽůĞ ƐŚŽƵůĚďĞŵĂŝŶƚĂŝŶĞĚĂŶĚƉƌŽƚĞĐƚĞĚ ůŽŶŐŝŶƚŽƚŚĞĨƵƚƵƌĞ͘dŚĞƌĞǁĂƐĂďƵnjnjŽĨ ĞŶƚŚƵƐŝĂƐŵĨƌŽŵĂůůŝŶƚŚĞƌŽŽŵĂŶĚĂ ĐŽůůĞĐƟǀĞĚĞƐŝƌĞƚŽůĞĂƌŶŵŽƌĞ͕ƐŽůǀĞŵŽƌĞ ƉƌŽďůĞŵƐ͕ĂŶĚƉƌŽǀŝĚĞĨƵƚƵƌĞĂĚǀĂŶĐĞŵĞŶƚ ƚŚƌŽƵŐŚ^dDƌĞƐĞĂƌĐŚ͘dŚƌŽƵŐŚŽƵƚƚŚĞĚĂLJ /ŵĞƚƉĞŽƉůĞǁŽƌŬŝŶŐŽŶƐŽŵĞŽĨƚŚĞŵŽƐƚ ŵŽĚĞƌŶƉƌŽďůĞŵƐĨĂĐŝŶŐŚƵŵĂŶŝƚLJ͕ĂƐǁĞůů ĂƐŵĂŶLJǁŽƌŬŝŶŐŽŶƉƌŽďůĞŵƐŽĨĂŶĂŐĞŽůĚ ƐŝŐŶŝĮĐĂŶĐĞ͘tŚĂƚƌĞĂůůLJƐƚŽŽĚŽƵƚŚŽǁĞǀĞƌ ǁĂƐƚŚĞŝŵƉŽƌƚĂŶĐĞŽĨ^dDƌĞƐĞĂƌĐŚĨŽƌŽƵƌ ĨƵƚƵƌĞƉƌŽŐƌĞƐƐĂŶĚƚŚĞƵŶĚĞŶŝĂďůĞƐŽĐŝĞƚĂů ďĞŶĞĮƚŽĨƐƵĐŚǁŽƌŬ͕ŶŽƚũƵƐƚĨŽƌƚŚĞh<ďƵƚ ƚŚĞǁŚŽůĞǁŽƌůĚ͘/ƚǁĂƐĞŶĐŽƵƌĂŐŝŶŐƚŽďĞĂ ƌWĂůŵĞƌΖƐǁŽƌŬ ƉĂƌƚŽĨƚŚĞĞǀĞŶƚĂŶĚůĞĂƌŶŵŽƌĞĂďŽƵƚǁŚĂƚ ŵLJƉĞĞƌƐĂƌĞƵƉƚŽ͕ĂŶĚĞŶĞƌŐŝƐŝŶŐƚŽƐĞĞ ƚĂƉůĂĐĞĂŶĚƟŵĞŝŶŽƵƌĐŽƵŶƚƌLJΖƐŚŝƐƚŽƌLJ ŽƚŚĞƌƐ͛ƉĂƐƐŝŽŶĨŽƌƚŚĞŝƌƐƵďũĞĐƚƐ͘ ǁŝƚŚŵƵĐŚĚĞďĂƚĞĂŶĚƵŶĐĞƌƚĂŝŶƚLJ͕ŝƚǁĂƐ ĨĂŶƚĂƐƟĐƚŽďĞĂƉĂƌƚŽĨĂŶĞǀĞŶƚƚŚĂƚ

22 DR RYAN PALMER

'ƌĞĂƚŝŶƚĞƌĞƐƚŽĨƌWĂůŵĞƌΖƐǁŽƌŬ

ƌZLJĂŶWĂůŵĞƌǁŝƚŚŚŝƐǁŽƌŬ

/ƚǁĂƐƐĂŝĚƚŚƌŽƵŐŚŽƵƚƚŚĞĚĂLJƚŚĂƚǁĞǁĞƌĞ ĂůůǁŝŶŶĞƌƐƚŽĞǀĞŶďĞƚŚĞƌĞƉƌĞƐĞŶƟŶŐ͕ ǁŚĞƚŚĞƌŽƌŶŽƚǁĞǁŽŶŽŶĞŽĨƚŚĞďŝŐƉƌŝnjĞƐ ͲŚŽǁĞǀĞƌ͕;ĂƚƚŚĞƌŝƐŬŽĨƐŽƵŶĚŝŶŐĐůŝĐŚĠͿ ƐĞĞŝŶŐƚŚĞďƌĞĂĚƚŚ͕ĚĞƉƚŚĂŶĚƐŽĐŝĞƚĂů ƌĞůĞǀĂŶĐĞŽĨƚŚĞƌĞƐĞĂƌĐŚĚŝƐƉůĂLJĞĚʹŽƵƌ ůŽĐĂůĂŶĚŐůŽďĂůĐŽŵŵƵŶŝƟĞƐǁŝůůďĞƚŚĞ ǁŝŶŶĞƌƐĂƐďŝŐƉƌŽďůĞŵƐĂƌĞƐŽůǀĞĚĂŶĚ as those talented researchers progress in ƚŚĞŝƌĐĂƌĞĞƌƐ͘dŚĞĨƵƚƵƌĞĨŽƌ^dDƌĞƐĞĂƌĐŚ ŝŶƚŚĞh<ůŽŽŬƐďƌŝŐŚƚŝĨ^dDĨŽƌZ/d/E ŝƐĂŶLJƚŚŝŶŐƚŽŐŽďLJʹĂŶĚůŽŶŐŵĂLJƚŚĂƚ ĐŽŶƟŶƵĞ͘

ƌZLJĂŶWĂůŵĞƌ /ŵĂŐĞƌĞĚŝƚͲƌZLJĂŶWĂůŵĞƌ

23 COLLOQUIUM

ŽůůŽƋƵŝƵŵʹϮϯƉƌŝůϮϬϭϵ WŚLJƐŝĐƐͿ͕ĂǀŝĚ'ŽŽĚ;ĂŵďƌŝĚŐĞ͕WƐLJĐŚŽůŽŐLJ ĂŶĚĞƐŝŐŶͿĂŶĚdŝŵŽŚƌŝŐ;DW/Dŝ^͕ dŝƚůĞ͗,ŽǁƚŽĮŶĚƐƚƌƵĐƚƵƌĞŝŶĚĂƚĂ͍ DĂƚŚƐͿĞdžƉůŽƌĞĚƚŚĞŝŵƉůŝĐĂƟŽŶƐĂƐƚŽǁŚĞŶ ĂŶĚŚŽǁĨĂƌŝƚŝƐƐĂĨĞƚŽƵƐĞƚŚĞŵŽĚĞůůŝŶŐ ^ƉĞĂŬĞƌ͗:ƺƌŐĞŶ:ŽƐƚ;ŝƌĞĐƚŽƌ͕DĂdžWůĂŶĐŬ ƚĞĐŚŶŝƋƵĞƐƚŚĂƚ͕ƚŽĚĂƚĞ͕ŚĂǀĞĨŽƌŵĞĚƚŚĞ /ŶƐƟƚƵƚĞĨŽƌDĂƚŚĞŵĂƟĐƐŝŶƚŚĞ^ĐŝĞŶĐĞƐ͕ ďĂĐŬďŽŶĞŽĨĚĞĐŝƐŝŽŶƐĐŝĞŶĐĞ͘ >ĞŝƉnjŝŐͿ 'ĞŽŵĞƚƌLJ͕ŚĞƵƌŝƐƟĐƐ͕ĂŶĚĚĂƚĂĂŶĂůLJƐŝƐ

ďƐƚƌĂĐƚ͗ tŚĞŶĐŽŶĨƌŽŶƚĞĚǁŝƚŚůĂƌŐĞ͕ƋƵŝĐŬůLJ ĐŚĂŶŐŝŶŐĚĂƚĂƐĞƚƐĨƌŽŵƉĞƌŚĂƉƐƵŶŬŶŽǁŶ ƐŽƵƌĐĞƐĂŶĚŽĨǀĂƌLJŝŶŐƌĞůŝĂďŝůŝƚLJĂŶĚ ƋƵĂůŝƚLJ͕ďŽƚŚŚƵŵĂŶƐĂŶĚŵĂĐŚŝŶĞůĞĂƌŶŝŶŐ ĂůŐŽƌŝƚŚŵƐŶĞĞĚƚŽŵĂŬĞĐĞƌƚĂŝŶƐƚƌƵĐƚƵƌĂů ĂƐƐƵŵƉƟŽŶƐŝŶŽƌĚĞƌƚŽŵĂŬĞƐĞŶƐĞŽĨƚŚĞŵ͘ dŚĞƐĞĂƐƐƵŵƉƟŽŶƐĂƌĞƵƐƵĂůůLJŽĨĂŐĞŽŵĞƚƌŝĐ ŶĂƚƵƌĞ͕ůŝŬĞƐŵŽŽƚŚŶĞƐƐ͕ƐLJŵŵĞƚƌLJ͕ ŚŝĞƌĂƌĐŚŝĐĂůƐƚƌƵĐƚƵƌĞŽƌĨĞǁƐŽƵƌĐĞƐŽŶůLJ͘ dŚĞƐĞŽŌĞŶƚƌĂŶƐůĂƚĞŝŶƚŽƉŽǁĞƌĨƵůŚĞƵƌŝƐƟĐƐ ĨŽƌŚƵŵĂŶƐĂŶĚĞĸĐŝĞŶƚŵĂĐŚŝŶĞůĞĂƌŶŝŶŐ dŚŝƐŽůůŽƋƵŝƵŵǁĂƐƵŶƵƐƵĂůŝŶƚŚĂƚŝƚ ĂůŐŽƌŝƚŚŵƐĨŽƌĐŽŵƉƵƚĞƌƐ͘ĚĞĞƉĞƌ ǁĂƐůŽŶŐĞƌƚŚĂŶŶŽƌŵĂů;ϵϬŵŝŶƵƚĞƐͿ ƵŶĚĞƌƐƚĂŶĚŝŶŐŝƐĂŵĂƚŚĞŵĂƟĐĂůĐŚĂůůĞŶŐĞĂƚ ĂŶĚŝŶǀŽůǀĞĚĨŽƵƌƐƉĞĂŬĞƌƐͲĂǀŝĚ'ŽŽĚ ƚŚĞŝŶƚĞƌĨĂĐĞŽĨŚŝŐŚĚŝŵĞŶƐŝŽŶĂůŐĞŽŵĞƚƌLJ͕ ;ĂŵďƌŝĚŐĞͿ͕ĂǀŝĚdƵĐŬĞƩ;h>Ϳ͕:ƺƌŐĞŶ ĚŝƐĐƌĞƚĞŵĂƚŚĞŵĂƟĐƐ͕ƐƚĂƟƐƟĐƐ͕ŝŶĨŽƌŵĂƟŽŶ :ŽƐƚ;>ĞŝƉnjŝŐͿĂŶĚ>ĞŽŶĂƌĚ^ŵŝƚŚ;>^Ϳ͕ ƚŚĞŽƌLJĂŶĚŽƚŚĞƌĮĞůĚƐ͘/ƐŚĂůůĚŝƐĐƵƐƐ ƉŝĐƚƵƌĞĚŚĞƌĞǁŝƚŚƌ<ŝŵDŽŽƌĞ;h> ƐŽŵĞĞdžĂŵƉůĞƐĂŶĚƚƌLJƚŽŽƵƚůŝŶĞƐŽŵĞ DĂƚŚĞŵĂƟĐƐZĞƐĞĂƌĐŚ&ĞůůŽǁͿ͘ ƉĞƌƐƉĞĐƟǀĞƐ͘

:ƺƌŐĞŶ͛ƐƚĂůŬǁĂƐĨŽůůŽǁĞĚďLJĂƉƌĞƐĞŶƚĂƟŽŶ ůĞĚďLJĂǀŝĚdƵĐŬĞƩ;h>ͿĨƌŽŵƚŚĞZh/^^ ŶĞƚǁŽƌŬ;ŚĂůůĞŶŐŝŶŐZĂĚŝĐĂůhŶĐĞƌƚĂŝŶƚLJ ŝŶ^ĐŝĞŶĐĞ͕^ŽĐŝĞƚLJĂŶĚƚŚĞŶǀŝƌŽŶŵĞŶƚͿ͘ dŚĞĚĞĐŝƐŝŽŶͲŵĂŬŝŶŐĐŚĂůůĞŶŐĞƐĨĂĐŝŶŐ 'ŽǀĞƌŶŵĞŶƚĂŶĚƵƐŝŶĞƐƐĂƌĞĐŽŵƉůĞdž͘tĞ ƵƐĞƚŚĞƚĞƌŵƌĂĚŝĐĂůƵŶĐĞƌƚĂŝŶƚLJƚŽƌĞĨĞƌ ƚŽĐŽŶƚĞdžƚƐŝŶǁŚŝĐŚ͕ĂƚƚŚĞƟŵĞLJŽƵĂƌĞ ŵĂŬŝŶŐĚĞĐŝƐŝŽŶƐ͕LJŽƵĐĂŶŶŽƚŬŶŽǁŝĨǁŚĂƚ LJŽƵĂƌĞĚĞĐŝĚŝŶŐǁŝůůǁŽƌŬŽƵƚĂƐĞdžƉĞĐƚĞĚ͘ DĂŶLJƌĞĂůͲǁŽƌůĚĚĞĐŝƐŝŽŶƐĂƌĞŽĨƚŚŝƐƚLJƉĞ ĂŶĚĂǀŝĚdƵĐŬĞƩ;h>^ŽĐŝŽůŽŐLJĂŶĚ WƐLJĐŚŽůŽŐLJͿ͕>ĞŶŶLJ^ŵŝƚŚ;>^͕DĂƚŚƐĂŶĚ /ŵĂŐĞĐƌĞĚŝƚͲWƌŽĨĞƐƐŽƌŵŝƚƌŝsĂƐƐŝůŝĞǀ

24 WIKITHON

h>DĂƚŚƐtŝŬŝƚŚŽŶ ƌŽƵŶĚϯϬƉĞŽƉůĞĂƩĞŶĚĞĚ͕ĂƐƌ:ĞƐƐtĂĚĞ ;/ŵƉĞƌŝĂůͿĂŶĚƌůŝĐĞtŚŝƚĞ;tĞůůĐŽŵĞ ϴƚŚKĐƚŽďĞƌϮϬϭϵ >ŝďƌĂƌLJͿƉƌŽǀŝĚĞĚŐƵŝĚĂŶĐĞĂƐƚŽŚŽǁƚŽ ĐƌĞĂƚĞĂŶĚĞĚŝƚǁŝŬŝƉĞĚŝĂƉĂŐĞƐ͕ĂŶĚŚŽǁƚŽ dŽĐĞůĞďƌĂƚĞĚĂ>ŽǀĞůĂĐĞĂLJ͕WƌŽĨĞƐƐŽƌ ĂǀŽŝĚĐŽŵŵŽŶƉŝƞĂůůƐ͘ ,ĞůĞŶtŝůƐŽŶĂŶĚƌ>ƵĐŝĂŶŽZŝůĂŽĨh> DĂƚŚĞŵĂƟĐƐƌĂŶĂtŝŬŝƚŚŽŶƚŽŝŶĐƌĞĂƐĞƚŚĞ ĚŝǀĞƌƐŝƚLJŽĨŵĂƚŚĞŵĂƟĐŝĂŶƐŽŶtŝŬŝƉĞĚŝĂ͘

ǀĞƌLJŽŶĞǁŽƌŬŝŶŐĂƐĂƚĞĂŵ

&ŽůůŽǁŝŶŐƚŚĞĞǀĞŶƚ͕ǁĞĂƐŬĞĚƌZŝůĂ ĚĂ>ŽǀĞůĂĐĞĂLJĂŝŵƐƚŽŝŶĐƌĞĂƐĞƚŚĞƉƌŽĮůĞ ŚŽǁŝƚŚĂĚŐŽŶĞ͗ ŽĨǁŽŵĞŶŝŶƐĐŝĞŶĐĞ͕ƚĞĐŚŶŽůŽŐLJ͕ĞŶŐŝŶĞĞƌŝŶŐ ΗdŚĞĞǀĞŶƚǁĂƐĂŐƌĞĂƚƐƵĐĐĞƐƐ͘tĞŚĂĚ ĂŶĚŵĂƚŚƐ;^dDͿĂŶĚƉƌŽǀŝĚĞƌŽůĞŵŽĚĞůƐ ƌĞƉƌĞƐĞŶƚĂƟǀĞƐĨƌŽŵƵŶĚĞƌŐƌĂĚƵĂƚĞ ĨŽƌLJŽƵŶŐƐƚƵĚĞŶƚƐďLJĐĞůĞďƌĂƟŶŐƚŚĞ ƐƚƵĚĞŶƚƐ͕WŚƐƚƵĚĞŶƚƐ͕ĞĂƌůLJĐĂƌĞĞƌ ĂĐŚŝĞǀĞŵĞŶƚƐŽĨǁŽŵĞŶŝŶ^dDĮĞůĚƐ͕ďŽƚŚ ĂĐĂĚĞŵŝĐƐĂŶĚƉƌŽĨĞƐƐŽƌƐ͕ĂůůǁŽƌŬŝŶŐ ĨƌŽŵŚŝƐƚŽƌLJĂŶĚƚŚĞŵŽĚĞƌŶĚĂLJ͘ƐƉĂƌƚŽĨ ƚŽŐĞƚŚĞƌ͘dŚĞĂŝŵŽĨƚŚĞtŝŬŝƚŚŽŶǁĂƐƚŽ ƚŚŝƐ͕WƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶĂŶĚƌ>ƵĐŝĂŶŽ ĂĚĚƌĞƐƐƚŚĞŐĞŶĚĞƌďŝĂƐŽŶtŝŬŝƉĞĚŝĂĂŶĚ ZŝůĂĂƌƌĂŶŐĞĚĂtŝŬŝƚŚŽŶƚŽŚĞůƉƉƌŽŵŽƚĞ ǁĞĚĞĐŝĚĞĚƚŽĞdžƚĞŶĚƚŚĂƚƚŽĂůůƵŶĚĞƌͲ ƚŚĞǁŽƌŬŽĨƵŶĚĞƌƌĞƉƌĞƐĞŶƚĞĚŐƌŽƵƉƐŝŶ represented groups. Also, as Ada Lovelace ŵĂƚŚĞŵĂƟĐƐ͘ ĂLJŝƐĂŶŝŶƚĞƌŶĂƟŽŶĂůĐĞůĞďƌĂƟŽŶŽĨǁŽŵĞŶ ŝŶ^dD͕ŝƚǁĂƐƚŚĞƉĞƌĨĞĐƚĚĂƚĞƚŽŝŵƉƌŽǀĞ ĚŝǀĞƌƐĞƌĞƉƌĞƐĞŶƚĂƟŽŶŝŶŵĂƚŚĞŵĂƟĐƐ͘dŚĞ ĨĞĞĚďĂĐŬǁĂƐǀĞƌLJƉŽƐŝƟǀĞ͕ĂŶĚǁĞƉůĂŶ ƚŽĐŽŶƟŶƵĞŽƵƌĞīŽƌƚƐƚŽĚƌŝǀĞĞƋƵĂůŝƚLJ ĂŶĚĚŝǀĞƌƐŝƚLJŝŶŵĂƚŚĞŵĂƟĐƐ͘tĞĂƌĞ ĐƵƌƌĞŶƚůLJŽƌŐĂŶŝƐŝŶŐĂŶĞƚǁŽƌŬĞǀĞŶƚĨŽƌ ƵŶĚĞƌŐƌĂĚƵĂƚĞƐƚƵĚĞŶƚƐŽĨĨƌŝĐĂŶͲĂƌŝďďĞĂŶ ĚĞƐĐĞŶƚŝŶ&ĞďƌƵĂƌLJǁŝƚŚŝŶǀŝƚĞĚŐƵĞƐƚ ƐƉĞĂŬĞƌƐĨŽůůŽǁĞĚďLJĂƌĞĐĞƉƟŽŶΗ͘

tŝŬŝƉĞĚŝĂƉĂŐĞƐďĞŝŶŐƵƉĚĂƚĞĚŽŶƚŚĞƚĂďůĞƚ /ŵĂŐĞĐƌĞĚŝƚͲDĂůĐŽůŵŚĂůŵĞƌƐ͕h>DW^ &ĂĐƵůƚLJ

25 THOMAS HARRIOT - ENGLAND'S LEADING MATHEMATICIAN

dŚŽŵĂƐ,ĂƌƌŝŽƚ;ϭϱϱϵͬϲϬʹϭϲϮϭͿŶŐůĂŶĚΖƐůĞĂĚŝŶŐ ŵĂƚŚĞŵĂƚŝĐĂůƐĐŝĞŶƚŝƐƚďĞĨŽƌĞEĞǁƚŽŶ

ďLJƌ:ŽŶs͘WĞƉƉĞƌ

&ŝƌƐƚ͕ Ă ĨĞǁ ĚĞƚĂŝůƐ ĂďŽƵƚ ,ĂƌƌŝŽƚΖƐ ůŝĨĞ͕ ďĞĨŽƌĞ / ƐƵŵŵĂƌŝƐĞ ŚŝƐ ƐĐŝĞŶƚŝĨŝĐ ĂŶĚ ŽƚŚĞƌ ĂĐŚŝĞǀĞŵĞŶƚƐ͕ǁŚŝĐŚǁĞƌĞĐŽŶƐŝĚĞƌĂďůĞĂŶĚƌĞĐŽŐŶŝƐĞĚŝŶŚŝƐŽǁŶƚŝŵĞƐ͕ďƵƚǁŚŝĐŚǁĞƌĞůĂƚĞƌ ůĂƌŐĞůLJŶĞŐůĞĐƚĞĚ͘,ĂƌƌŝŽƚǁĂƐďŽƌŶŝŶŽƌŶĞĂƌKdžĨŽƌĚ͕ŵŽƐƚƉƌŽďĂďůLJĂďŽƵƚϭϱϲϬ͘,ŝƐƉĂƌĞŶƚĂŐĞŝƐ ŶŽƚŬŶŽǁŶ͕ďƵƚ ŚĞŚĂĚĨĂŵŝůLJĐŽŶŶĞĐƚŝŽŶƐŝŶƚŚĞEĞǁďƵƌLJĂƌĞĂ;ƐŽƵƚŚŽĨKdžĨŽƌĚͿůĂƚĞƌŽŶ͘,Ğ ŵĂƚƌŝĐƵůĂƚĞĚĂƚ^ƚDĂƌLJ,Ăůů;ŶŽǁŝŶĐŽƌƉŽƌĂƚĞĚŝŶƚŽKƌŝĞůŽůůĞŐĞ͕KdžĨŽƌĚͿŝŶϭϱϳϳ͕ŐƌĂĚƵĂƚŝŶŐ͘͘ ŝŶϭϱϴϬ͘ĨƚĞƌƚŚĂƚ͕ŚĞƉŽƐƐŝďůLJǁŽƌŬĞĚŝŶ>ŽŶĚŽŶĨŽƌĂƐŚŽƌƚǁŚŝůĞŝŶƚŚĞƐĞƌǀŝĐĞŽĨ^ŝƌ,ƵŵƉŚƌĞLJ 'ŝůďĞƌƚ͕ƐƚĞƉͲďƌŽƚŚĞƌ ƚŽ^ŝƌ tĂůƚĞƌ ZĂůĞŐŚ͘'ŝůďĞƌƚ ǁĂƐ ůŽƐƚ Ăƚ ƐĞĂ ůĂƚĞƌ ŝŶ ϭϱϴϯ͘ ,ĂƌƌŝŽƚ ǁĂƐ ƚŚĞŶ ŝŶ ƚŚĞ ƐĞƌǀŝĐĞ ŽĨ ^ŝƌtĂůƚĞƌ͕ĂƐŚŝƐƐĐŝĞŶƚŝĨŝĐĂĚǀŝƐĞƌĂŶĚŵĂŶŽĨďƵƐŝŶĞƐƐ͘hŶƚŝůƚŚĞůĂƚĞ ϭϱϵϬƐ͕ǁŚĞŶŚĞŵŽǀĞĚŝŶƚŽƚŚĞƐĞƌǀŝĐĞ ŽĨ ,ĞŶƌLJ WĞƌĐLJ͕ ĞĂƌů ŽĨ EŽƌƚŚƵŵďĞƌůĂŶĚ ;Ă ĐĂƌĚƉůĂLJŝŶŐ ĨƌŝĞŶĚ ŽĨ ^ŝƌ tĂůƚĞƌͿ͕ ǁŚĞƌĞŚĞƌĞŵĂŝŶĞĚ͕ǁŝƚŚƐŝŵŝůĂƌĚƵƚŝĞƐ͕ƵŶƚŝůŚŝƐĚĞĂƚŚŝŶϭϲϮϭĂƚƚŚĞ ŚŽƵƐĞŽĨĂŶŽůĚĨƌŝĞŶĚŝŶdŚƌĞĂĚŶĞĞĚůĞ^ƚƌĞĞƚ͘sĞƌLJŶĞĂƌƚŚĞĨŽƌŵĞƌƐŝƚĞŽĨ^ƚDĂƌLJͲůĞͲ^ƚŽĐŬƐ͕ ǁŚĞƌĞŚĞǁĂƐďƵƌŝĞĚ͕ĂŶĚǁŚŝĐŚŝƐĐŽǀĞƌĞĚďLJƚŚĞƉƌĞƐĞŶƚĂŶŬŽĨŶŐůĂŶĚ͘

ĨƚĞƌŚŝƐLJŽƵƚŚ͕ŽĨǁŚŝĐŚǁĞŬŶŽǁŶŽƚŚŝŶŐ͕ŚĞǁĂƐŶĞǀĞƌƚŚĞƚLJƉŝĐĂůƉŽŽƌƐĐŚŽůĂƌ͕ďƵƚĞĂƌŶĞĚ ŐŽŽĚ ŵŽŶĞLJ͕ŚĂĚĚĞĐĞŶƚƉƌŽƉĞƌƚLJ͕ĂŶĚǁĂƐǁĞůůͲƌĞƐƉĞĐƚĞĚŝŶĂǁŝĚĞƌĂŶŐĞŽĨ ƐŽĐŝĞƚLJĨŽƌŚŝƐ ƐĐŝĞŶƚŝĨŝĐĂĐŚŝĞǀĞŵĞŶƚƐ͕ďŽƚŚŝŶŶŐůĂŶĚĂŶĚƉĂƌƚƐŽĨŶŽƌƚŚǁĞƐƚĂŶĚĐĞŶƚƌĂůƵƌŽƉĞďĞĨŽƌĞϭϲϬϬ͘ tŚLJƚŚĞŶŝƐŚĞƐŽůŝƚƚůĞŬŶŽǁŶŶŽǁĂĚĂLJƐ͍DŽĚĞƌŶƐĐŚŽůĂƌƐŚĂǀĞĂŶĂƐƚLJŚĂďŝƚŽĨŝŐŶŽƌŝŶŐƚŚĞ ŬƐǁŚŝĐŚƚŚĞŝƌƉƌĞĚĞĐĞƐƐŽƌƐ ŚĂǀĞŶΖƚ ǁƌŝƚƚĞŶ͘ dŚĞ ƐŝŵƉůĞ ĂŶƐǁĞƌ ŝƐ ƚŚĂƚ͕ ĂƉĂƌƚ ĨƌŽŵ Ă ƐŚŽƌƚ ĐŽůŽŶŝƐŝŶŐ ƚƌĂĐƚ ƚŚĂƚĐĂŵĞŽƵƚŝŶϭϱϴϴ;ƉƌŽďĂďůLJͿ͕ŚĞƉƵďůŝƐŚĞĚŶŽƚŚŝŶŐŝŶƉƌŝŶƚŽĨŚŝƐƐĐŝĞŶƚŝĨŝĐ ǁŽƌŬ͘,ĞĚŝĚŶΖƚƉƵďůŝƐŚ͕ƐŽŚĞƉĞƌŝƐŚĞĚ͊dŚĞƋƵĞƐƚŝŽŶƌĞŵĂŝŶƐŽĨǁŚLJŚĞĚŝĚŶΖƚƉƵďůŝƐŚ͕ĂŶĚƚŚĞƌĞ ĂƌĞĂŶƵŵďĞƌŽĨ ƉŽƐƐŝďůĞƌĞĂƐŽŶƐ͘&ŝƌƐƚ͕ŚĞĚŝĚŶΖƚŚĂǀĞƚŽʹŚĞǁĂƐĂůǁĂLJƐǁĞůůͲƌĞǁĂƌĚĞĚďLJŚŝƐ ƉĂƚƌŽŶƐ͕ĂŶĚƉƵďůŝĐĂƚŝŽŶ ǁĂƐŽĨƚĞŶĂŵĞĂŶƐŽĨĂƚƚƌĂĐƚŝŶŐǁĞĂůƚŚLJƉĂƚƌŽŶƐ͕ǁŚŝĐŚǁĂƐŶΖƚŶĞĐĞƐƐĂƌLJ ŝŶŚŝƐĐĂƐĞ͘EĞdžƚ͕ŚŝƐǁŽƌŬǁĂƐŽĨƚĞŶŽŶƚŚĞďŽƵŶĚĂƌŝĞƐŽĨƌĞƐĞĂƌĐŚŽĨŚŝƐƚŝŵĞ͕ĨŽƌǁŚŝĐŚĂ ƉŽƚĞŶƚŝĂůĂƵĚŝĞŶĐĞǁĂƐĂůǁĂLJƐƐŵĂůů͘/ŵƉŽƌƚĂŶƚǁŽƌŬĐŽƵůĚĂůǁĂLJƐďĞĐŝƌĐƵůĂƚĞĚŝŶƚŚĞ͞ŝŶǀŝƐŝďůĞ ĐŽůůĞŐĞƐ͟ŽĨƚŚĞƚŝŵĞƐ͘ >ŝŶŬĞĚƚŽƚŚŝƐǁĞƌĞƚŚĞƚĞĐŚŶŝĐĂůŶĞĞĚƐŽĨƐƵĐŚƉƌŝŶƚŝŶŐ͕ĨŽƌǁŚŝĐŚƚŚĞ ƉƌĞƐƐĞƐŽĨ;ƐĂLJͿƚŚĞ>ŽǁŽƵŶƚƌŝĞƐǁĞƌĞďĞƚƚĞƌ͘ ŶŐůĂŶĚ ǁĂƐ ŽŶůLJ ďĞŐŝŶŶŝŶŐ ƚŽ ƌĞĐŽǀĞƌ ĨƌŽŵ ƚŚĞ ƉŽůŝƚŝĐĂů ĂŶĚ ƌĞůŝŐŝŽƵƐ ƚƵƌŵŽŝů ŽĨ ƚŚĞƉƌĞǀŝŽƵƐ ĨĞǁƌĞŝŐŶƐ͕ĂŶĚ ƚŽƐƉƌĞĂĚŝƚƐ ǁŝŶŐƐ ŝŶƚŚĞ ǁŝĚĞƌǁŽƌůĚ͘ dŚĞƌĞ ǁĂƐĂůƐŽ ƚŚĞ͞ƌĞƐƚƌŝĐƚĞĚ͟ŶĂƚƵƌĞ ŽĨ ŚŝƐ ǁŽƌŬ͕ ĂƐ ǁĞ ǁŽƵůĚ ƐĂLJ ŶŽǁĂĚĂLJƐ͖ ŝƚ ǁŽƵůĚ ŶŽƚ ĚŽ ƚŽ ůĞƚ ƚŚĞ ŬŝŶŐ ŽĨ ^ƉĂŝŶ͕ ĨŽƌĞdžĂŵƉůĞ͕ŝŶƚŽƐŽŵĞŽĨŚŝƐŵĂƚŚĞŵĂƚŝĐĂůĂŶĚ ƐĐŝĞŶƚŝĨŝĐǁŽƌŬ͘

26 DR JON V. PEPPER

dŚĞƌĞǁĞƌĞĂůƐŽ ŚĞĂůƚŚ ƉƌŽďůĞŵƐ͕ĨŝƌƐƚ ŵĞŶƚŝŽŶĞĚŝŶĂůĞƚƚĞƌƚŽ ƚŚĞ^ĞĐƌĞƚĂƌLJŽĨ^ƚĂƚĞ͕^ŝƌ ZŽďĞƌƚĞĐŝů͕ůĂƚĞƌĞĂƌůŽĨ^ĂůŝƐďƵƌLJ͕ŝŶϭϲϬϱ͕ǁŚŝĐŚĚŽŐŐĞĚŚŝŵĨŽƌƚŚĞƌĞƐƚŽĨŚŝƐůŝĨĞ͘ Ƶƚ ŵŽƐƚŽĨĂůů͕ĐĞƌƚĂŝŶůLJ ĨŽƌ ŚŝƐ ůĂƚĞƌ ƌĞƉƵƚĂƚŝŽŶ͕ ƚŚĞƌĞ ǁĂƐ ƚŚĞ ƋƵĞƐƚŝŽŶ ŽĨ ŚŝƐ ĂĐƚƵĂů ƉĂƚƌŽŶĂŐĞ͘ ĨƚĞƌ ƚŚĞŵŝĚͲϭϱϵϬƐ͕ ďŽƚŚ ZĂůĞŐŚ ĂŶĚ WĞƌĐLJ ǁĞƌĞ ŵĂƌŬĞĚ ŵĞŶ ʹ ƚŚĞLJ ǁĞƌĞ ĐĞƌƚĂŝŶůLJ ƐŽĐŝĂůůLJ ĞůĞǀĂƚĞĚ;WĞƌĐLJŵƵĐŚŵŽƌĞƐŽʹůŝnjĂďĞƚŚ͕ƵŶůŝŬĞŚĞƌĨĂƚŚĞƌ͕ĚŝĚŶΖƚƉƌŽŵŽƚĞŵĞŶǁŚŽĐĂŵĞĨƌŽŵ ŶŽǁŚĞƌĞͿ͕ďƵƚƚŚĞLJǁĞƌĞĚĂŶŐĞƌŽƵƐƚŽŬŶŽǁ͘ĨƚĞƌ:ĂŵĞƐĐĂŵĞƚŽƚŚĞƚŚƌŽŶĞŝŶϭϲϬϯ͕ǁŝƚŚƚŚĞ ŝŶƚĞŶƚŝŽŶŽĨĐŽŵŝŶŐƚŽƚĞƌŵƐǁŝƚŚ^ƉĂŝŶ͕ďŽƚŚŵĞŶĐĂŵĞƵŶĚĞƌƐƵƐƉŝĐŝŽŶ͕ĂŶĚǁĞƌĞŚĞůĚŝŶƚŚĞ dŽǁĞƌ͕ĂŶĚ,ĂƌƌŝŽƚ ŚŝŵƐĞůĨďƌŝĞĨůLJŝŵƉƌŝƐŽŶĞĚŝŶϭϲϬϱ͘WĞƌĐLJǁĂƐŶΖƚƌĞůĞĂƐĞĚƵŶƚŝůϭϲϮϭ͕ĂŶĚ ZĂůĞŐŚŚĂĚĚŝĞĚŽŶƚŚĞƐĐĂĨĨŽůĚŝŶ ϭϲϭϴ ;ǁŝƚŚ ŚŝƐ ĨĂŝƚŚĨƵů ŽůĚ ƐĞƌǀĂŶƚ͕ ,ĂƌƌŝŽƚ͕ ƚŚĞƌĞ ƚŽ ŵĂŬĞ ŶŽƚĞƐ͕ ǁŚŝĐŚƐƚŝůů ƐƵƌǀŝǀĞ͕ ŽĨ ŚŝƐůĞŶŐƚŚLJƐƉĞĞĐŚŽŶƚŚĂƚĚŝƐŵĂůŽĐĐĂƐŝŽŶͿ͘

^ŽŵƵĐŚĨŽƌƐŽĐŝĂůďĂĐŬŐƌŽƵŶĚ͕ďƵƚǁŚĂƚĂďŽƵƚƚŚĞĂĐƚƵĂůĂĐĂĚĞŵŝĐǁŽƌŬ͍dŚŝƐĨĂůůƐŝŶƚŽĂ ŶƵŵďĞƌ ŽĨĐĂƚĞŐŽƌŝĞƐ͕ǁŝĚĞͲƌĂŶŐŝŶŐĂƐŽŶĞǁŽƵůĚĞdžƉĞĐƚŽĨĂƉƌŽŵŝŶĞŶƚůĂƚĞƌĞŶĂŝƐƐĂŶĐĞƐĐŚŽůĂƌ͘dŚĞƌĞ ǁĂƐ͞ďƌŝĞĨĞĂŶĚƚƌƵĞƌĞƉŽƌƚŽĨƚŚĞŶĞǁĨŽƵŶĚůĂŶĚŽĨsŝƌŐŝŶŝĂ͟;ĂĐƚƵĂůůLJŵŽĚĞƌŶEŽƌƚŚ ĂƌŽůŝŶĂ͕ŝŶƉĂƌƚŝĐƵůĂƌƚŚĞĂƌĞĂŽĨĂŶĚďĞŚŝŶĚƚŚĞKƵƚĞƌĂŶŬƐͿƌĞĨĞƌƌĞĚƚŽĂďŽǀĞ͕ǁŚŝĐŚŐŝǀĞƐĂ ĨĂŝƌŝĨŚŽƉĞĨƵůĂĐĐŽƵŶƚŽĨƚŚĞůĂŶĚĂŶĚŝƚƐƉĞŽƉůĞ͕ǁŚĞƌĞŚĞŚĂĚůŝǀĞĚĨŽƌĂďŽƵƚĂLJĞĂƌŝŶ ϭϱϴϱͲϴϲ͘ /ƚŝƐƚŚŝƐůŝƚƚůĞŬƚŚĂƚĞdžƉůĂŝŶƐǁŚLJ,ĂƌƌŝŽƚŝƐďĞƚƚĞƌŬŶŽǁŶŝŶEŽƌƚŚŵĞƌŝĐĂƚŚĂŶŝŶ ŚŝƐŽǁŶĐŽƵŶƚƌLJ͕ĂŶĚŝƐƐƚŝůůŝŶƉƌŝŶƚŝŶŽŶĞĨŽƌŵŽƌĂŶŽƚŚĞƌŽǀĞƌϰϬϬLJĞĂƌƐůĂƚĞƌ͕ǁŝƚŚŝůůƵƐƚƌĂƚŝŽŶƐ ďĂƐĞĚŽŶƚŚĞĚŝƐƚŝŶŐƵŝƐŚĞĚĚƌĂǁŝŶŐƐŽĨ:ŽŚŶtŚŝƚĞ͕ǁŚŽŚĂĚďĞĞŶƚŚĞƌĞǁŝƚŚ,ĂƌƌŝŽƚ͘,ĂƌƌŝŽƚŚĂĚ ůĞĂƌŶĞĚƚŚĞůŽĐĂůůŐŽŶƋƵŝĂŶůĂŶŐƵĂŐĞ͕ĂŶĚĚĞǀŝƐĞĚĂƉŚŽŶĞƚŝĐƐĐƌŝƉƚƚŽǁƌŝƚĞŝƚĚŽǁŶ͕ ŵŝƐĚĞƐĐƌŝďĞĚůĂƚĞƌŽŶĂƐŚŝƐ͞ƐĞĐƌĞƚƐĐƌŝƉƚ͘͟dŚĞƌĞǁĂƐŚŝƐĞĂƌůLJǁŽƌŬŝŶŵĂƚŚĞŵĂƚŝĐĂůŶĂǀŝŐĂƚŝŽŶŝŶ ƚŚĞϭϱϴϬƐǁŚŝĐŚĞŶĐŽŵƉĂƐƐĞĚĂůůƚŚĞƚŽƉŝĐƐŽĨŝŶƚĞƌĞƐƚĂƚƚŚĞƚŝŵĞ͕ĂƉĂƌƚĨƌŽŵƚŚĞůŽŶŐŝƚƵĚĞ ƉƌŽďůĞŵ͕ǁŚŝĐŚǁĂƐŶΖƚƚŽďĞĂĚĞƋƵĂƚĞůLJĚĞĂůƚǁŝƚŚĨŽƌŶĞĂƌůLJƚǁŽŵŽƌĞĐĞŶƚƵƌŝĞƐďLJ:ŽŚŶ ,ĂƌƌŝƐŽŶǁŝƚŚŚŝƐĐŚƌŽŶŽŵĞƚĞƌƐŽƌdŽďŝĂƐDĂLJĞƌǁŝƚŚŚŝƐůƵŶĂƌ ĚŝƐƚĂŶĐĞƐ͘ WƌŝŽƌ ƚŽ ƚŚĂƚ͕ ƚƌĂǀĞƌƐĞƐ ŚĂĚ ƚŽ ďĞĞƐƚŝŵĂƚĞĚ͕ ǁŚŝĐŚ ůĞĚ ŽŶ ŽĐĐĂƐŝŽŶ ƚŽ ƐŽŵĞƐƉĞĐƚĂĐƵůĂƌ ĚŝƐĂƐƚĞƌƐ Ăƚ ƐĞĂ͘ Ƶƚ ŝŶ ƚŚĞ ůĂƚĞƌƐŝdžƚĞĞŶƚŚ ĐĞŶƚƵƌLJ͕ ƚŚĞ ŶŐůŝƐŚ͕ ĂůƚŚŽƵŐŚ ƚƌĂŝůŝŶŐ ƚŚĞWŽƌƚƵŐƵĞƐĞĂŶĚƚŚĞ ^ƉĂŶŝƐŚ͕ǁĞƌĞďĞŐŝŶŶŝŶŐƚŽĐĂƚĐŚƵƉ͘ĚǁĂƌĚtƌŝŐŚƚ͕ĂĨĞůůŽǁ ŵĂƚŚĞŵĂƚŝĐŝĂŶ͕ĨƌŽŵĂŵďƌŝĚŐĞ͕ ůĂƚĞƌƉƌŽĚƵĐĞĚŚŝƐ͞ĞƌƚĂŝŶĞĞƌƌŽƌƐŝŶŶĂǀŝŐĂƚŝŽŶ͙ĐŽƌƌĞĐƚĞĚ͟ŽĨϭϱϵϵ;ϮŶĚ ĞĚŶϭϲϭϬͿ͕ǁŚŝĐŚ͕ ǁŝƚŚĂĨƵƌƚŚĞƌĞĚŝƚŝŽŶ͕ǁĂƐƚŚĞƐƚĂŶĚĂƌĚƐŽƵƌĐĞŝŶŶŐůĂŶĚŽŶƚŚĞƐĞŵĂƚƚĞƌƐĨŽƌ ŵƵĐŚŽĨƚŚĞƌĞƐƚ ŽĨƚŚĞĐĞŶƚƵƌLJ͕ĂŶĚŝŶĐůƵĚĞĚƚŚĞƌĞƋƵŝƐŝƚĞƚĂďůĞƐĂŶĚĞdžƉůĂŶĂƚŝŽŶƐŽĨƚŚĞŵĞƚŚŽĚƐ͘

/ŶŚŝƐǁŽƌŬ͕ŝŶĂĚĚŝƚŝŽŶƚŽƚŚĞƉƌŽďůĞŵƐŽĨĂŵƉůŝƚƵĚĞƐĂŶĚůĂƚŝƚƵĚĞƐ͕,ĂƌƌŝŽƚƐŽůǀĞĚƚŚĞƉƌŽďůĞŵ ŽĨĐŽŶƐƚƌƵĐƚŝŶŐĂĐŽŶĨŽƌŵĂůŵĂƉƉŝŶŐŽĨƚŚĞ;ƐƉŚĞƌŝĐĂůͿŐůŽďĞ͕ǁŚŝĐŚŚĂĚďĞĞŶƉƌŽƉŽƐĞĚďLJ 'ĞƌŚĂƌĚDĞƌĐĂƚŽƌŝŶϭϱϲϵ;ĂŶĚŚŝŶƚĞĚĂƚďLJĂĨĞǁĞĂƌůŝĞƌǁƌŝƚĞƌƐͿ͕ďLJƚŚĞĂĚĚŝƚŝŽŶŽĨƐĞĐĂŶƚƐ͕ĂŶĚ ůĂƚĞƌďLJĂŵĞƚŚŽĚ ƐƚƌƵĐƚƵƌĂůůLJ ĞƋƵŝǀĂůĞŶƚ ƚŽ ƚŚĞŵŽĚĞƌŶ ůŽŐĂƌŝƚŚŵŝĐ ĨŽƌŵƵůĂ͕ ĂŶĚ ĐŽŶƐƚƌƵĐƚĞĚ ƚŚĞŶĞĐĞƐƐĂƌLJƚĂďůĞƐŽĨƚŚĞƐŽͲĐĂůůĞĚŵĞƌŝĚŝŽŶĂůƉĂƌƚƐ͘dŚĞůĂƚƚĞƌǁĂƐŶŽƚƌŝǀŝĂůŵĂƚƚĞƌ͘&ŝƌƐƚ͕ŚĞ ƉƌŽǀĞĚ;ƉƌŽďĂďůLJĨŽƌƚŚĞĨŝƌƐƚƚŝŵĞͿƚŚĞĐŽŶĨŽƌŵĂůŝƚLJŽĨƐƚĞƌĞŽŐƌĂƉŚŝĐƉƌŽũĞĐƚŝŽŶ͘ dŚĞŶŚĞ ŽďƚĂŝŶĞĚƚŚĞĨƵŶĚĂŵĞŶƚĂůĞdžƉŽŶĞŶƚŝĂůĞƋƵĂƚŝŽŶŝŶǀŽůǀŝŶŐƚĂŶŐĞŶƚƐĂŶĚĂ ďĂƐĞ ĂŶŐůĞ͕ǁŚŝĐŚ ĐĂŵĞĨƌŽŵƚŚĞŐĞŽŵĞƚƌLJŽĨƚŚĞƐƉŚĞƌĞ ĂŶĚ ƚŚĞ ƌŚƵŵď ůŝŶĞƐ ;ůŽdžŽĚƌŽŵĞƐͿ ƉƌŽũĞĐƚĞĚ ŽŶƚŽ ƚŚĞ ĞƋƵĂƚŽƌŝĂů ƉůĂŶĞ͘dŚŝƐ ůĞĚ͕ ĂĨƚĞƌ ƚŚĞƐĐĂůĞĨĂĐƚŽƌŚĂĚďĞĞŶŽďƚĂŝŶĞĚ͕ƚŽƚŚĞƌĞƐƵůƚĚсŬůŶ ĐŽƚ;ĂͬϮͿ͕ďƵƚƚŚŝƐ͕ĂƐĞdžƉƌĞƐƐĞĚŚĞƌĞ͕ŝƐƌĂƚŚĞƌŵŝƐůĞĂĚŝŶŐ͕ĂƐŵŽĚĞƌŶůŽŐĂƌŝƚŚŵƐŚĂĚŶΖƚLJĞƚďĞĞŶ ĚĞĨŝŶĞĚ͕ĂŶĚǁŚĞŶƚŚĞLJǁĞƌĞ͕ƚŚĞLJǁĞƌĞŶΖƚƋƵŝƚĞƚŚĞƐĂŵĞ͘ ;ŶĚƚŚĞLJǁĞƌĞĐŚĂŶŐĞĚďLJ,ĞŶƌLJ ƌŝŐŐƐĂĨĞǁLJĞĂƌƐůĂƚĞƌ͘Ϳ /ŶĐŝĚĞŶƚĂůůLJ͕ƚŚŝƐƌĞƐƵůƚŝƐĂůŵŽƐƚŝĚĞŶƚŝĐĂůƚŽƚŚĞĨƵŶĚĂŵĞŶƚĂůĨŽƌŵƵůĂ ŝŶŚLJƉĞƌďŽůŝĐŶŽŶͲĞƵĐůŝĚĞĂŶŐĞŽŵĞƚƌLJ͕ǁŚŝĐŚƐŚŽƵůĚŶΖƚƐƵƌƉƌŝƐĞĂŶLJŽŶĞ͕ĂƐƚŚĂƚŝƐƌĞƉƌĞƐĞŶƚĂďůĞ ŽŶƚŚĞƐƵƌĨĂĐĞŽĨĐŽŶƐƚĂŶƚŶĞŐĂƚŝǀĞĐƵƌǀĂƚƵƌĞ͕ƌĂƚŚĞƌƚŚĂŶƚŚĞƐƉŚĞƌĞŽĨĐŽŶƐƚĂŶƚƉŽƐŝƚŝǀĞ ĐƵƌǀĂƚƵƌĞ͘

EĞdžƚŚĞƌĞĐƚŝĨŝĞĚƚŚĞƌĞƐƵůƚĂŶƚĞƋƵŝĂŶŐƵůĂƌƐƉŝƌĂů͕ƵƐŝŶŐƚŚƌĞĞƐĞƉĂƌĂƚĞŵĞƚŚŽĚƐ;ũƵƐƚƚŽďĞ ƐƵƌĞ͊Ϳ͗ĂůŐĞďƌĂŝĐĂů͕ ĂƌŝƚŚŵĞƚŝĐĂů ĂŶĚ ŐĞŽŵĞƚƌŝĐĂů͕ ƚŚĞ ůĂƐƚ ƵƐŝŶŐ Ă ŶĞĂƚ ĚŝƐƐĞĐƚŝŽŶ͕ ƚŚĞĨŝƌƐƚ ŬŶŽǁŶƌĞĐƚŝĨŝĐĂƚŝŽŶŽĨĂŶLJĐƵƌǀĞ͖ĂŶĚĂůƐŽŽĨƚŚĞƚǁŝƐƚĞĚůŽdžŽĚƌŽŵĞ͘ ,ĞĂůƐŽĨŽƵŶĚƚŚĞ ƋƵĂĚƌĂƚƵƌĞŽĨƚŚĞƐƉŝƌĂů͕ ďƵƚ ƌĐŚŝŵĞĚĞƐ ŚĂĚ ĚŽŶĞ ƚŚĂƚ ĨŽƌ ƚŚĞ ƉĂƌĂďŽůĂ ;ĂůƐŽ ďLJ ƚŚƌĞĞ ĚŝĨĨĞƌĞŶƚ ǁĂLJƐͿ ůŽŶŐ ĂŐŽ͘;,ĂƌƌŝŽƚƵƐĞĚƚŚĞĞĂƌůŝĞƌƌĞƐƵůƚŝŶŝƚƐĚŝĨĨĞƌĞŶĐĞĨŽƌŵŝŶĐŽŶƐƚƌƵĐƚŝŶŐŚŝƐ ƌĞƐƵůƚĂŶƚƚĂďůĞƐ͘Ϳ,ĞŶĞĞĚĞĚƚŚĞ ƌĞĐƚŝĨŝĐĂƚŝŽŶ ĂƐ Ă ƉƌŽdžLJ ĨŽƌ ƚŚĞ ŝŶƚĞŐƌĂƚŝŽŶ ŽĨ ƚŚĞ ƐĞĐĂŶƚ ĨƵŶĐƚŝŽŶ͕ ǁŚŝĐŚ ŽĨ ĐŽƵƌƐĞ ǁĂƐŶΖƚĂǀĂŝůĂďůĞ ƚŽ Śŝŵ͘ ,ĞƚŚĞŶŚĂĚ ƚŽ ĐĂůĐƵůĂƚĞƚŚĞƐŽͲĐĂůůĞĚ ĨƵŶĚĂŵĞŶƚĂů ĐŽŶƐƚĂŶƚ͕ ǁŚŝĐŚ ǁĞ ǁŽƵůĚǁƌŝƚĞ ĂƐ ƚŚĞ ŶĞŐĂƚŝǀĞ ĞdžƉŽŶĞŶƚŝĂů ŽĨ ŽŶĞ ŵŝŶƵƚĞ ŽĨ ĂƌĐ͘ Ƶƚ ŚĞ ƵƐĞĚ Ă ĚŝĨĨĞƌĞŶƚ ĂŶĚ ĂůŐĞďƌĂŝĐƉƌŽĐĞĚƵƌĞ͕ƐƚŝůůŐĞƚƚŝŶŐĂƌĞƐƵůƚĐŽƌƌĞĐƚƚŽƚŚĞĨŝƌƐƚ ĞůĞǀĞŶĨŝŐƵƌĞƐ͕ĂƐŝƚŚĂĚƚŽďĞƚŽĞŶƐƵƌĞƚŚĞĨŝŐƵƌĞƐŝŶŚŝƐĨŝŶĂůƚĂďůĞƐǁĞƌĞĐŽƌƌĞĐƚƚŽƐŝdžŽƌƐĞǀĞŶ

27 THOMAS HARRIOT - ENGLAND'S LEADING MATHEMATICIAN

ĨŝŐƵƌĞƐ͕ ĂƐ ƚŚĞLJ ǁĞƌĞ͘ /Ŷ ƚŚŝƐ ǁŽƌŬ ŚĞ ƵƐĞĚĂĚĞǀĞůŽƉŵĞŶƚŽĨƚŚĞĂůŐĞďƌĂŝĐƐLJŵďŽůŝƐŵŽĨŚŝƐ ŶĞĂƌĐŽŶƚĞŵƉŽƌĂƌLJ͕&ƌĂŶĕŽŝƐsŝğƚĞ;ϭϱϰϬʹϭϲϬϯͿ͕ǁŚŝĐŚŚĂĚŽŶůLJũƵƐƚďĞĞŶƉƵďůŝƐŚĞĚ͘;,ĞŵŝŐŚƚ ŽĨĐŽƵƌƐĞŚĂǀĞŬŶŽǁŶĂďŽƵƚŝƚƐŽŵĞǁŚĂƚĞĂƌůŝĞƌ ǀŝĂĐŽƌƌĞƐƉŽŶĚĞŶĐĞǁŝƚŚŚŝƐĨƌŝĞŶĚEĂƚŚĂŶŝĞů dŽƌƉŽƌůĞLJ;ϭϱϲϰʹϭϲϯϮͿǁŚŽǁĂƐŝŶƚŽƵĐŚǁŝƚŚsŝĞƚĂ ŝŶ&ƌĂŶĐĞ Ăƚ ĂďŽƵƚ ƚŚŝƐ ƚŝŵĞ͖ Ă ƐŽƌƚ ŽĨ ĞĂƌůLJƉƌĞƉƌŝŶƚ ĂƌƌĂŶŐĞŵĞŶƚ͘Ϳ ,Ğ ƚŚĞŶƉůƵŶŐĞĚŝŶƚŽ ƚŚĞ ĚŝƌĞĐƚĐĂůĐƵůĂƚŝŽŶŽĨƚŚĞŵĞƌŝĚŝŽŶĂůƉĂƌƚƐ͕ ďƵƚŶŽƚŝŵŵĞĚŝĂƚĞůLJ͕ĂƐƚŚĞƌĞǁĞƌĞƐŽŵĞůŽŽƐĞĞŶĚƐƚŽƚŝĞƵƉ͘/ŶƚŚĞ ĐĂůĐƵůĂƚŝŽŶƐ ŚĞ ǁĂƐ ŚĞůƉĞĚ ďLJ ŚŝƐ ĂƐƐŝƐƚĂŶƚ ŚƌŝƐƚŽƉŚĞƌ dŽŽŬĞ͕ƵƐŝŶŐ ĂǀĂƌŝĞƚLJ ŽĨ ĚŝƌĞĐƚ ĂŶĚŝŶƚĞƌƉŽůĂƚŝŽŶŵĞƚŚŽĚƐ͕ǁŚŝĐŚ ǁĞŶŽǁĂƐƐŽĐŝĂƚĞǁŝƚŚƚŚĞŶĂŵĞƐŽĨ>ĂƉůĂĐĞĂŶĚEĞǁƚŽŶ͘dŚŝƐ ǁŽƌŬĂůƐŽŝŶĐůƵĚĞĚŽďƚĂŝŶŝŶŐƚŚĞ ĞdžƉŽŶĞŶƚŝĂůƐĞƌŝĞƐ͕ǁŚŝĐŚŚĞĨŽƵŶĚĂƐƚŚĞůŝŵŝƚŽĨĂďŝŶŽŵŝĂůƐĞƌŝĞƐ͘ dŚĞƌĞƐƵůƚĂŶƚ ƚĂďůĞƐ ǁĞƌĞ ďLJ ĨĂƌ ƚŚĞ ďĞƐƚ ĂǀĂŝůĂďůĞ͕ ĞǀĞŶ ĂĨƚĞƌ/ŶƚĞƌŶĂƚŝŽŶĂů ,LJĚƌŽŐƌĂƉŚŝĐ ƵƌĞĂƵƉƵďůŝĐĂƚŝŽŶŽĨƚŚĞϭϵϮϬƐ͘ ;DŽĚĞƌŶƚĂďůĞƐĂůƐŽŝŶĐůƵĚĞƚŚŽƐĞƚĂŬŝŶŐŝŶƚŽĂĐĐŽƵŶƚƚŚĞƐůŝŐŚƚ ĨůĂƚƚĞŶŝŶŐĂƚƚŚĞƉŽůĞƐ͘ͿdŚĞ ĂĐĐƵƌĂĐLJŽĨ,ĂƌƌŝŽƚΖƐƚĂďůĞƐǁĂƐĨĂƌďĞLJŽŶĚƚŚĂƚĐĂůůĞĚĨŽƌŝŶƚŚĞŶĂǀŝŐĂƚŝŽŶŽĨƚŚĞƐŚŝƉƐŽĨŚŝƐ ƚŝŵĞ͖ƚĂďůĞƐƉƌŽĚƵĐĞĚďLJĂĨĞǁĂŚŝƐĐŽŶƚĞŵƉŽƌĂƌŝĞƐďLJƐŝŵƉůLJĂĚĚŝŶŐƐĞĐĂŶƚƐĂƚ ƐŵĂůůŝŶƚĞƌǀĂůƐ ǁĞƌĞƉĞƌĨĞĐƚůLJĂĚĞƋƵĂƚĞ͕ĞdžĐĞƉƚƉĞƌŚĂƉƐĂƚƚŚĞŚŝŐŚůĂƚŝƚƵĚĞƐŽĨƚŚĞƌĐƚŝĐĞdžƉůŽƌĞƌƐ͘

tŚĞŶ ƐŽŵĞ ŽĨ ŚŝƐ ƉĂƉĞƌƐ ǁĞƌĞ ƌĞĐŽǀĞƌĞĚ ƚŽǁĂƌĚƐ ƚŚĞ ĞŶĚ ŽĨ ƚŚĞ ĞŝŐŚƚĞĞŶƚŚ ĐĞŶƚƵƌLJ͕ ƚŚĞLJ ǁĞƌĞũƵĚŐĞĚ ƚŽ ŚĂǀĞ ͞ŽŶůLJ͟ ŚŝƐƚŽƌŝĐ ŝŶƚĞƌĞƐƚ͖ ŵĂƚŚĞŵĂƚŝĐƐ ŚĂĚ ŵŽǀĞĚ ŽŶ͘/Ŷ ƉĂƌƚŝĐƵůĂƌ͕ ŚŝƐ ĂůŐĞďƌĂ͕ǁŚŝĐŚ:ŽŚŶtĂůůŝƐŚĂĚƉƌĂŝƐĞĚůĂƚĞƌŝŶƚŚĞƐĞǀĞŶƚĞĞŶƚŚĐĞŶƚƵƌLJ͕ĂŶĚǁŚŝĐŚŚĂĚďĞĞŶ ƉƵďůŝƐŚĞĚŝŶ ĂŶŝŶĐŽŵƉůĞƚĞ ĂŶĚ ƐŽŵĞǁŚĂƚ ŵĂŶŐůĞĚ ĨŽƌŵ ŝŶ ϭϲϯϭ͕ ƚĞŶ LJĞĂƌƐ ĂĨƚĞƌ ŚŝƐ ĚĞĂƚŚ͕ ŚĂĚ ŶĞǀĞƌƚŚĞůĞƐƐĞdžƉůĂŝŶĞĚŚŽǁƌŽŽƚƐŽĨĞƋƵĂƚŝŽŶƐǁĞƌĞƌĞůĂƚĞĚƚŽďŝŶŽŵŝĂůĨĂĐƚŽƌƐ͘dŚŝƐŵŝŐŚƚ ƐĞĞŵŽďǀŝŽƵƐƚŽƵƐŶŽǁ͕ďƵƚƐŽŵĞŽŶĞŚĂƐƚŽƐĂLJŝƚĨŽƌƚŚĞĨŝƌƐƚƚŝŵĞ͕ĂŶĚƚŚĞĐŽŶǀĞƌƐĞŝƐŶΖƚ ĂĐƚƵĂůůLJŽďǀŝŽƵƐĂƚĂůů͘;/ƚ ŝƐƐƚŝůůĚŝƐƉƵƚĞĚǁŚĞƚŚĞƌ'ĂƵƐƐΖƉƌŽŽĨŝƐƌĞĂůůLJĂƉƌŽŽĨ͘ͿdŚĞƉƵďůŝĐĂƚŝŽŶ ĂůƐŽĚŝƐĐƵƐƐĞƐŝŶƐŽŵĞ ĚĞƚĂŝůŶƵŵĞƌŝĐĂů ŵĞƚŚŽĚƐ ŽĨ ƐŽůǀŝŶŐ ƉŽůLJŶŽŵŝĂů ĞƋƵĂƚŝŽŶƐ ŽĨ ǀĂƌŝŽƵƐ ĚĞŐƌĞĞƐ͕ ĂŶĚ ŽďƚĂŝŶƐ ƐŽŵĞŝŶĞƋƵĂůŝƚŝĞƐ͘/ƚĂůƐŽŝŶƚƌŽĚƵĐĞƐƐŽŵĞŶŽƚĂƚŝŽŶƐƚŚĂƚƌĞŵĂŝŶǁŝƚŚ ƵƐ͕ĂůďĞŝƚŝŶĂƐŝŵƉůŝĨŝĞĚĨŽƌŵ͕ Ğ͘Ő͘ƚŚĞŝŶĞƋƵĂůŝƚLJƐŝŐŶƐ͘ŵŽĚĞƌŶ;ϮϬϬϳͿƚƌĂŶƐůĂƚŝŽŶŝƐŶŽǁ ĂǀĂŝůĂďůĞ͕ĨƌŽŵƚŚĞ>ĂƚŝŶ͘;,ĂƌƌŝŽƚǁĂƐĂůƐŽ Ă ǀĞƌLJ ŐŽŽĚ 'ƌĞĞŬ ƐĐŚŽůĂƌ͕ ĂƉƉĂƌĞŶƚůLJ͕ ƉƌĂŝƐĞĚ ďLJ 'ĞŽƌŐĞ ŚĂƉŵĂŶ͕ ŚŝƐ ĐŽŶƚĞŵƉŽƌĂƌLJ ĂŶĚůŽŶŐͲƚŝŵĞĨƌŝĞŶĚ͕ĂŶĚƚŚĞƚƌĂŶƐůĂƚŽƌŽĨ,ŽŵĞƌ;ĐĨ͘KŶ ĨŝƌƐƚůŽŽŬŝŶŐŝŶƚŽŚĂƉŵĂŶΖƐ,ŽŵĞƌ͕ďLJ:ŽŚŶ<ĞĂƚƐͿ͘ ,ĂƌƌŝŽƚǁĂƐ͕ĨŽƌŚĂƉŵĂŶ͕͞ŵĂƐƚĞƌŽĨĂůů ƚƌƵĞĂŶĚĞƐƐĞŶƚŝĂůŬŶŽǁůĞĚŐĞ͟ĂŶĚŽŶĞ ͞ǁŚŽƐĞũƵĚŐĞŵĞŶƚĂŶĚŬŶŽǁůĞĚŐĞ/ŬŶŽǁƚŽďĞ ŝŶĐŽŵƉĂƌĂďůĞ͘͟ǀĞŶĂůůŽǁŝŶŐĨŽƌƚŚĞŶĂƚƵƌĞŽĨĚĞĚŝĐĂƚŝŽŶƐƚŚĞŶ͕ƚŚŝƐŝƐŶŽŵĞĂŶƉƌĂŝƐĞ͕ĂŶĚĨƌŽŵ ƐŽŵĞŽŶĞǁŚŽƐĞŽǁŶũƵĚŐĞŵĞŶƚĐŽƵůĚďĞƌĞůŝĞĚŽŶŝŶƐƵĐŚŵĂƚƚĞƌƐ͘

,ĂƌƌŝŽƚŚĂĚŶƵŵĞƌŽƵƐŽƚŚĞƌƚŚŝŶŐƐƚŽŽĨĨĞƌ͘ dŚĞƌĞǁĂƐŚŝƐĂƐƚƌŽŶŽŵLJ͕ŝŶǁŚŝĐŚŚĞďĞĂƚ'ĂůŝůĞŽ ƚŽƚĞůĞƐĐŽƉŝĐŽďƐĞƌǀĂƚŝŽŶŽĨƚŚĞŵŽŽŶ͕:ƵƉŝƚĞƌΖƐƐĂƚĞůůŝƚĞƐ͕ƐƵŶƐƉŽƚƐ;ŚĞĞƐƚŝŵĂƚĞĚƚŚĞƌŽƚĂƚŝŽŶŽĨ ƚŚĞƐƵŶĨƌŽŵƚŚĞƐĞͿĂŶĚƚŚĞĐŽŵĞƚƐŽĨϭϲϬϳĂŶĚϭϲϭϴ͘ <ĞƉůĞƌǁƌŽƚĞƚŽŚŝŵĨƌŽŵWƌĂŐƵĞ;ϭϲϬϲͿ ĂŶĚƚŚĞƌĞĞŶƐƵĞĚĂďƌŝĞĨĐŽƌƌĞƐƉŽŶĚĞŶĐĞŽǀĞƌƚŚĞŶĞdžƚĨĞǁLJĞĂƌƐ͕ƚŚĞƉĞƌŝŽĚŽĨŚŝƐ;<ĞƉůĞƌΖƐͿ ǁŽƌŬŽŶDĂƌƐĐŽŵŝŶŐŽƵƚ͘ ,ĂƌƌŝŽƚŚĂĚĐůŽƐĞĐŽŶŶĞĐƚŝŽŶƐǁŝƚŚƵƚĐŚŵĂƚƚĞƌƐ͕ǀŝĂƚŚĞĞĂƌůŽĨ >ĞŝĐĞƐƚĞƌ͕ǁŚŽǁĂƐŽŶĞ ŽĨƚŚĞĞdžĞĐƵƚŽƌƐŽĨŚŝƐ ĞƐƚĂƚĞůĂƚĞƌŽŶ͘ ;KŶĞŽĨ >ĞŝĐĞƐƚĞƌΖƐƚŝƚůĞƐ ǁĂƐ >ŝƐůĞ͘ dŚĞĨĂŵŝůLJŶĂŵĞǁĂƐ^ŝĚŶĞLJʹ^ŝƌWŚŝůŝƉǁĂƐŚŝƐĞůĚĞƌďƌŽƚŚĞƌ͘KŶĞĚĂŵ,ĂƌƌŝŽƚ͕ĂƉƌŝĞƐƚ͕ŝƐ ƌĞĐŽƌĚĞĚĂƚ <ŝŶŐƐƚŽŶ>ŝƐůĞ͕ŝŶƚŚĞKdžĨŽƌĚĂƌĞĂ͕ƐĞǀĞƌĂůĚĞĐĂĚĞƐĞĂƌůŝĞƌ͘dŚĞĞĂƌůŚŝŵƐĞůĨŚĂĚďĞĞŶĂ 'ŽǀĞƌŶŽƌŽĨ&ůƵƐŚŝŶŐŝŶ ƚŚĞ EĞƚŚĞƌůĂŶĚƐ͘ dŚĞ ĨĂŵŝůLJ ĐŽŶŶĞĐƚŝŽŶ ŚĂƐ ŶĞǀĞƌ ďĞĞŶ ƉƌŽǀĞĚ͕ ďƵƚŽĨ ƐƵĐŚƚŚŝŶŐƐ ŚŝƐƚŽƌLJ ŝƐƐŽŵĞƚŝŵĞƐ ŵĂĚĞ͘Ϳ dŚŝƐ ŵŝŐŚƚ ĞdžƉůĂŝŶ ŚŝƐ ĞĂƌůLJ ŬŶŽǁůĞĚŐĞ ŽĨ ƚŚĞ ƚĞůĞƐĐŽƉĞ͕ǁŚŝĐŚ ŚĂĚ ďĞĞŶĚĞǀĞůŽƉĞĚ ŝŶ ƚŚĞ EĞƚŚĞƌůĂŶĚƐ͘ ,Ğ ŵĂĚĞ͕ Žƌ ŚĂĚ ŵĂĚĞ ĨŽƌ Śŝŵ͕ ƚĞůĞƐĐŽƉĞƐǁŝƚŚ Ă ƌĂŶŐĞ ŽĨŵĂŐŶŝĨŝĐĂƚŝŽŶƐ͘ ŽŶŶĞĐƚĞĚ ǁŝƚŚ ĂƐƚƌŽŶŽŵLJ͕ ŚĞ ƐƚƵĚŝĞĚ ŽƉƚŝĐƐ ŝŶ ƚŚĞ ƉĞƌŝŽĚĨƌŽŵ ĂďŽƵƚ ϭϱϵϳ ƚŽϭϲϬϮ͕ ĚĞƌŝǀŝŶŐ ĨƌŽŵ ĞdžƉĞƌŝŵĞŶƚƐ ƚŚĞ ƐŝŶĞ ůĂǁ ŽĨ ƌĞĨƌĂĐƚŝŽŶ͕ ǁŚŝĐŚ ŚĞĂƉƉůŝĞĚ ƚŽ ƋƵĞƐƚŝŽŶƐ ŽĨĚŝƐƉĞƌƐŝŽŶĂŶĚƚŚĞŚĞŝŐŚƚŽĨƚŚĞƉƌŝŵĂƌLJƌĂŝŶďŽǁ͕ǁŚŝĐŚŚĞ ƐŚŽǁĞĚŽĐĐƵƌƌĞĚǁŚĞŶƚĂŶ ŝсϮƚĂŶƌ;ƚŚĞƐŽͲĐĂůůĞĚƚƌŽƉŝĐĂůĂŶŐůĞƐ͖ƌĞƉůĂĐŝŶŐƚŚĞ͞Ϯ͟ďLJŽƚŚĞƌ ŝŶƚĞŐĞƌƐŐŝǀĞƐƚŚĞŚĞŝŐŚƚŽĨĂǁŚŽůĞƐĞƌŝĞƐŽĨ ƌĂŝŶďŽǁƐ͕ ƚŚĞ ĨŝƌƐƚ ƚǁŽ ŽƌƚŚƌĞĞ ŽĨ ǁŚŝĐŚ ĂƌĞ ƐŽŵĞƚŝŵĞƐ ƚŽďĞ ƐĞĞŶͿ͘ ůů ŽĨ ƚŚŝƐ ǁŽƌŬ ŝƐ ŶŽǁĐƌĞĚŝƚĞĚƚŽĞŝƚŚĞƌĞƐĐĂƌƚĞƐ;ϭϱϵϲʹϭϲϱϬͿŝŶ ϭϲϯϳŽƌ^ŶĞůů;ϭϱϴϭʹϭϲϮϱͿŝŶϭϲϮϭ͕ƚŚĞĨŽƌŵĞƌĂůƐŽŐĞƚƚŝŶŐ ƚŚĞ ŚŽŶŽƵƌ ĨŽƌ ŵŽƐƚ ŽĨ ŚŝƐ ƉƌĞĚĞĐĞƐƐŽƌΖƐ ǁŽƌŬ ŝŶĂůŐĞďƌĂ͘ dŚĂƚ ĂƚƚƌŝďƵƚŝŽŶ ƐĞĞŵƐ ƚŽ ŚĂǀĞďĞĐŽŵĞŝŶĚĞůŝďůĞ͕ǁŝƚŚĞƐĐĂƌƚĞƐ ;ϭϱϵϲʹϭϲϱϬͿ;ϭϲϯϳͿŐĞƚƚŝŶŐƚŚĞƐŽůĞĐƌĞĚŝƚĨŽƌ͞ƚŚĞŝŶǀĞŶƚŝŽŶŽĨĂůŐĞďƌĂŝĐ ŐĞŽŵĞƚƌLJ͟;ƉĞƌŚĂƉƐ ƐŚĂƌĞĚ ǁŝƚŚ &ĞƌŵĂƚ;ϭϲϬϭ ʹ ϲϱͿ ďLJ ƚŚĞ ŵŽƌĞ ŬŶŽǁůĞĚŐĞĂďůĞ͖ ŚŝƐǁŽƌŬ ǁĂƐ ŽŶůLJ ƉƵďůŝƐŚĞĚ ďLJ ŚŝƐ ƐŽŶ ŝŶ ƚŚĞϭϲϳϬƐͿ͕ ǁŚĞŶ ,ĂƌƌŝŽƚ ĂŶĚ sŝĞƚĂ ĂƌĞ ƚŚĞ ƚƌƵĞ ŵŽĚĞƌŶŝŶǀĞŶƚŽƌƐ͕ĂƐƚŚĞŝƌƐƵƌǀŝǀŝŶŐ ŬƐŽƌƉĂƉĞƌƐĐůĞĂƌůLJƐŚŽǁ͘ŶĚƐŽͲĐĂůůĞĚ͞ĐĂƌƚĞƐŝĂŶĐŽͲŽƌĚŝŶĂƚĞƐ͟ĂƌĞŶŽǁŚĞƌĞƚŽďĞƐĞĞŶŝŶ ĞƐĐĂƌƚĞƐΖǁƌŝƚŝŶŐƐ͖ŝƚΖƐĐĂůůĞĚĐƵůƚƵƌĂůĂƉƉƌŽƉƌŝĂƚŝŽŶ͘,ĂƌƌŝŽƚΖƐ ƐƵƌǀŝǀŝŶŐƉĂƉĞƌƐƐŚŽǁĂůůƐŽƌƚƐ

28 DR JON V. PEPPER

ŽĨ ŽƚŚĞƌ ŐŽŽĚ ƚŚŝŶŐƐ͕ ƐƵĐŚ ĂƐ ƚŚĞ ƐƋƵĂƌĞ ƌŽŽƚƐ ŽĨ ŶĞŐĂƚŝǀĞ ƋƵĂŶƚŝƚŝĞƐ͕ĂŶĚďŝŶĂƌLJ ĂƌŝƚŚŵĞƚŝĐ͕ ĨŽƌ ǁŚŝĐŚ ůĂƚĞƌ ƉĞŽƉůĞ ůŝŬĞ 'ĂƵƐƐ ĂŶĚ >ĞŝďŶŝnj ƵƐƵĂůůLJ ŐĞƚ ŵŽƐƚ ŽĨ ƚŚĞĐƌĞĚŝƚ͘dŚĞƌĞŝƐĂůƐŽĂ ƐŽůƵƚŝŽŶ;ƉƌŽďĂďůLJƚǁŽͿŽĨůŚĂnjĞŶΖƐƉƌŽďůĞŵŝŶŽƉƚŝĐƐ͕ŽŶǁŚŝĐŚďŽƚŚĂƌƌŽǁĂŶĚ,ƵLJŐĞŶƐ ǁƌŽƚĞůĂƚĞƌŽŶ͘

/ŶĨĂĐƚ͕ŚĞƌĞŝƐĂůŽŶŐůŝƐƚŽĨƚŚĞŶĂŵĞƐŽĨƉĞŽƉůĞŽĨǁŚŽŵ,ĂƌƌŝŽƚǁĂƐĂĐůĞĂƌĨŽƌĞƌƵŶŶĞƌŝŶǀĂƌŝŽƵƐ ŵĂƚƚĞƌƐ͗ ,ĂůůĞLJ͕ ĂƌƌŽǁ͕ EĞǁƚŽŶ͕ ĞƌŶŽƵůůŝ͕ ĞƐĐĂƌƚĞƐ͕ ^ŶĞůů͕ :ĂŵĞƐ 'ƌĞŐŽƌLJ͕ ,ƵLJŐĞŶƐ͕>ĂƉůĂĐĞ͘ ŶĚŚĞƌĞĂƌĞŽƚŚĞƌƚŚŝŶŐƐƚŚĂƚŚĞĚŝĚ͕ŝŶƐƵŵŵĂƌLJ͘/ŵƉĂĐƚƐĂŶĚĞůĂƐƚŝĐŝƚLJ͕ďĂůůŝƐƚŝĐƐĂŶĚƉƌŽũĞĐƚŝůĞƐ͕ ƐŚŝƉĚĞƐŝŐŶĂŶĚďƵŝůĚŝŶŐ;ƵůĞƌĂůƐŽǁƌŽƚĞĞdžƚĞŶƐŝǀĞůLJŽŶƚŚĞƐĞͿ͕ĐĂůĞŶĚĂƌ͕ĐŽŵďŝŶĂƚŽƌŝĐƐ͕ ƐƉŚĞƌŝĐĂůƚƌŝĂŶŐůĞƐ;ŚĞǁĂƐƉƌŽďĂďůLJƚŚĞĨŝƌƐƚƚŽĚĞƌŝǀĞƚŚĞŝƌĂƌĞĂʹƌŝŐŐƐƐĂŝĚƐŽŝŶϭϲϯϬͿ͘,Ğ ĂůƐŽƐĂǁƚŚĞĐůŽƐĞ ĐŽŶŶĞĐƚŝŽŶ ďĞƚǁĞĞŶ ŚŝƐ ŵĞƌͲƉĂƌƚƐ ĂŶĚ ůŽŐĂƌŝƚŚŵƐ͕ ĂŶĚ ŚŝƐƚĂďůĞƐ ǁĞƌĞ ŵŽƌĞ ĂĐĐƵƌĂƚĞ ƚŚĂŶEĂƉŝĞƌΖƐĂŶĚŚĞŬŶĞǁŝƚ͖ƚŚĞŝƌĨƵŶĚĂŵĞŶƚĂůĐŽŶƐƚĂŶƚƐǁĞƌĞĨŽƌŵĞĚŝŶ ĚŝĨĨĞƌĞŶƚǁĂLJƐ͕ŽŶĞǁĂƐĂƌŽŽƚ͕ƚŚĞŽƚŚĞƌĂŶĞdžƉŽŶĞŶƚŝĂů͘ŶĚďĞƚǁĞĞŶŝŶǀĞƌƐŝŽŶĂŶĚ ĐŽŶĨŽƌŵĂůŝƚLJ͘/ƚΖƐĚŝĨĨŝĐƵůƚƚŽƐĞĞƚŚĂƚŚĞ ŚĂĚƚŝŵĞĨŽƌĂŶLJƚŚŝŶŐĞůƐĞ͕ďƵƚŚĞĚŝĚŚĂǀĞ͘,ĞƌĂŶ ZĂůĞŐŚΖƐĞƐƚĂƚĞƐŝŶzŽƵŐŚĂůĨŽƌĂǁŚŝůĞŝŶƚŚĞϭϱϵϬƐ͘

,Ğ ŚĂĚ ŚŝƐ ŽǁŶ ƐŵĂůů ĞƐƚĂƚĞƐ ŝŶ ŽƌŶǁĂůů ĂŶĚ EŽƌĨŽůŬ͕ ĂŶĚ ǁŽƌŬĞĚ ĨŽƌ ŝƚƐ ĞĂƌů ƵƉ ŝŶ EŽƌƚŚƵŵďĞƌůĂŶĚ͘ WĞƌŚĂƉƐ ŝƚΖƐ ŶŽƚ ƐŽ ƐƵƌƉƌŝƐŝŶŐ ƚŚĂƚ ŚĞ ŶĞǀĞƌ ŐŽƚ ĂƌŽƵŶĚ ƚŽ ƉƵďůŝĐĂƚŝŽŶ͘ ,Ğ ŚĂĚŝŶƚĞƌĞƐƚƐŝŶƚŚĞŽůŽŐLJĂƐǁĞůů͕ǁŚŝĐŚŚĂĚŝƚƐĚĂŶŐĞƌƐŝŶƚŚŽƐĞďĞŶŝŐŚƚĞĚƚŝŵĞƐ͖ŽŶĞŽĨƚŚĞƚŚŝŶŐƐ ƚŚĂƚŚĞǁƌŽƚĞƚŽ<ĞƉůĞƌ;ŝŶ>ĂƚŝŶͿǁĂƐ͞,ĞƌĞŝƚŝƐŶŽƚƉŽƐƐŝďůĞĨŽƌƵƐƚŽƉŚŝůŽƐŽƉŚŝƐĞĨƌĞĞůLJ͘tĞĂƌĞ ƐƚƵĐŬŝŶƚŚĞŵƵĚ͘͟;EĂƚƵƌĂůƉŚŝůŽƐŽƉŚLJǁĂƐƚŚĞŶĂŵĞŐŝǀĞŶƚŽƐĐŝĞŶĐĞĂƚƚŚĂƚƚŝŵĞ͕ĂŶĚĨŽƌůŽŶŐ ĂĨƚĞƌ͘Ϳ

,ŽǁĚŽǁĞŬŶŽǁĂůůƚŚĂƚǁĞĚŽŬŶŽǁĂďŽƵƚŚŝŵ͍dŚĞŶĞǁZŽLJĂů^ŽĐŝĞƚLJůŽŽŬĞĚĨŽƌŚŝƐ ƐƵƌǀŝǀŝŶŐ ƉĂƉĞƌƐŝŶƚŚĞϭϲϲϬƐ͕ďƵƚǁŝƚŚŽƵƚƐƵĐĐĞƐƐ͘dŚĞLJƐĞĞŵƚŽŚĂǀĞďĞĞŶůŽƐƚ͕ůŝŬĞƌŝƐƚŽƚůĞΖƐůĞĐƚƵƌĞ ŶŽƚĞƐŶĞĂƌůLJƚǁŽƚŚŽƵƐĂŶĚLJĞĂƌƐĞĂƌůŝĞƌ;ƌŝƐƚŽƚůĞΖƐŽƚŚĞƌǁŽƌŬƌĞĂůůLJŚĂĚďĞĞŶůŽƐƚͿ͘ƵƚƚŽǁĂƌĚƐ ƚŚĞĞŶĚŽĨƚŚĞĞŝŐŚƚĞĞŶƚŚĐĞŶƚƵƌLJƚŚŽƵƐĂŶĚƐŽĨƚŚĞŵƚƵƌŶĞĚƵƉĂŵŽŶŐƚŚĞƐƚĂďůĞĂĐĐŽƵŶƚƐĂƚ WĞƚǁŽƌƚŚ͕ƚŚĞ^ƵƐƐĞdž ƐĞĂƚ ŽĨ ŚŝƐ ůĂƚĞƌ ƉĂƚƌŽŶ͘ĨƚĞƌ ƐŽŵĞ ƚŽͲŝŶŐ ĂŶĚ ĨƌŽͲŝŶŐ͕ ƚŚĞLJ ǁĞƌĞŶΖƚ ĚĞĞŵĞĚ ǁŽƌƚŚLJŽĨƉƵďůŝĐĂƚŝŽŶ ʹ ƚŚĞ ŵĂƚŚĞŵĂƚŝĐĂů ƐĐŝĞŶĐĞƐ ŚĂĚ ŵŽǀĞĚ ŽŶ͕ Žƌ ŵĂŶLJ ŽĨ ƚŚĞŵ ŚĂĚ͕ ďƵƚ ŽŶĞ ŽƌƚǁŽĂĐĐŽƵŶƚƐŽĨƚŚĞŵǁĞƌĞƉƵďůŝƐŚĞĚŽǀĞƌƚŚĞŶĞdžƚĨĞǁĚĞĐĂĚĞƐ͘DŽƐƚ͕ďƵƚŶŽƚ ĂůůŽĨƚŚĞŵ͕ǁĞŶƚƚŽƚŚĞƌŝƚŝƐŚDƵƐĞƵŵĂďŽƵƚϭϴϭϬ͘&͘t͘ĞƐƐĞůΖƐǀĞƌLJĨŝƌƐƚƉĂƉĞƌǁĂƐŽŶ ,ĂƌƌŝŽƚΖƐĐŽŵĞƚŽďƐĞƌǀĂƚŝŽŶƐ ŽĨϭϲϬϳ͖ &ƌĂŶnj͕ ĂƌŽŶ ǀŽŶ ĂĐŚ͕ ƚŚĞ 'ĞƌŵĂŶ ĂƐƚƌŽŶŽŵĞƌ ǁŚŽ ŚĂĚ ĨŽƵŶĚ ƚŚĞƉĂƉĞƌƐ ŝŶ WĞƚǁŽƌƚŚ͕ƉƵďůŝƐŚĞĚ ĂĐĐŽƵŶƚƐ ŽĨ ƐŽŵĞ ŽĨ ƚŚĞŵ͕ ĂŶĚ ^ƚĞƉŚĞŶ ZŝŐĂƵĚ͕ ƚŚĞ KdžĨŽƌĚĂƐƚƌŽŶŽŵĞƌ͕ ƉƵďůŝƐŚĞĚ ĂůĞŶŐƚŚLJĂĐĐŽƵŶƚ ŝŶ ϭϴϯϯ͘^ŽŵĞŵĞƌŝĐĂŶƐůĂƚĞƌ ŚĂĚ ĂŶ ŝŶƚĞƌĞƐƚ ŝŶ ŚŝƐĐŽŶŶĞĐƚŝŽŶ ǁŝƚŚ ƚŚĞ KƵƚĞƌĂŶŬƐŽĨEŽƌƚŚĂƌŽůŝŶĂĂŶĚǁŚĂƚŚĂĚďĞĞŶƚŚĞĨŝƌƐƚ ŶŐůŝƐŚĐŽůŽŶLJŝŶEŽƌƚŚŵĞƌŝĐĂ͖ŝƚǁĂƐŶΖƚ ƚŚĞWŝůŐƌŝŵ&ĂƚŚĞƌƐ;ϭϲϮϬͿŽƌĞǀĞŶƚŚĞ:ĂŵĞƐƚŽǁŶ ĐŽůŽŶLJŝŶϭϲϬϴ͕ďƵƚƚŚĞĞdžƉĞĚŝƚŝŽŶŽĨϭϱϴϱͲϴϲ ǁŚŝĐŚůĞĚƚŽ͞ůŽƐƚĐŽůŽŶLJ͟ŽĨϭϱϴϴ͕ŶŽƚĂŐŽŽĚLJĞĂƌ ĨŽƌŽǀĞƌƐĞĂƐǀĞŶƚƵƌĞƐďLJŶŐůĂŶĚ͘ĨƚĞƌϭϵϰϱƐĐŚŽůĂƌƐďĞŐĂŶĂŐĂŝŶƚŽƐŚŽǁĂŶĂĐƚŝǀĞŝŶƚĞƌĞƐƚŝŶ ,ĂƌƌŝŽƚΖƐEĂĐŚůĂƐƐ͘/ƚǁĂƐŽŶůLJŽŶĞŽĨƚŚĞŝƌŝŶƚĞƌĞƐƚƐ͕ďƵƚŝƚůĞĚĞǀĞŶƚƵĂůůLJƚŽĂƐĞƌŝĞƐŽĨŽǀĞƌƚǁĞŶƚLJ ĂŶŶƵĂůůĞĐƚƵƌĞƐďĞŝŶŐŐŝǀĞŶŝŶKdžĨŽƌĚ͕ĂƐǁĞůůĂƐ ƐĞŵŝŶĂƌƐďĞŝŶŐŚĞůĚŝŶďŽƚŚKdžĨŽƌĚĂŶĚ ƵƌŚĂŵ͕ǁŝƚŚŶƵŵĞƌŽƵƐƉĂŵƉŚůĞƚƐ;ŬůĞƚƐͿĂůƐŽƉƵďůŝƐŚĞĚ͘ dŚĞŵĂŶƵƐĐƌŝƉƚƐŚĂǀĞďĞĞŶŵĂĚĞ ĂǀĂŝůĂďůĞŽŶůŝŶĞ͖ƉƌĞǀŝŽƵƐůLJŝŶyĞƌŽdžĐŽƉLJĂŶĚŵŝĐƌŽĨŝůŵ͕ĂŶĚƐŽŵĞƉĞŽƉůĞ ŚĂǀĞ ƐƉŽŬĞŶ ŽĨ ͞,ĂƌƌŝŽƚ ƌĞǀŝǀĞĚ͘͟ ďƌŽŶnjĞ ĐŽƉLJ ŽĨ ,ĂƌƌŝŽƚΖƐ ŵĞŵŽƌŝĂů ŝŶƐĐƌŝƉƚŝŽŶ ǁĂƐƵŶǀĞŝůĞĚŝŶƚŚĞĨŽLJĞƌŽĨ ƚŚĞĂŶŬŽĨŶŐůĂŶĚŽŶƚŚĞϯϱϬƚŚĂŶŶŝǀĞƌƐĂƌLJŽĨŚŝƐĚĞĂƚŚ͕ƚŚĞϮŶĚ:ƵůLJϭϵϳϭ͘;EĞdžƚLJĞĂƌǁŝůůďĞƚŚĞ ϰϬϬƚŚĂŶŶŝǀĞƌƐĂƌLJ͘Ϳ

džƚĞŶƐŝǀĞ ďŝďůŝŽŐƌĂƉŚŝĞƐ ĐŽǀĞƌŝŶŐ ƚŚĞ ƉĞƌŝŽĚƐ ŽĨ ϭϵϳϰͲϮϬϬϬ ĂŶĚ ϮϬϬϬͲϮϬϭϮ ĂƉƉĞĂƌ ŝŶ ƚŚĞ ƚǁŽǀŽůƵŵĞƐŽĨƚŚĞĂŶŶƵĂůůĞĐƚƵƌĞƐƐŽĨĂƌƉƵďůŝƐŚĞĚ͕dŚŽŵĂƐ,ĂƌƌŝŽƚ͕ĂŶůŝnjĂďĞƚŚĂŶŵĂŶŽĨ ƐĐŝĞŶĐĞ͕ZŽďĞƌƚ&Ždž;ĞĚ͘Ϳ;ƐŚŐĂƚĞ͕ϮϬϬϬͿĂŶĚdŚŽŵĂƐ,ĂƌƌŝŽƚĂŶĚŚŝƐǁŽƌůĚ͕ZŽďĞƌƚ&Ždž;ĞĚ͘Ϳ ;ƐŚŐĂƚĞ͕ϮϬϭϮͿ͘ĂƌůŝĞƌǁŽƌŬƐĂƌĞůŝƐƚĞĚŝŶƚŚĞďŝďůŝŽŐƌĂƉŚLJŽĨ:ŽŚŶ^ŚŝƌůĞLJΖƐ dŚŽŵĂƐ,ĂƌƌŝŽƚ͕Ă ďŝŽŐƌĂƉŚLJ;KdžĨŽƌĚ͕ϭϵϴϯͿƉƉ͘ϰϳϲͲϰϵϬ͘/ƚǁŽƵůĚƚĂŬĞƵƉƚŽŽŵƵĐŚƐƉĂĐĞƚŽůŝƐƚƚŚĞĚŽnjĞŶƐŽĨƉĞŽƉůĞ ǁŚŽŚĂǀĞĐŽŶƚƌŝďƵƚĞĚƚŽ,ĂƌƌŝŽƚƐƚƵĚŝĞƐŝŶƚŚĞůĂƐƚĨŝĨƚLJLJĞĂƌƐŽƌƐŽ͘ /ŶƐƚĞĂĚ/ǁŝůůŝůůƵƐƚƌĂƚĞƚŚĞ ŽƚŚĞƌƉůĂƋƵĞ͕ǁŚŝĐŚŝƐŶŽǁƚŽďĞƐĞĞŶĂƚ^ŝŽŶ,ŽƵƐĞ;/ƐůĞǁŽƌƚŚͿ͕ǁŚĞƌĞ,ĂƌƌŝŽƚŚĂĚĂŚŽƵƐĞ;ŶŽ ůŽŶŐĞƌ ƐƚĂŶĚŝŶŐͿďƵŝůƚĨŽƌŚŝŵďLJ,ĞŶƌLJWĞƌĐLJŝŶϭϲϬϴ͘dŚŝƐŐŝǀĞƐƚŚĞǀŝƐŝƚŽƌĂŶŝŶĚŝĐĂƚŝŽŶŽĨ ,ĂƌƌŝŽƚΖƐĂĐŚŝĞǀĞŵĞŶƚƐ͘

29 CHALKDUST

ŚĂůŬĚƵƐƚDĞŵŽƌŝĞƐ ŚĂƉƉĞŶ͕ǁĞƐƚĂƌƚĞĚƚŚĞĚĂLJǁŝƚŚŶŽƚŚŝŶŐ ŵŽƌĞƚŚĂŶĂĐŽůůĞĐƟŽŶŽĨĂƌƟĐůĞƐŝŶǀĂƌŝŽƵƐ dŽĐŽŵŵĞŵŽƌĂƚĞƚŚĞϱƚŚďŝƌƚŚĚĂLJŽĨ ƐƚĂŐĞƐŽĨĐŽŵƉůĞƟŽŶ͕ĂĨĞǁŚĂůĨͲĨŽƌŵĞĚŝĚĞĂƐ ŚĂůŬĚƵƐƚŵĂŐĂnjŝŶĞĂŶĚůĂƵŶĐŚŽĨƚŚĞϭϬƚŚ ĨŽƌũŽŬĞƐĂŶĚƉůĂĐĞƐƚŽŚŝĚĞĂƐĐŽƌƉŝŽŶ͕ďƵƚ ŝƐƐƵĞǁĞĚĞĐŝĚĞĚƚŽƐŚĂƌĞŽƵƌĨĂǀŽƵƌŝƚĞ ĂŌĞƌŵĂŶLJŚŽƵƌƐ͕ĐƵƉƐŽĨƚĞĂ͕ƉŝnjnjĂĂŶĚƐŽŵĞ ŵĞŵŽƌŝĞƐ͊,ĞƌĞŝƐǁŚĂƚŝƚ͛ƐůŝŬĞďĞŚŝŶĚƚŚĞ ƐĞƌŝŽƵƐ>ĂdĞyŵĂƐƚĞƌLJǁĞŚĂĚĂŵĂŐĂnjŝŶĞ ƐĐĞŶĞƐ͗ ƌĞĂĚLJƚŽŐŽ͘dŚĞƌĞ͛ƐĂůǁĂLJƐĂďƵnjnjĂƌŽƵŶĚ ƚŚŝƐƐƚĂŐĞŽĨƚŚĞŵĂŐĂnjŝŶĞ͕ĂŶĚLJŽƵĮŶŝƐŚ KŶĞŽĨƚŚĞĮƌƐƚƚŚŝŶŐƐƚŚĂƚ/ŐŽƚƚŽĚŽ ƟƌĞĚďƵƚĞdžƚƌĞŵĞůLJƐĂƟƐĮĞĚ͘ ĂƐƉĂƌƚŽĨŚĂůŬĚƵƐƚǁĂƐƚŽŝŶƚĞƌǀŝĞǁ DĂƌĐƵƐĚƵ^ĂƵƚŽLJ͘,ĞŚĂĚĂůǁĂLJƐďĞĞŶĂŶ ŝŶƐƉŝƌĂƟŽŶƚŽŵĞǁŚĞŶ/ǁĂƐĂƚƐĐŚŽŽůĂŶĚ ĂŶƵŶĚĞƌŐƌĂĚƵĂƚĞ͕ĂŶĚǁŚĞŶ/ũŽŝŶĞĚƚŚĞ ƚĞĂŵŵLJĮƌƐƚũŽďǁĂƐƚŽĮŶĚĂŶŝŶƚĞƌǀŝĞǁ ƐƵďũĞĐƚ͘/ǁĂƐƋƵŝƚĞŶĞƌǀŽƵƐ͕ďƵƚDĂƌĐƵƐǁĂƐ ĞdžƚƌĞŵĞůLJĨƌŝĞŶĚůLJĂŶĚĞŶŐĂŐŝŶŐĂŶĚŚĂĚ ůŽƚƐŽĨŐƌĞĂƚƟƉƐĨŽƌƐĐŝĞŶĐĞĐŽŵŵƵŶŝĐĂƟŽŶ ƚŚĂƚŚĂǀĞŚĞůƉĞĚŵĞĞǀĞƌƐŝŶĐĞ͕ďŽƚŚǁŚĞŶ ǁƌŝƟŶŐĨŽƌƚŚĞŵĂŐĂnjŝŶĞĂŶĚǁŚĞŶĚŽŝŶŐŵLJ ŽǁŶƌĞƐĞĂƌĐŚ͘/ƚǁĂƐĂŵĂnjŝŶŐƚŽŚĂǀĞƐƵĐŚ a great opportunity so early on, and it really ŚĞůƉĞĚŵĞĨĞĞůůŝŬĞĂǀĂůƵĞĚƉĂƌƚŽĨƚŚĞƚĞĂŵ ĂŶĚƚŚƵƐĐůŽƐĞƌƚŽŵLJWŚĐŽůůĞĂŐƵĞƐ͘

ŚĂůŬLJ^ĂƚƵƌĚĂLJ

/ŶϮϬϭϲ͕/ǁĞŶƚƚŽƚŚĞDdZ/yĐŽŶĨĞƌĞŶĐĞ ŝŶ>ĞĞĚƐ͘DdZ/yŝƐĂĐŽŶĨĞƌĞŶĐĞĂŝŵĞĚ ĂƚƉĞŽƉůĞŝŶǀŽůǀĞĚŝŶŵĂƚŚƐŽƵƚƌĞĂĐŚĂŶĚ ƉƵďůŝĐĞŶŐĂŐĞŵĞŶƚ͕ĂŶĚǁĂƐĂƩĞŶĚĞĚďLJ ƐƚƵĚĞŶƚƐ͕ĂĐĂĚĞŵŝĐƐ͕ĨƌĞĞůĂŶĐĞƌƐ͕ĂŶĚĂĨĞǁ ĨĂŵŽƵƐĨĂĐĞƐ͘dŚĞĨĂŵŽƵƐĨĂĐĞƐŝŶĐůƵĚĞĚZŽď ĂƐƚĂǁĂLJ͕ĂƵƚŚŽƌŽĨŵĂŶLJŬƐŝŶĐůƵĚŝŶŐ ΗdŚĞ,ŝĚĚĞŶDĂƚŚĞŵĂƟĐƐŽĨ^ƉŽƌƚΗĂŶĚ ŚĂůŬĚƵƐƚdĞĂŵĐĞůĞďƌĂƟŶŐƚŚĞϭϬƚŚŝƐƐƵĞ ΗtŚLJŽƵƐĞƐŽŵĞ/ŶdŚƌĞĞƐ͍Η Ɛ/ǁĂƐƚĂŬŝŶŐƚŚĞƐĞĐŽŶĚƐŝƉŽĨŵLJƉŝŶƚ͕Ă dŚĞĮƌƐƚƟŵĞƚŚĂƚ/ƚŽŽŬƉĂƌƚŝŶŚĂůŬLJ ǀŽŝĐĞƐĂŝĚ͗ΗDĂƩŚĞǁ͕ŝƐŶΖƚŝƚ͍ĂŶ/ũŽŝŶLJŽƵ͕ ^ĂƚƵƌĚĂLJ͕ƚŚĞďŝͲĂŶŶƵĂůĚĂLJǁŚĞƌĞǁĞĂůů /ΖǀĞďĞĞŶŵĞĂŶŝŶŐƚŽĐĂƚĐŚLJŽƵĂůůĚĂLJ͍Η/ ĐŽŵĞƚŽŐĞƚŚĞƌĂŶĚŵĂŬĞƚŚĞŵĂŐĂnjŝŶĞ ůŽŽŬĞĚƵƉƚŽƐĞĞZŽďĂƐƚĂǁĂLJ͊,ĞƐĂƚĚŽǁŶ

30 CHALKDUST

ĂŶĚĂƐŬĞĚŵĞĂůůĂďŽƵƚŚĂůŬĚƵƐƚ͕ƚŚĞŶ ƐƉŽƫŶŐƚŚĞĮƌƐƚƚLJƉŽLJŽƵŚĂǀĞĨŽƌŐŽƩĞŶʹ ŽīĞƌĞĚƚŽǁƌŝƚĞĂŶĂƌƟĐůĞĨŽƌƵƐ;ΗdŚŝŶŬŝŶŐ WƌŝĐĞůĞƐƐ͊ ŽƵƚƐŝĚĞŽƵƚƐŝĚĞƚŚĞďŽdžΗ͕ŝŶŝƐƐƵĞϬϳͿ͘ dŚŝƐǁĂƐƚŚĞĮƌƐƚƟŵĞƚŚĂƚĂŶĞƐƚĂďůŝƐŚĞĚ ŚĂůŬĚƵƐƚdĞĂŵ ŶĂŵĞŝŶƉŽƉƵůĂƌŵĂƚŚƐĐŽŵĞƚŽĂƐŬŵĞ ĂďŽƵƚƚŚĞŵĂŐĂnjŝŶĞ͕ƌĂƚŚĞƌƚŚĂŶŵĞŐŽŝŶŐ ƚŽŝŶƚƌŽĚƵĐĞƚŚĞŵƚŽŝƚ͕ĂŶĚŝƚǁĂƐƚŚĞƉŽŝŶƚ ĂƚǁŚŝĐŚŚĂůŬĚƵƐƚďĞŐĂŶƚŽĨĞĞůůŝŬĞƉĂƌƚŽĨ ƚŚĞŵĂƚŚƐŽƵƚƌĞĂĐŚĐŽŵŵƵŶŝƚLJƌĂƚŚĞƌƚŚĂŶ ĂƐŵĂůůƉƌŽũĞĐƚƚŚĂƚ/ǁŽƌŬĞĚŽŶǁŝƚŚĂĨĞǁ friends.

ŚĂůŬĚƵƐƚdĞĂŵǁŝƚŚĨƌĞƐŚůLJƉƌŝŶƚĞĚϭϬƚŚŝƐƐƵĞ

WůĞĂƐĞǀŝƐŝƚĐŚĂůŬĚƵƐƚŵĂŐĂnjŝŶĞ͘ĐŽŵƚŽǀŝĞǁ all the issues.

ŚĂůŬĚƵƐƚĂďƌŽĂĚ

DLJĨĂǀŽƵƌŝƚĞŵĞŵŽƌŝĞƐĨƌŽŵŚĂůŬĚƵƐƚĂƌĞ ĂůůƚŽĚŽǁŝƚŚƚŚĞůĂƵŶĐŚƉĂƌƟĞƐǁĞŽƌŐĂŶŝƐĞ ƚŽŵĂƌŬƚŚĞƌĞůĞĂƐĞŽĨĂŶĞǁŝƐƐƵĞ͊WƌŽĚƵĐŝŶŐ ĂŵĂŐĂnjŝŶĞĨƌŽŵƐĐƌĂƚĐŚŝƐĂůŽƚŽĨŚĂƌĚǁŽƌŬ͕ ďƵƚŝƚŵĂŬĞƐƚŚĞĐĞůĞďƌĂƟŽŶ͕ŽŚƐŽƐǁĞĞƚ͘ dŚĞĂƚŵŽƐƉŚĞƌĞŝƐĂůǁĂLJƐĂŵĂnjŝŶŐ͕ƉĞŽƉůĞ ůĂƵŐŚŝŶŐĂƚƚŚĞŵĂƚŚƐƉƵŶƐ͕ŚĂǀŝŶŐŚĞĂƚĞĚ ĚŝƐĐƵƐƐŝŽŶƐĂďŽƵƚƚŚĞǁŝƉĞŽƵƚƌŽƵŶĚŽƌũƵƐƚ ŵƵŶĐŚŝŶŐŽŶƐŽŵĞƉŝnjnjĂĂŶĚĐĂŬĞƐ͊^ĞĞŝŶŐ ĞǀĞƌLJŽŶĞŚĂƉƉLJ͕ĂŶĚĞŶũŽLJŝŶŐƚŚĞŵĂŐĂnjŝŶĞ ŝƐƚŚĞĂďƐŽůƵƚĞďĞƐƚĨĞĞůŝŶŐ͊

KƉĞŶŝŶŐĂďŽdžŽĨŚĂůŬĚƵƐƚ͕ĂŌĞƌĐĂƌƌLJŝŶŐϱϬ ŽĨƚŚĞŵƵƉϮŇŝŐŚƚƐŽĨƐƚĂŝƌƐĂŶĚƚŚĞŶŚŽůĚŝŶŐ ŝŶLJŽƵƌŚĂŶĚƐĂĐŽƉLJŽĨƚŚĞŶĞǁĞƐƚŝƐƐƵĞ ǁŝƚŚƚŚĂƚĨƌĞƐŚůLJƉƌŝŶƚĞĚƐŵĞůůŝŶƚŚĞĂŝƌ͕ĂŶĚ /ŵĂŐĞƌĞĚŝƚͲŚĂůŬĚƵƐƚdĞĂŵ

31 SCALING, PDEs AND ICEBERG MELTING

Scaling,
PDEs
and
Iceberg
Melting

E\'U0DKLU+DGß]LF $VVRFLDWH3URIHVVRU

1
Stefan
problem Stefan
problem
is
one
of
the
best
known
free
boundary
problems.
It
wa s
i ntroduced
by
the
Slovenian
physicist
Joˇzef
Stefan
at
the
end
of
the
19th
century
with
the
aim
of
describing
ice
melting/freezing.
It
is
one
of
the
best-known
phase
t ransition
models,
wh e r e
the
two
phases,
e.g.
water
and
ice
are
separated
by
an
i nterface
which
is
allowed
to
move.
It
is
also
one
of
the
early
examples
of
a
free
boundary
problem
in
the
world
of
partial
differential
equations.

Figure
1:
Joˇzef
Stefan,
1835-1893 (photo
from
Wikipedia)

The
goal
of
this
article
is
to
give
an
informal
statement
of
one
of
the
results
from
[1]
about
the rate
of
melting
of
perfectly
round
ice
blocks
and
explain
its
significance.
Assume
that
a
round disk
of
ice
of
radius
λ(t)
>
0
is
kept
at
a
constant
temperature
0.
It
is
surrounded
by
an
infinite body
of
water
at
a
warmer
temperature,
which
starts
to
melt
it
and
consequently
the
radius λ(t)
starts
to
shrink.
If
we
denote
the
temperature
of
the
water
at
time
t
and
radial
distance r
>
0
from
the
origin
by
v(t,
r),
the
Stefan
problem
takes
the
form

32 DR MAHIR HADZIC

1 ∂ v(t, r) − (∂ + ∂ )v(t, r)=0,r>λ(t) (1.1) t rr r r v(t, r)=0,r= λ(t) (1.2)

−∂rv(t, x)=λ˙ (t),r= λ(t). (1.3) Equation (1.1) is natural and tells us that the temperature of the water evolves by the well- known heat equation, which we are likely to have encountered in a course on basic PDEs. The boundary condition (1.2) simply states that at the interface between the water and ice the tem- perature has to be exactly 0. Finally, the second boundary condition (1.3) is crucial - it states that the heat flux through the boundary determines the speed of the moving interface!

Ice Water Water λ(t)

v ≡ 0 v>0 v>0

Assume that initially the water temperature v0(r) is strictly positive, i.e.

v0(r) > 0 for all r>λ(0). (1.4) A standard maximum principle argument shows that v(t, r) remains strictly positive for all r>λ(t) for as long as the solution to (1.1)–(1.3) exists. This has a simple consequence: since v(t, λ(t)) = 0, we must have −∂rv(t, λ(t)) ≤ 0 and consequently λ˙ (t) ≤ 0. The ice has started to melt! In fact it will melt after some finite amount of time T and the question we are interested in is the following: Question 1.1. What is the generic rate of melting, i.e. can we express λ(t) as a function of T − t at the leading order, as t approaches the melting time T ? If so, is such a behaviour stable in some precise sense? The above question is really about relating the spatial scale determined by the radius λ(t)of the melting block of ice to the time scale in the problem. The hope is that on approach to the “singular” time T , there would be some universal law dictating to the leading order a functional relationship λ(t)=f(T − t) + lower order corrections. (1.5) Such
universal
laws
are
usually
encoded
in
the
symmetries
or
invariances
of
a
problem
at
hand.
In
that
regard,
self-similarity
is
one
of
the
most
striking
features
of
many
problems
one
encoun- ters
in
mathematics
and
nature
alike.
It
roughly
corresponds
to
the
ability
of
a
given
system
to
replicate
the
same
behaviour
on
“ever
smaller
scales”,
where
the
correct
notion
of
scale
can
be
deduced
by
studying
the
scaling
invariances
of
the
equation.
In
the
physics
literature
this
corre- sponds
to
the
so-called
dimensional
analysis. To
make
some
educated
guesses,
let
us
turn
to
the
heat
equation
for
a
moment.

33 SCALING, PDEs AND ICEBERG MELTING

1.1 Heat equation and scaling Coonsidderr fof rar mom meent onneooftheh mom stt iconnic papartialdl diffiffere enentitiall eqe uaatit onns-s thhehe eaeatet equuattioionn. HeH ree thheunknon wnw iss thete temmpep raatuurer fuf nctionon u(t, x),), whhere t ∈ R rer prp essenntst tht etimmeve ara iai blb e ana d x ∈ Rd these spatiiall vvariiaba lel .TThe heh ata eqe uauatitionn taakek stthee formr

∂tu(t, x) − Δu(t,t, x)== 0. (1( .66)

GiG vev nan aninin tit al dad tuum u(00,xx)=) u0(x)o) onnee cac nsn ollvev thheiinin tiial vavalul epe prooblblem foor(11.6)6 and momostt teextboookksws illttelellul stthah t  2 1 − |y| u t,t x u ∗ G x u x − y e 4t dydy. ( )=) ( 0 )()( )= d 0( ) (1( .77) (4( πtt) 2 Rd

ThThefformumulal (1(1.7.7)i) srs remmararkakablle:e itt isis exexplliccitit anandtd eaachchess usus allotot ababouuttt theh soolulutitionon.WWiti hih itst heh lpp onnece can riigog ror ususly prprovveiimpmporo tatantt prpropo ere titiess susuchch asas ththeie infinfiniitet spspeeedod fpf pror paagatiiono , innsttantataneneouusrs egulu ararissattioionan andd mam nyy ottheh rsrs.P. Pere hahapsp ththeme mosstct uru ioousus ofo ala liists heh ror lel plplayayedd byy thhefunnctioon

2 1 − |x| 4t G(t,t x):) := d e , (11.88) (4πtπt) 2

| | ala soo knknowwnaasttheh heh atat keernnel.I. Itct onntataini sacuuririoouusds epepenendeencnceeoontn thee raattio √x anandtd thihisis isas a t fuundn amamene taalmannififestaatiionn off thhesscac lilingg ininvavariana cecesooftf thee prproobleemm. LeL tuusuunddere sttandtthih saa litttlele bib tbbetettet r.r FoF rar anyy λλ>0aandd anany α ∈ R itt iss ststraaighthtfoorrwwarrdtd to checcktthah tit if u solvl ess (1.66),), soo dod ese   t x u (tt,, x):) = λαu , . (11.9.9) λ,α λ2 λ

OnO ese ayysts thah ttt he prproobleemam alll owwsfforo a1a 1-ppararamametterr faamim lyy ooff ini vavariianancecesppararaammetetriisesedbd byty heh chc oiice of theeexpx ono ennt α.IIsttheh rere a“a “prprefe ere reed”d” chchoioicec off α?H? Here e“e “prp efeferrreed”d sosounundsds dad nger- ouousls yly laackiingg ofof prp eccisioion,n anandweae addddresss tht iss pop inntbbyry resesorortit ng to ananottheherpr powwere fuulcl ononceeptpt - ththatt ofo coc nserrvevedqd uau nntititiees.s AsA suumim ng reassonabblele deccaycconondid tit ono sas atst papatitiall ininfinnitty,y asa simimplpleie inttegegraratitionon-bby-y pap rtrtsas arggumumenent tetelllsuusts thahatfforr annysy solo ututionnoof((1.1 6)) thhete ototall “masass”s”  I(t)= u(t,t x) dxdx (1(1.110)0 Rd  iss inn fafactct innded pependdenntot oftf imime.e Itt isis accononsseervrvede ququanantitityy susuchch thhatt I(t)=) = I(0( )== Rd u0(x) dxdx foorar lll t ∈ R.IItiists theh reefof ree rereasa ononabablel toto asskwk hih chc chhoio cecesoof α inn (1(1.9.9)wwillaalsl opo reesseervrvete theh tot taal“l massss””. Byy asa immplecchahangn eoe fvf varriaiablbleses     t u t,t x dxdx λα+d u ,yy dyy λλ,,α( ) = 2 Rd Rd λ

34 DR MAHIR HADZIC

and we conclude that α = −d is the unique choice that allows the scaling invariance to be com- patible with “mass”-conservation. The scaling transformation   t x u (t, x):=λ−du , (1.11) λ λ2 λ is therefore aptly termed to be mass-critical. What does all of this have to do with the heat kernel introduced in (1.8)? Let us provide a “complicated” derivation of G, one which is typically not found in most textbooks on partial differential equations. Let t → λ(t) be a time-dependent and for the moment unknown function. Motivated by (1.9) let us introduce new variables ds u(t, x)=λ(t)−dv(s, y), = λ(t)−2,y= xλ(t)−1. (1.12) dt We have thereby introduced the self-similar time variable s. As a result, a simple change of vari- ables turns (1.6) into ∂ λ ∂ v − s (dv + y ·∇v) − Δv =0. (1.13) s λ Exact self-similar solutions correspond to special solutions of the form ∂ λ v(s, y)=φ(y)and − s = b = const. λ Plugging it back into (1.13) we obtain the stationary problem Δφ + b (dφ + y ·∇φ)=0, (1.14) which can be equivalently written in the form   2 2 − b|y| − b|y| div e 2 ∇φ + bde 2 φ =0. (1.15)

It is now easy to check that a particularly easy solution of (1.15) is given by

b|y|2 φb(y)=e 2 . (1.16)  φ y b − π − ∂sλ b ds λ t −2 Normalising Rd b( ) = 1, gives = 2 and from λ = and dt = ( ) , we easily conclude 1 λ(t)=(4πt) 2 . (1.17) Combining (1.16)–(1.17) and going back to (t, x) coordinates using (1.9) and (1.12) we finally obtain a mass-critical self-similar solution to the heat equation 2 1 − |x| 4t G(t, x)= d e , (1.18) (4πt) 2 which of course is the heat kernel from (1.8). Remarkably G(t, x) is manifestly not smooth at








√








t
=
0
and
along
any
parabola
of
the
form
x(t)
=
c
t,
we
have
limt→0+
G(t,
x(t))
=
∞.
This
is
therefore
also
a
prime
example
of
a
self-similar
singular
solution
to
an
evolutionary
PDE!
What
we
have
learned
is
that

35 SCALING, PDEs AND ICEBERG MELTING

• The heat kernel corresponds to a steady state of a suitably rescaled version of the heat equation.

• Dependence on the self-similar variable y translates into a functional dependence on √x . t This in turn reflects the scaling invariance of the problem.

• Nature likes to honour the invariances.

1.2 Stefan problem and scaling Motivated by the above analysis we may study the scaling invariances of the Stefan problem. After a little bit of algebra, we conclude that there is a unique scaling invariant transformation for the Stefan problem. For any μ>0 the pair (vμ,λμ) defined by   t r v (t, r)=v , ,λ(t)=μλ(t) (1.19) μ μ2 μ μ

also solves the Stefan problem. The heat-like scaling (1.19) suggests that a reasonable guess for the functional relation (1.5), if it is to be consistent with self-similarity, should be √ λ(t) ∼t→T T − t. (1.20)

The central result of [1] is that the prediction (1.20) is wrong!

Theorem 1.2 ([1]). There exists an open set of initial data (v0,λ0) in a suitable topology such that λ(t) vanishes at a finite time T>0 and moreover √ √ √ − 2 log |T −t| λ(t)= T − te 2 + ot→T (1). (1.21)

In addition, this behaviour is stable with respect to small perturbations.

The existence of initial data that lead to the asymptotic behaviour (1.21) was first predicted in a beautiful work of Herrero and Velazquez [2]. The proof of both the existence and stability is contained in [1]. From (1.21) we see that on approach to singularity (λ(t) → 0) we have √ λ(t)  T − t as t → T. (1.22)

This remarkable departure from self-similarity can, in a nutshell, be attributed to the nonlinear character of the Stefan problem (1.1)–(1.3). This explanation is vague, but suggestive as related phenomena are encountered in a number of different nonlinear problems coming from maths, physics, even biology [3, 4, 5]. The proof of Theorem 1.2 is intricate as it combines ideas from spectral theory and nonlinear energy methods. We will not attempt to swamp the reader with technical details, but instead give a one paragraph overview of the main idea. After a rescaling b − ∂sλ analogous to (1.12), if we set = λ the dynamics in the rescaled coordinates splits into two

36 DR MAHIR HADZIC

“orthogonal” components. One of them is a finite-dimensional dynamical system, which at the leading order is given by

2b2 ∂ λ ds 1 ∂ b + =0,b+ s =0, = . s | log b| λ dt λ2

The solution of this system of ODEs leads precisely to the rate (1.21)! The remainder of the dynamics is infinite-dimensional, but considerably less scary since that part is dynamically dissi- pated away, much like one would expect from a heat-like equation. For all the details see [1].

References

[1] Hadˇzi´c M., Rapha¨el, P., On melting and freezing for the 2D radial Stefan problem. To ap- pear in J. Eur. Math. Soc.

[2] Herrero M., A., Vel´azquez, J. L., On the melting of ice balls. SIAM J. Math. Anal. 28 (1997), no. 1, 1–32

[3] Rapha¨el, P., Rodnianski, I., Stable blow up dynamics for critical corotational wave maps and the equivariant Yang Mills problems, Publ. Math. Inst. Hautes Etudes Sci. 115 (2012), 1–122.

[4] Rapha¨el, P., Schweyer, R., Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow, Comm. Pure Appl. Math. 66 (2013), no. 3, 414–480.

[5] Rapha¨el, P., Schweyer, R., On the stability of critical chemotactic aggregation, Math. An- nalen 359 (2014), 267

37 IMSS EVENTS 2019

/ŶƐƟƚƵƚĞĨŽƌDĂƚŚĞŵĂƟĐĂůĂŶĚ ƉĂƚŚƐ͕ŝŶƐƉŝƌĞĚƚŚĞLJŽƵŶŐĞƌĂƩĞŶĚĂŶƚƐĂŶĚ ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞƐĂƚh> ƌĞƐŽŶĂƚĞĚǁŝƚŚƚŚĂƚŽĨŽƚŚĞƌĂůƵŵŶŝ͘ ĐĂĚĞŵŝĐ>ĂƵŶĐŚǀĞŶƚ KŶĞŽĨƚŚĞŵĂũŽƌĂŶĚŵŽƌĞĞdžĐŝƟŶŐŐŽĂůƐĨŽƌ ƚŚĞĚĞƉĂƌƚŵĞŶƚŝŶƚŚĞĐŽŵŝŶŐLJĞĂƌƐŝƐƚŚĞ ͞/ĂŵƉƌŽƵĚƚŽŵĂŬĞĂďŝƚŽĨŚŝƐƚŽƌLJ͕ĂƐ ĐƌĞĂƟŽŶŽĨƚŚĞ/ŶƐƟƚƵƚĞĨŽƌDĂƚŚĞŵĂƟĐĂů ƚŚŝƐŝƐƚŚĞĮƌƐƚƟŵĞƚŚĂƚLJŽƵǁŝůůƐĞĞƚŚĞ ĂŶĚ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞƐ;/D^^ͿĂƚh>͘dŚĞ /D^^ŚĞĂĚĞƌŝŶĂƚĂůŬ͘͟dŚŝƐŝƐŚŽǁWĞƚƌŽƐ /D^^ĂŝŵƐƚŽďĞ>ŽŶĚŽŶΖƐůĞĂĚŝŶŐĐĞŶƚƌĞ ĞůůĂƉŽƌƚĂƐƐƵŵŵĂƌŝƐĞd the relevance of ĨŽƌƌĞƐĞĂƌĐŚ͕ƚĞĂĐŚŝŶŐĂŶĚĐŽůůĂďŽƌĂƟŽŶ ƚŚĞĮƌƐƚĂĐĂĚĞŵŝĐŵĞĞƟŶŐŝŶƉƌĞƉĂƌĂƟŽŶĨŽƌ ŝŶŵĂƚŚĞŵĂƟĐƐĂŶĚƐƚĂƟƐƟĐƐ͕ĞƐƚĂďůŝƐŚŝŶŐ /D^^͕ǁŚŝĐŚƚŽŽŬƉůĂĐĞŽŶϯϬƚŚ:ĂŶƵĂƌLJϮϬϭϵ h>ĂƐĂŐůŽďĂůůĞĂĚĞƌŝŶƚŚĞƐĞĮĞůĚƐ͘dŚĞ at the Wesley Hotel. The sentence captured ƉƌŽũĞĐƚ͕ǁŚŝĐŚŝŶĐůƵĚĞƐƚŚĞĐŽͲůŽĐĂƟŽŶĂŶĚ ƚŚĞŐĞŶĞƌĂůŽƉƟŵŝƐŵĂŶĚĞŶƚŚƵƐŝĂƐŵŽĨƚŚĞ ĞdžƉĂŶƐŝŽŶŽĨďŽƚŚƚŚĞDĂƚŚĞŵĂƟĐƐĂŶĚ ĂƩĞŶĚĂŶƚƐ͘dŚĞŐŽŽĚŵŽŽĚǁĂƐũƵƐƟĮĞĚ͗ ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞĚĞƉĂƌƚŵĞŶƚƐ͕ƌĞƋƵŝƌĞƐĂůƐŽ WƌŽĨĞƐƐŽƌ/ǀĂŶWĂƌŬŝŶ͕ƚŚĞĞĂŶŽĨƚŚĞDW^ ĚĞǀĞůŽƉŝŶŐĂƐƚƌŽŶŐũŽŝŶƚĐŽŵŵƵŶŝƚLJ͘dŚŝƐ &ĂĐƵůƚLJ͕ƐŚĂƌĞĚĂƉŽƐŝƟǀĞŽƵƚůŽŽŬŽŶƚŚĞ LJĞĂƌǁĞŚĂĚƚŚĞĮƌƐƚƚǁŽĞǀĞŶƚƐůŽŽŬŝŶŐƚŽ ĐƌĞĂƟŽŶŽĨƚŚĞŝŶƐƟƚƵƚĞ͘dŚĞŶ͕ǁĞŚĂĚƚŚĞ ĨŽƐƚĞƌƐƵĐŚĂĐŽŵŵƵŶŝƚLJ͘ ƌĂƌĞŽƉƉŽƌƚƵŶŝƚLJƚŽŚĞĂƌǁŚĂƚĐŽůůĞĂŐƵĞƐ ĨƌŽŵďŽƚŚĚĞƉĂƌƚŵĞŶƚƐĂƌĞǁŽƌŬŝŶŐŽŶ͘ :ŽŝŶƚůƵŵŶŝĂŶĚ^ƚƵĚĞŶƚDŝdžĞƌ WƌŽĨĞƐƐŽƌ<ĂƌĞŶWĂŐĞĂŶĚWƌŽĨĞƐƐŽƌ:ĞĂŶͲ DĂƌĐsĂŶĚĞŶͲƌŽĞĐŬĨƌŽŵŽƵƌĚĞƉĂƌƚŵĞŶƚ /ƚŝƐŶŽƚĂƐƵƌƉƌŝƐĞƚŚĂƚƚŚĞĮƌƐƚĞǀĞŶƚ ĂŶĚƌŽĚŝŶĂŽƚĂƌĂŶĚƌWĞƚƌŽƐ organised aroundƚŚĞ/D^^ǁĂƐĚŝƌĞĐƚĞĚƚŽ ĞůůĂƉŽƌƚĂƐĨƌŽŵ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞƐŚĂƌĞĚ ŽƵƌƐƚƵĚĞŶƚƐĂŶĚĂůƵŵŶŝĂƐƚŚĞLJĂƌĞĂƚƚŚĞ ƚŚĞŵĂŝŶƐƵďũĞĐƚƐŽĨƚŚĞŝƌĐƵƌƌĞŶƚƌĞƐĞĂƌĐŚ ŚĞĂƌƚŽĨŽƵƌĞĚƵĐĂƟŽŶĂůŵŝƐƐŝŽŶ͘ďŽƵƚ ǁŝƚŚĂƉƉůŝĐĂƟŽŶƐŝŶďŝŽůŽŐLJ͕ŇƵŝĚĚLJŶĂŵŝĐƐ͕ ϴϬƉĂƌƟĐŝƉĂŶƚƐŝŶĐůƵĚŝŶŐĂůƵŵŶŝ͕ƐƚƵĚĞŶƚƐ͕ ƉŚLJƐŝĐƐĂŶĚŵĂĐŚŝŶĞůĞĂƌŶŝŶŐ͘ ĂŶĚƐƚĂīŽĨďŽƚŚĚĞƉĂƌƚŵĞŶƚƐŵĞƚŽŶ  ƌĞĂƟŶŐĂǀŝďƌĂŶƚũŽŝŶƚƌĞƐĞĂƌĐŚ dŚƵƌƐĚĂLJϭϰƚŚDĂƌĐŚϮϬϭϵĨŽƌĂŶĞǀĞŶŝŶŐ ĐŽŵŵƵŶŝƚLJŝƐŵƵĐŚŵŽƌĞƚŚĂŶďĞŝŶŐĐŽͲ ƚŽƐƚĂLJĐŽŶŶĞĐƚĞĚǁŝƚŚŽůĚĂĐƋƵĂŝŶƚĂŶĐĞƐ ůŽĐĂƚĞĚ͘dŚĞƐĞĞǀĞŶƚƐǁĞƌĞĂĮƌƐƚƐƚĞƉ ĂŶĚŵĂŬĞŶĞǁĐŽŶƚĂĐƚƐ͘dŚĞŵĂŝŶĞǀĞŶƚŽĨ ƚŽĐŽŶŶĞĐƚĂŶĚƉƌĞƉĂƌĞƚŽĚŽǁŽƌůĚĐůĂƐƐ ƚŚĞĞǀĞŶŝŶŐ͗ƚǁŽƐƵĐĐĞƐƐĨƵůĂůƵŵŶŝƐŚĂƌĞĚ ƌĞƐĞĂƌĐŚƵŶĚĞƌŽŶĞďĂŶŶĞƌ͘džƉĞĐƚŵŽƌĞŽĨ ƚŚĞŝƌĐĂƌĞĞƌĞdžƉĞƌŝĞŶĐĞƐŝŶŝŶĚƵƐƚƌLJ͗dŚĂƌŝŶĚŝ these events in the future. ,ĂƉƵĂƌĂĐŚĐŚŝ;D^ĐŝDĂƚŚĞŵĂƟĐƐ;ϮϬϭϬͿ͕ DĂƐƚĞƌŝŶDĂƚŚĞŵĂƟĐĂůDŽĚĞůůŝŶŐ;ϮϬϭϭͿ͕ ƌĂŵŝůŽ'ĂƌĐŝĂdƌŝůůŽƐ ĂŶĚWŚŽDW>y;ϮϬϭϱͿͿĐƵƌƌĞŶƚůLJWƌŽŐƌĂŵ DĂŶĂŐĞƌĂƚĞĞƉDŝŶĚ͖ĂŶĚ͕:Ž<ĂĐnjŵĂƌƐŬĂ ;D^Đ^ƚĂƟƐƟĐƐ;ϮϬϬϵͿ͕ĂŶĚWŚ^ƚĂƟƐƟĐƐ ;ϮϬϭϯͿͿĐƵƌƌĞŶƚůLJ^ĞŶŝŽƌWƌŝŶĐŝƉĂůDŽĚĞůůĞƌ ĂƚZŝƐŬDĂŶĂŐĞŵĞŶƚ^ŽůƵƟŽŶƐʹZD^͘dŚĞŝƌ ƐƚŽƌŝĞƐ͕ĂďŽƵƚƚŚĞŝƌƟŵĞĂƚh>͕ĂďŽƵƚƚŚĞ ĐŚĂůůĞŶŐĞƐĨĂĐĞĚĂŌĞƌůĞĂǀŝŶŐ͕ĂŶĚĂďŽƵƚ ŚŽǁƚŚĞŝƌƟŵĞŚĞƌĞŚĂĚŚĞůƉĞĚƚŚĞŵƚŽ ƌĞĂůŝƐĞƚŚĞŝƌƉŽƚĞŶƟĂůĂŶĚƚŚƌŝǀĞŝŶƚŚĞŝƌ

38 THE MICHAEL SINGERS

dŚĞDŝĐŚĂĞů^ŝŶŐĞƌƐ ŵĞŵďĞƌƐŽŶƚŚĞŝƌƌĞƐƉĞĐƟǀĞŝŶƐƚƌƵŵĞŶƚƐ͘ tĞƉĞƌĨŽƌŵĞĚƚŚĞƐĞƐŽŶŐƐĂŐĂŝŶŝŶ^ĞŶĂƚĞ dŚĞDŝĐŚĂĞů^ŝŶŐĞƌƐ͕ŽƵƌĚĞƉĂƌƚŵĞŶƚĂů ,ŽƵƐĞďĞĨŽƌĞƚŚĞĞDŽƌŐĂŶŝŶŶĞƌ͕ĂŶĚŝŶ ĐŚŽŝƌ͕ĂƌĞƐƟůůŐŽŝŶŐƐƚƌŽŶŐ͊KƵƌŵĞŵďĞƌƐ ƚŚĞŽƉĞŶĂŝƌŽŶĂƐƵŵŵĞƌƚŽƵƌŽĨ>ŽŶĚŽŶ ĂƌĞŵĂƚŚĞŵĂƟĐŝĂŶƐĂŶĚƐLJŵƉĂƚŚŝƐĞƌƐ͕ squares. ŽĨĂůůŶĂƟŽŶĂůŝƟĞƐ͕ĨƌŽŵh>ĂŶĚĂĐƌŽƐƐ >ŽŶĚŽŶ͘KƵƌŵƵƐŝĐƌĞŇĞĐƚƐƚŚŝƐĚŝǀĞƌƐŝƚLJ͕ ǁŝƚŚƐŽŶŐƐĚƌĂǁŶĨƌŽŵĂƌŽƵŶĚƚŚĞǁŽƌůĚĂŶĚ throughout history. tĞƐĂŶŐĨĞƐƟǀĞƐŽŶŐƐŝŶƚŚĞh>ĐůŽŝƐƚĞƌƐ ďĞĨŽƌĞƚŚĞŚƌŝƐƚŵĂƐƉĂƌƚLJůĂƐƚLJĞĂƌ͕ĂŶĚŝŶ ĂũŽŝŶƚĐŽŶĐĞƌƚǁŝƚŚŽŶƚĞŵƉŽƌĂƌLJDƵƐŝĐĨŽƌ ůů;ŽDͿ^ŝŶŐĞƌƐŝŶƚŚĞ,ĂůĚĂŶĞZŽŽŵ͘dŚŝƐ LJĞĂƌǁĞƐĂŶŐĂƚ/ŵƉĞƌŝĂůΖƐŚƌŝƐƚŵĂƐƉĂƌƚLJ ĂŶĚ^ƚWĂŶĐƌĂƐƐƚĂƟŽŶ͕ĂƐǁĞůůĂƐƚĂŬŝŶŐŽƵƌ ǀŽŝĐĞƐƚŽh>,ƚŽďƌŝŶŐĐŚĞĞƌƚŽƚŚĞĞůĚĞƌůLJ dŚĞDŝĐŚĂĞů^ŝŶŐĞƌƐĂƚĂƉƌĂĐƟĐĞ ƉĂƟĞŶƚƐŽŶƚŚĞŝƌǁĂƌĚƐ͘ tĞĂƌĞŽƉĞŶƚŽh>ŵĂƚŚĞŵĂƟĐŝĂŶƐƉĂƐƚ ĂŶĚƉƌĞƐĞŶƚ͕ĂŶĚƚŚĞŝƌĨƌŝĞŶĚƐĂŶĚĨĂŵŝůLJ͕ƐŽ ĚŽĨĞĞůĨƌĞĞĐŽŵĞĂůŽŶŐĂŶĚƐŝŶŐǁŝƚŚƵƐ͊

WĞƌĨŽƌŵŝŶŐĂƚ^ƚWĂŶĐƌĂƐ^ƚĂƟŽŶ

KƵƌϮϬϭϵƌĞƉĞƌƚŽŝƌĞŚĂĚĂƚŽƉŝĐĂů ĞŶǀŝƌŽŶŵĞŶƚĂůƚŚĞŵĞ͕ĞŶĐŽŵƉĂƐƐŝŶŐ ŝŵƉƌŽǀŝƐĞĚĂŶŝŵĂůĐƌŝĞƐĂŶĚŶŐůŝƐŚĨŽůŬ ŵŝůLJDĂǁ ƐŽŶŐƐĂůŝŬĞ͊tĞǁŽƌŬĞĚŽŶƚŚŝƐŵƵƐŝĐŝŶĂ ũŽŝŶƚǁŽƌŬƐŚŽƉĂŶĚĐŽŶĐĞƌƚǁŝƚŚĞůƐŝnjĞ ŽŵŵƵŶŝƚLJŚŽŝƌŝŶDĂƌĐŚ͕ŝŶĐůƵĚŝŶŐĂ WůĂŶĞƚĂƌƚŚďĂůůĂĚĂƌƌĂŶŐĞĚƚŽƚŚĞƚƵŶĞŽĨ ͚,ŽƵƐĞŽĨƚŚĞZŝƐŝŶŐ^ƵŶ͛ďLJŽƵƌĨĂŶƚĂƐƟĐ ĐŽŶĚƵĐƚŽƌ^ŚĞĞŶĂWŚŝůůŝƉƐ͘dŚĞƐŝŶŐŝŶŐ /ŵĂŐĞƌĞĚŝƚƉ͘ϯϴͲƌĂŵŝůŽ'ĂƌĐŝĂdƌŝůůŽƐ ǁĂƐĂĐĐŽŵƉĂŶŝĞĚďLJŵƵůƟƚĂůĞŶƚĞĚĐŚŽŝƌ /ŵĂŐĞƌĞĚŝƚƉ͘ϯϵͲŵŝůLJDĂǁ

39 AWARDS

/ŵƉĂĐƚ/ŶǀĞƐƚŵĞŶƚŚĂŵƉŝŽŶƐŚŝƉ dŚĞ'ƌĞĞŶh>

KŶϳƚŚĞĐĞŵďĞƌϮϬϭϵ͕ƚŚĞ^ŽĐŝĂů dŚĞĚĞƉĂƌƚŵĞŶƚĂĐŚŝĞǀĞĚĂ'ŽůĚǁĂƌĚĨŽƌ ŶƚĞƌƉƌŝƐĞƐŝǀŝƐŝŽŶŽĨh>ƵƐŝŶĞƐƐ^ŽĐŝĞƚLJ ƐƵƐƚĂŝŶĂďŝůŝƚLJĨƌŽŵ'ƌĞĞŶh>͘DĂŶLJƚŚĂŶŬƐ ŚĞůĚƚŚĞŝƌǀĞƌLJĮƌƐƚ/ŵƉĂĐƚ/ŶǀĞƐƚŵĞŶƚ ƚŽƚŚĞ'ƌĞĞŶdĞĂŵ͕ŚĞĂĚĞĚďLJWƌŽĨĞƐƐŽƌ ŚĂŵƉŝŽŶƐŚŝƉ͘dŚĞŽŶĞͲĚĂLJĞǀĞŶƚǁĂƐ ZŽďďDĐŽŶĂůĚ͕ĨŽƌŵĂŬŝŶŐƚŚŝƐŚĂƉƉĞŶ͘ ĂƩĞŶĚĞĚďLJĂƉĂŶĞůŽĨƐƉĞĂŬĞƌƐĂŶĚũƵĚŐĞƐ ĨƌŽŵĮƌŵƐƐƵĐŚĂƐ/ŵƉĂdžƐƐĞƚDĂŶĂŐĞŵĞŶƚ͕ ZŽďĞĐŽ͕ĂŶĚWĂůůĂĚŝƵŵ'ƌŽƵƉ͘dŚĞŐƵĞƐƚƐ ĐĂŵĞƚŽŐĞƚŚĞƌƚŽĚŝƐĐƵƐƐƚŚĞĮĞůĚŽĨŝŵƉĂĐƚ ŝŶǀĞƐƟŶŐĂŶĚŝƚƐǀĂůƵĞŝŶƚŽĚĂLJ͛ƐǁŽƌůĚ͘ DŽƌĞƚŚĂŶϱϱƐƚƵĚĞŶƚƐĨƌŽŵh>͕<ŝŶŐΖƐ ŽůůĞŐĞ>ŽŶĚŽŶ͕/ŵƉĞƌŝĂůŽůůĞŐĞ>ŽŶĚŽŶ͕ ĂŶĚhŶŝǀĞƌƐŝƚLJŽĨĚŝŶďƵƌŐŚĂƩĞŶĚĞĚƚŚĞ ĞǀĞŶƚĂŶĚƉĂƌƟĐŝƉĂƚĞĚŝŶĂĐĂƐĞƐƚƵĚLJ ĐŽŵƉĞƟƟŽŶ͕ƐƉŽŶƐŽƌĞĚďLJZŽďĞĐŽ͕/ŵƉĂdž ƐƐĞƚDĂŶĂŐĞŵĞŶƚ͕ĂŶĚ/>ΘWĂƌƚŶĞƌƐ͘ WƌŽĨĞƐƐŽƌZŽďďDĐŽŶĂůĚĂŶĚƌZƵďĠŶWĠƌĞnj ,ĞƌĞŝƐƚŚĞh>ǁŝŶŶŝŶŐƚĞĂŵ͗ ĂƌƌĂƐĐŽǁŝƚŚƚŚĞ'ŽůĚǁĂƌĚ ͲƵďƌLJDĂ͘&ŝƌƐƚzĞĂƌĚƵĐĂƟŽŶ^ƚƵĚŝĞƐ Ͳ:ĞŶŶĂyƵ͘&ŝƌƐƚzĞĂƌ^ĐDĂƚŚĞŵĂƟĐƐĂŶĚ /ŶƚĞƌŶĂƟŽŶĂůDĂƚŚĞŵĂƟĐƐ ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞ ŽŵƉĞƟƟŽŶĨŽƌhŶŝǀĞƌƐŝƚLJ^ƚƵĚĞŶƚƐ ͲŚĂƌŵŝ^ĂƵũĂŶŝ͘&ŝƌƐƚzĞĂƌ^ĐDĂƚŚĞŵĂƟĐƐ ĂŶĚ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞ džĞů<ĞƌďĞĐĂŶĚ<ƌnjLJƐnjƚŽĨ<ĂĐƉƌnjLJŬͲƌĞĐĞŝǀĞĚ ͲůĂŝƌĞtŝůůĞŵƐĞ͘&ŝƌƐƚzĞĂƌ^ĐDĂƚŚĞŵĂƟĐƐ dŚŝƌĚWƌŝnjĞ͘dŚĞƚĞĂŵǁĂƐƚƌĂŝŶĞĚďLJWĞƚƌƵ ǁŝƚŚĐŽŶŽŵŝĐƐ͘ ŽŶƐƚĂŶƟŶĞƐĐƵ͕Ăh>WŚƐƚƵĚĞŶƚŝŶƚŚĞ >ŽŶĚŽŶ^ĐŚŽŽůŽĨ'ĞŽŵĞƚƌLJĂŶĚEƵŵďĞƌ dŚĞŽƌLJ;>^'EdͿ͘

/ŵĂŐĞƌĞĚŝƚͲWƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶ /ŵĂŐĞƌĞĚŝƚͲWƌŽĨĞƐƐŽƌZŽďďDĐŽŶĂůĚ

40 STAFF AND GRADUATE STUDENT AWARDS

^ƚĂīǁĂƌĚƐ 'ƌĂĚƵĂƚĞ^ƚƵĚĞŶƚǁĂƌĚƐ

ƌ>ĂƵƌŝKŬƐĂŶĞŶǁĂƐĂǁĂƌĚĞĚƚŚĞĂůĚĞƌſŶ DĂƩĞŽĂƉŽĨĞƌƌŝŚĂƐďĞĞŶĂǁĂƌĚĞĚƚŚĞ WƌŝnjĞ͕ĨŽƌŚŝƐĚŝƐƟŶŐƵŝƐŚĞĚĐŽŶƚƌŝďƵƟŽŶƐƚŽ DW^&ĂĐƵůƚLJĚƵĐĂƟŽŶǁĂƌĚϮϬϭϵŝŶƚŚĞ ƚŚĞĮĞůĚŽĨŝŶǀĞƌƐĞƉƌŽďůĞŵƐ͘ WŽƐƚŐƌĂĚƵĂƚĞdĞĂĐŚŝŶŐƐƐŝƐƚĂŶƚĂƚĞŐŽƌLJ͘

ƌ>ĂƌƐ>ŽƵĚĞƌŚĂƐďĞĞŶƚŚĞƌĞĐŝƉŝĞŶƚŽĨ dŚĞϮϬϭϵDW^&ĂĐƵůƚLJWŽƐƚŐƌĂĚƵĂƚĞdĂƵŐŚƚ ƚŚĞĂŶĂĚŝĂŶDĂƚŚĞŵĂƟĐĂů^ŽĐŝĞƚLJ͛Ɛ;D^Ϳ WƌŝnjĞǁĂƐĂǁĂƌĚĞĚƚŽDĂƚŚĞŵĂƟĐƐƐƚƵĚĞŶƚ ϮϬϭϵ'͘ĚĞ͘ZŽďŝŶƐŽŶǁĂƌĚĨŽƌŚŝƐƉĂƉĞƌ ,ĂLJůĞLJ'ŽŽůĚĨŽƌŚĞƌŝŵƉƌĞƐƐŝǀĞǁŽƌŬŝŶŚĞƌ ͞^ƚĂĐŬŝŶŐƐĂŶĚƚŚĞtͲĐLJĐůĞƐŽŶũĞĐƚƵƌĞ͟ D^ĐDĂƚŚĞŵĂƟĐĂůDŽĚĞůůŝŶŐĚƵƌŝŶŐƚŚĞůĂƐƚ ;ĂŶĂĚŝĂŶDĂƚŚĞŵĂƟĐĂůƵůůĞƟŶsŽů͘ϲϬ;ϯͿ͕ ĂĐĂĚĞŵŝĐƐĞƐƐŝŽŶ͘,ĂLJůĞLJǁĂƐǁŝĚĞůLJƉƌĂŝƐĞĚ ϮϬϭϳƉƉ͘ϲϬϰͲϲϭϮͿ͘dŚĞ'͘ĚĞ͘ZŽďŝŶƐŽŶ ĨŽƌŚĞƌĚĞĚŝĐĂƟŽŶ͕ƉĂŝŶƐƚĂŬŝŶŐĞīŽƌƚĂŶĚŚĞƌ ǁĂƌĚƌĞĐŽŐŶŝƐĞƐŽƵƚƐƚĂŶĚŝŶŐĐŽŶƚƌŝďƵƟŽŶƐ ƐƵƉĞƌďŝŶƚĞůůĞĐƚƵĂůĂďŝůŝƚLJ͕ǁŚŝĐŚŽƵƌ,ĞĂĚ ƚŽƚŚĞĂŶĂĚŝĂŶ:ŽƵƌŶĂůŽĨDĂƚŚĞŵĂƟĐƐ ŽĨĞƉĂƌƚŵĞŶƚƉƌĂŝƐĞĚĂƐΗƐƚƵŶŶŝŶŐďLJĂŶLJ ;:DͿŽƌƚŚĞĂŶĂĚŝĂŶDĂƚŚĞŵĂƟĐĂůƵůůĞƟŶ ŵĞĂƐƵƌĞΗ͘ ;DͿ͘ DĂƚŚĞŵĂƟĐƐWŚƐƚƵĚĞŶƚůĞdžŽĂŬƌĞĐĞŝǀĞĚ ƌ^ŽŶLJĂƌŽǁĞ͕WƌŽĨĞƐƐŽƌŚƌŝƐƟŶĂWĂŐĞů ĂDW^&ĂĐƵůƚLJĞĂŶ͛ƐŽŵŵĞŶĚĂƟŽŶĨŽƌŚŝƐ ĂŶĚWƌŽĨĞƐƐŽƌDĂƌƟŶhƚůĞLJŽĨKZhǁĞƌĞ ƌĞƐĞĂƌĐŚ͕ŽŶĞŽĨŽŶůLJƚǁŽĂǁĂƌĚĞĚƚŽƌĞƐĞĂƌĐŚ ĂǁĂƌĚĞĚƚŚĞKZ^ŽĐŝĞƚLJΖƐ>LJŶdŚŽŵĂƐDĞĚĂů ƐƚƵĚĞŶƚƐǁŝƚŚŝŶƚŚĞ&ĂĐƵůƚLJ͘ ĨŽƌΗĂĐĂĚĞŵŝĐKZƌĞƐĞĂƌĐŚǁŚŝĐŚďĞƐƚ ĚĞŵŽŶƐƚƌĂƚĞƐŶŽǀĞůƚLJĂŶĚƌĞĂůͲǁŽƌůĚŝŵƉĂĐƚ͕ ďĂĐŬĞĚƵƉďLJĞǀŝĚĞŶĐĞΗ͘dŚŝƐǁĂƐĨŽƌƚŚĞŝƌ ƉƌŽŐƌĂŵŵĞŽĨǁŽƌŬŝŶŽŶŐĞŶŝƚĂů,ĞĂƌƚ Surgery.

WƌŽĨĞƐƐŽƌŶĚƌĞŝzĂĨĂĞǀŚĂƐďĞĞŶĂǁĂƌĚĞĚĂ >ĞǀĞƌŚƵůŵĞdƌƵƐƚŐƌĂŶƚĞŶƟƚůĞĚΗŝŽƉŚĂŶƟŶĞ ƉƌŽďůĞŵƐƌĞůĂƚĞĚƚŽ^ŚŝŵƵƌĂǀĂƌŝĞƟĞƐΖΖ͘

ƌ/ƐŝĚŽƌŽƐ^ƚƌŽƵƚŚŽƐŚĂƐďĞĞŶĂǁĂƌĚĞĚƚŚĞ WƌŽǀŽƐƚ͛ƐĚƵĐĂƟŽŶǁĂƌĚĨŽƌŚŝƐĚĞĚŝĐĂƟŽŶ to teaching. His colleagues appreciate all ŽĨŚŝƐŚĂƌĚǁŽƌŬĂŶĚŚĂǀĞĞǀĞŶƐĂŝĚƚŚĂƚ /ƐŝĚŽƌŽƐŝƐ͞ǁŝƚŚŽƵƚĂĚŽƵďƚŽŶĞŽĨƚŚĞďĞƐƚ ůĞĐƚƵƌĞƌƐƚŚŝƐĚĞƉĂƌƚŵĞŶƚŚĂƐĞǀĞƌŚĂĚ͘͟

WƌŽĨĞƐƐŽƌŶĚƌĞǁ'ƌĂŶǀŝůůĞŚĂƐďĞĞŶ ĂǁĂƌĚĞĚƚŚĞWĂƵůZ͘,ĂůŵŽƐͲ>ĞƐƚĞƌZ͘&ŽƌĚ ǁĂƌĚϮϬϭϵĨƌŽŵƚŚĞDĨŽƌŚŝƐƉĂƉĞƌ ΗhƐŝŶŐLJŶĂŵŝĐĂů^LJƐƚĞŵƐƚŽŽŶƐƚƌƵĐƚ /ŶĮŶŝƚĞůLJDĂŶLJWƌŝŵĞƐΗ͘

41 UNDERGRADUATE AND MSC PRIZES

WƌŝnjĞƐǁĂƌĚĞĚƚŽ^ƚƵĚĞŶƚƐ^ƵŵŵĞƌϮϬϭϵ &ŝƌƐƚzĞĂƌWƌŝnjĞƐ &ŝŶĂůzĞĂƌWƌŝnjĞƐ;^ĐŽƌD^ĐŝͿ <ĞƐƚĞůŵĂŶWƌŝnjĞϭƐƚLJĞĂƌ ŶĚƌĞǁZŽƐĞŶWƌŝnjĞ ŚƌŝƐƚŽƉŚĞƌƵŶŬŝŶ ŚƵŚƵŝ,Ğ

^ƚĞǀĞŶƐŽŶWƌŝnjĞ dŚĞ/ŶƐƟƚƵƚĞŽĨDĂƚŚĞŵĂƟĐƐĂŶĚŝƚƐ ŚƌŝƐƚŽĨŽƌŽƐ<ĂƐƐŝĂŶŝĚĞƐ ƉƉůŝĐĂƟŽŶƐ;/DͿWƌŝnjĞƐ KŶĞLJĞĂƌŵĞŵďĞƌƐŚŝƉŽĨƚŚĞ/D ĞƉĂƌƚŵĞŶƚĂůWƌŝnjĞƐŝŶDĂƚŚĞŵĂƟĐƐ ĂŶŝĞůƵƐƐĞůů͖zŽŚĂŶĐĞKƐďŽƌŶĞ ĚŵŽŶĚ>Ž ĂǀŝĚsŝůůƌŝŶŐĞƌ &ŽƵƌƚŚzĞĂƌWƌŝnjĞƐ WĂƵůŚĂŶŐ ůůĞŶtĂƚƐŽŶDĞŵŽƌŝĂů^ĐŚŽůĂƌƐŚŝƉ Seth Hardy ŶŵŽůŐŐĂƌǁĂů ^ŚŝnjŚĞyƵ Seul Kang ĂǀŝĚ'>ĂƌŵĂŶWƌŝnjĞ ůĞdžĂŶĚƌŽƐ'ƌŽƵƟĚĞƐ :ŽƐŚƵĂĂŶŝĞůƐͲ,ŽůŐĂƚĞ

^ĞĐŽŶĚzĞĂƌWƌŝnjĞƐ ^ƵƐĂŶEƌŽǁŶWƌŝnjĞ ŽƐĂŶƋƵĞƚWƌŝnjĞ ZŽďďŝĞŽƵůƐŽŶ ŶĞĂ^ŚĂƌdžŚŝ &ŽƵƌƚŚzĞĂƌWƌŽũĞĐƚWƌŝnjĞ <ĞƐƚĞůŵĂŶWƌŝnjĞ :ŽƐŚƵĂ^ŵŝƚŚ džĞů<ĞƌďĞĐ &ŽƵƌƚŚzĞĂƌ^ĞƐƐŝŽŶĂůƉƌŝnjĞ ŶĚƌĞǁZŽƐĞŶWƌŝnjĞ Daniel Bussell ,ƵǁtŝůůŝĂŵƐ :ŽŝŶƚ,ŽŶŽƵƌƐWƌŝnjĞƐ ĞƉĂƌƚŵĞŶƚĂůWƌŝnjĞŝŶDĂƚŚĞŵĂƟĐƐ ĂƌƚůĞƩWƌŝnjĞ;:ŽŝŶƚDĂƚŚĞŵĂƟĐƐΘ ^ŚŝnjĂEĂƋǀŝ ^ƚĂƟƐƟĐĂů^ĐŝĞŶĐĞͿ Karsana Muhunthan dŚŝƌĚzĞĂƌD^ĐŝWƌŝnjĞƐ  dŚĞEĂnjŝƌŚŵĂĚWƌŝnjĞ ĂƐƟůůĞũŽWƌŝnjĞ;:ŽŝŶƚDĂƚŚĞŵĂƟĐƐΘ sŝǀŝĞŶŶĞ>ĞĞĐŚ WŚLJƐŝĐƐͿ DŽƵƐƚĂĨĂ^ĂůĞŚ'ĂŵĂůĞůĚŝŶ dŚŝƌĚzĞĂƌ^ĐWƌŝnjĞƐ tLJŶŶĞZŽďĞƌƚƐWƌŝnjĞ D^ĐWƌŝnjĞƐ zŽŚĂŶĐĞKƐďŽƌŶĞ &ƌĂŶŬd^ŵŝƚŚWƌŝnjĞ Hayley Goold DĂƚŚĞŵĂƟŬĂWƌŝnjĞ ůĞdžĂŶĚƌŽƐ<ŽŶƐƚĂŶƟŶŽƵ :ŽŝŶŝŶŐ^ƚƵĚĞŶƚWƌŝnjĞ WĂŶŽƐdŽĨĂƌŝĚĞƐWƌŝnjĞ 'ĞŽƌŐŝŽƐEĂƚŚĂŶĂĞů

42 PHD SCHOLARSHIPS AND PRIZES

WŚ^ĐŚŽůĂƌƐŚŝƉƐϮϬϭϵͲϮϬ

:ŽŚŶ,ĂǁŬĞƐ^ĐŚŽůĂƌƐŚŝƉ ƌĐŚŝďĂůĚZŝĐŚĂƌĚƐŽŶ^ĐŚŽůĂƌƐŚŝƉ ^ƚĞƉŚĂŶŝĞŚĂŶ ůďĞƌƚtŽŽĚ &ƌĂŶĐĞƐĐŽŝ'ŝŽǀĂŶŶŝ tƌĞŶ&ƵŶĚ^ĐŚŽůĂƌƐŚŝƉ &ĂďŝĂŶ>ĞŚŵĂŶŶ Xiaoshu Sun Baoren Xiao ŽƌƚĞ^ƚƵĚĞŶƚƐŚŝƉ Sally Said DŽŶŝĐĂ,ƵůƐĞ^ĐŚŽůĂƌƐŚŝƉ ŝŚƵĂ>ŝƵ ^ŝƌ'ĞŽƌŐĞ:ĞƐƐĞů^ƚƵĚĞŶƚƐŚŝƉ ĂƌŵĞŶĂďƌĞƌĂƌŶĂƵ Davide Bela DŝŚĂŝEĞĐŚŝƚĂ ĚǁŝŶWŽǁĞƌ^ĐŚŽůĂƌƐŚŝƉ Hang Lou DĂLJĞƌĚĞZŽƚŚƐĐŚŝůĚ^ĐŚŽůĂƌƐŚŝƉ ŚƌŝƐǀĂŶƐ ::^LJůǀĞƐƚĞƌ^ĐŚŽůĂƌƐŚŝƉ ^ƚĞĨĂŶŝĞŚĂŶ >ƵŝƐďƌĞŐŽ

ĂǀŝĚtĂƌƌĞŶ&ƵŶĚ^ĐŚŽůĂƌƐŚŝƉ tŝůůŝĂŵ:ĂĐŬŵĂŶ

WŚWƌŝnjĞƐϮϬϭϵͲϮϬ

ŶĚƌĞǁZŽƐĞŶWƌŝnjĞ;ƉƉůŝĞĚͿ ĂǀĞŶƉŽƌƚWƌŝnjĞ;WƵƌĞͿ 'ĞŽƌŐŝŶĂůͲĂĚƌŝ WĞƚƌƵŽŶƐƚĂŶƟŶĞƐĐƵ

43 PHD AWARDS

^ƚƵĚĞŶƚƐǁŚŽŚĂǀĞƌĞĐĞŶƚůLJŽďƚĂŝŶĞĚWŚƐ ĨƌŽŵƚŚĞĞƉĂƌƚŵĞŶƚŝŶĐůƵĚĞ͗

ŶŶĂ>ĂŵďĞƌƚ;^ƵƉĞƌǀŝƐĞĚďLJ&ƌĂŶŬ^ŵŝƚŚͿΖΖDĂƚŚĞŵĂƟĐĂůĂŶĂůLJƐŝƐĨŽƌƚǁŽĐĞůůĐƵůƚƵƌĞ ƉƌŽďůĞŵƐ͗ƉŽƉƵůĂƟŽŶďĂůĂŶĐĞĨƌĂŵĞǁŽƌŬƐĂŶĚŐůLJĐŽƉƌŽƚĞŝŶƉƌŽĚƵĐƟŽŶΖΖ

ĞƌŶŚĂƌĚWĮƌƐĐŚ ;^ƵƉĞƌǀŝƐĞĚďLJ>ĞŽŶŝĚWĂƌŶŽǀƐŬŝĂŶĚůĞdž^ŽďŽůĞǀͿΖΖ^njĞŐƅͲƚLJƉĞƚƌĂĐĞ ĂƐLJŵƉƚŽƟĐƐĨŽƌŽƉĞƌĂƚŽƌƐǁŝƚŚƚƌĂŶƐůĂƟŽŶĂůƐLJŵŵĞƚƌLJΗ

zƵƉĞŶŐ:ŝĂŶŐ;^ƵƉĞƌǀŝƐĞĚďLJŶĚƌĞĂDĂĐƌŝŶĂĂŶĚDĂƌĐ,ĞŶƌĂƌĚͿΗ:ŽŝŶƚĚŝƐƚƌŝďƵƟŽŶŽĨ ƉĂƐƐĂŐĞƟŵĞƐŽĨĂŶKƌŶƐƚĞŝŶͲhŚůĞŶďĞĐŬĚŝīƵƐŝŽŶĂŶĚƌĞĂůͲƟŵĞĐŽŵƉƵƚĂƟŽŶĂůŵĞƚŚŽĚƐĨŽƌ ĮŶĂŶĐŝĂůƐĞŶƐŝƟǀŝƟĞƐΗ

ůĞdžŽĂŬ;^ƵƉĞƌǀŝƐĞĚďLJ:ĞĂŶͲDĂƌĐsĂŶĚĞŶͲƌŽĞĐŬͿΗ^ƚĞĂĚLJƚǁŽͲĚŝŵĞŶƐŝŽŶĂůĂŶĚ ĂdžŝƐLJŵŵĞƚƌŝĐƉŽƚĞŶƟĂůĨƌĞĞͲƐƵƌĨĂĐĞŇŽǁƐΗ

,ƵŐŽĂƐƟůůŽ^ĂŶĐŚĞnj;^ƵƉĞƌǀŝƐĞĚďLJ,ĞůĞŶtŝůƐŽŶͿΗŚĂŶŶĞůŇŽǁŝŶƐƚĂďŝůŝƟĞƐŽĨĐŽŵƉůĞdž ŇƵŝĚƐΗ

DĂƩŚĞǁ^ĐƌŽŐŐƐ;^ƵƉĞƌǀŝƐĞĚďLJƌŝŬƵƌŵĂŶͿΗĸĐŝĞŶƚĐŽŵƉƵƚĂƟŽŶĂŶĚĂƉƉůŝĐĂƟŽŶƐŽĨƚŚĞ ĂůĚĞƌſŶƉƌŽũĞĐƚŽƌΗ

ƚŚĞĞƚĂŚŝŶŐ;^ƵƉĞƌǀŝƐĞĚďLJ^ƚĞǀĞĂŝŐĞŶƚͿΗĂůĂŶĐĞŵĂŶŝĨŽůĚƐŝŶ>ŽƚŬĂͲsŽůƚĞƌƌĂƐLJƐƚĞŵƐΗ

DĂƫĂDŝŐůŝŽƌĂŶnjĂ;^ƵƉĞƌǀŝƐĞĚďLJ&Ğůŝdž^ĐŚƵůnjĞͿΗsŽůƵŵĞͲƉƌĞƐĞƌǀŝŶŐŵĞĂŶĐƵƌǀĂƚƵƌĞŇŽǁŽŶ ĂZŝĞŵĂŶŶŝĂŶΖΗ

ĂǀŝĚĞĞůůĂ;^ƵƉĞƌǀŝƐĞĚďLJ&ƌĂŶŬ^ŵŝƚŚͿΗ^ƚŽĐŚĂƐƟĐ^ŽůŝĚŝĮĐĂƟŽŶ'ƌŽǁƚŚŝŶ^ƵƉĞƌĐŽŽůĞĚ Water Droplets''

DĂƩĞŽĂƉŽĨĞƌƌŝ;^ƵƉĞƌǀŝƐĞĚďLJŝŵĂsĂƐƐŝůŝĞǀͿΖΖDŝĐƌŽůŽĐĂůĂŶĂůLJƐŝƐŽĨŐůŽďĂůŚLJƉĞƌďŽůŝĐ ƉƌŽƉĂŐĂƚŽƌƐŽŶŵĂŶŝĨŽůĚƐǁŝƚŚŽƵƚďŽƵŶĚĂƌLJΖΖ

^ĂŵWŽƌƌŝƩ;^ƵƉĞƌǀŝƐĞĚďLJŶĚƌĞǁ'ƌĂŶǀŝůůĞͿΖΖWŽůLJŶŽŵŝĂůƐŽǀĞƌĂĮŶŝƚĞĮĞůĚ͗ƐŽŵĞĂŶĂůLJƟĐ ŶƵŵďĞƌƚŚĞŽƌĞƟĐƌĞƐƵůƚƐΖΖ

ZƵĚŽůĨ<ŽŚƵůĂŬ ;^ƵƉĞƌǀŝƐĞĚďLJ&ƌĂŶŬ^ŵŝƚŚͿΖΖ,ĞĂƚͲƚƌĂŶƐĨĞƌŵŽĚĞůůŝŶŐŝŶĨƌĞĞnjĞͲĚƌLJŝŶŐĂŶĚ related processes''

ŽŶŐƌĂƚƵůĂƟŽŶƐƚŽĂůů͊

44 NEW ACADEMIC STAFF

EĞǁĐĂĚĞŵŝĐ^ƚĂī ĐŽŶũĞĐƚƵƌĞ͘,ŝƐƌĞƐĞĂƌĐŚĨƌĞƋƵĞŶƚůLJƌĞůŝĞƐŽŶ ĂŶĂůLJƐŝŶŐĂďƐƚƌĂĐƚĐŽŶĐĞƉƚƐƵƐŝŶŐĞdžƉůŝĐŝƚ ƌDĂƌĐŽ:ĂǀĂƌŽŶĞͲKZh>ĞĐƚƵƌĞƌ ŵĂƚŚĞŵĂƟĐĂůŵĞƚŚŽĚƐĂŶĚŝƐŽŌĞŶĂŝĚĞĚďLJ DĂƌĐŽůďĞƌƚŽ:ĂǀĂƌŽŶĞŝƐĂ>ĞĐƚƵƌĞƌŝŶ ŶƵŵĞƌŝĐĂůĞdžƉĞƌŝŵĞŶƚƐ͘ ƉƉůŝĞĚDĂƚŚĞŵĂƟĐƐ͕ĂŶĚŚŝƐƌĞƐĞĂƌĐŚ ŝŶƚĞƌĞƐƚƐĂƌĞŵĂŝŶůLJŝŶƚŚĞĂƌĞĂŽĨƐƚĂƟƐƟĐĂů ƌƵŶĐĂŶ,ĞǁŝƩͲ>ĞĐƚƵƌĞƌŝŶƉƉůŝĞĚ ƉŚLJƐŝĐƐŽĨĐŽŵƉůĞdžƐLJƐƚĞŵƐ͘EŽƚĂďůLJ͕DĂƌĐŽ DĂƚŚĞŵĂƟĐƐ ƐƚƵĚŝĞƐĞǀŽůƵƟŽŶĂƌLJŐĂŵĞƚŚĞŽƌLJ͕ĐŽŵƉůĞdž /ĂŵĂŶĂƉƉůŝĞĚŵĂƚŚĞŵĂƟĐŝĂŶĂŶĚŇƵŝĚ ŶĞƚǁŽƌŬƐ͕ƚŚĞŽƌĞƟĐĂůŶĞƵƌŽƐĐŝĞŶĐĞ͕ĂŶĚ ĚLJŶĂŵŝĐŝƐƚ͕ĂŶĚ/ĂŵŝŶƚĞƌĞƐƚĞĚŝŶƵƐŝŶŐ ĨŽƵŶĚĂƟŽŶĂůƉƌŽďůĞŵƐŝŶĚĞĞƉůĞĂƌŶŝŶŐ͘ ŵĂƚŚĞŵĂƟĐƐƚŽŵŽĚĞůĂŶĚƵŶĚĞƌƐƚĂŶĚ His research is focused on understanding ƉŚLJƐŝĐĂůƉƌŽĐĞƐƐĞƐŝŶƚŚĞǁŽƌůĚĂƌŽƵŶĚƵƐ͘ ƚŚĞĞŵĞƌŐĞŶĐĞŽĨĐŽŽƉĞƌĂƟŽŶ͕ƚŚĞ ŚƵŵĂŶĐŽŶƐĐŝŽƵƐŶĞƐƐ͕ĂŶĚŵĂƚŚĞŵĂƟĐĂů ƌůĞdž;ůĞũĂŶĚƌŽͿŝĂnjĞ>ĂKͲKZh ĂƉƉůŝĐĂƟŽŶƐŝŶŝŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJƌĞƐĞĂƌĐŚ͘ >ĞĐƚƵƌĞƌ More recently, Marco started focusing on ĞĨŽƌĞh>͕ůĞdžŝĂnjǁĂƐĂ^ĞŶŝŽƌ>ĞĐƚƵƌĞƌ ƚŽƉŝĐƐŝŶŵĂƚŚĞŵĂƟĐĂůƉŚLJƐŝĐƐ͘ at the University of Liverpool and a ǀŝƐŝƟŶŐĨĞůůŽǁĂƚƚŚĞůĂŶdƵƌŝŶŐ/ŶƐƟƚƵƚĞ͘ ƌŶŐĞůŝŬĂDĂŶŚĂƌƚͲ>ĞĐƚƵƌĞƌŝŶƉƉůŝĞĚ ,ĞŝƐĐƵƌƌĞŶƚůLJĂŶW^Z&ĞůůŽǁůĞĂĚŝŶŐ DĂƚŚĞŵĂƟĐƐ dͲEdZ/͗ĞǀĞůŽƉŝŶŐĐĐŽƵŶdďůĞ /ĂŵĂDĂƚŚĞŵĂƟĐĂůŝŽůŽŐŝƐƚǁŝƚŚĂŶ ŽŵƉƵƚĂƟŽŶĂůŶŐŝŶĞĞƌŝŶŐdŚƌŽƵŐŚZŽďƵƐƚ ŝŶƚĞƌĞƐƚŝŶŵŽĚĞůůŝŶŐ͕ƐŝŵƵůĂƟŶŐĂŶĚ /ŶĨĞƌĞŶĞ͕ǁŚĞƌĞŚĞŝƐĚĞǀĞůŽƉŝŶŐĂLJĞƐŝĂŶ ĂŶĂůLJƐŝŶŐĐĞůůďŝŽůŽŐŝĐĂůƐLJƐƚĞŵƐƵƐŝŶŐ ƚĞĐŚŶŝƋƵĞƐĨŽƌŶƵŵĞƌŝĐĂůŵĞƚŚŽĚƐƚŚĂƚ ŵĂƚŚĞŵĂƟĐĂůƚŽŽůƐ͕ŝŶƉĂƌƟĐƵůĂƌƉĂƌƟĂů ƋƵĂŶƟĨLJƵŶĐĞƌƚĂŝŶƚLJĚƵĞƚŽĐŽŵƉƵƚĂƟŽŶ͘ ĚŝīĞƌĞŶƟĂůĞƋƵĂƟŽŶƐ͘ƚƚŚĞŚĞĂƌƚŽĨŵLJ tŝƚŚŝŶKZh͕ŚĞŝƐŝŶĐŚĂƌŐĞŽĨĂŶĂůLJƐŝŶŐ ƌĞƐĞĂƌĐŚůŝĞƐƚŚĞƋƵĞƐƟŽŶŽĨŚŽǁŵŝĐƌŽ ŵĂƐƐŝǀĞĚĂƚĂƐĞƚƐĨƌŽŵŚŽƐƉŝƚĂůƐƚŽĚĞǀĞůŽƉ ƐĐĂůĞĞīĞĐƚƐůĞĂĚƚŽŵĂĐƌŽƐĐĂůĞƌĞƐƵůƚƐ͕ ŵĞƚŚŽĚƐƚŚĂƚĞŶŚĂŶĐĞĐůŝŶŝĐĂůĚĞĐŝƐŝŽŶ ƌĞůĞǀĂŶƚĨŽƌĞdžĂŵƉůĞĨŽƌĐĞůůŵŽǀĞŵĞŶƚŽĨ ŵĂŬŝŶŐ͘,ŝƐĐŽŶƟŶƵŽƵƐŝŶǀŽůǀĞŵĞŶƚǁŝƚŚ ĐŽůůĞĐƟǀĞďĞŚĂǀŝŽƵƌ͘/ǁĂƐďŽƌŶĂŶĚƌĂŝƐĞĚ ŝŶĚƵƐƚƌŝĂůƉĂƌƚŶĞƌƐŚĂƐůĞĚƚŽƐĞǀĞƌĂůƉƌŽũĞĐƚƐ ŝŶsŝĞŶŶĂ͕ƵƐƚƌŝĂ͕ǁŚĞƌĞ/ĚŝĚďŽƚŚŵLJƚǁŽ ǁŝƚŚĐŽŵƉĂŶŝĞƐ͕ŐŽǀĞƌŶŵĞŶƚďŽĚŝĞƐĂŶĚ ƵŶĚĞƌŐƌĂĚƵĂƚĞĚĞŐƌĞĞƐŝŶDĂƚŚĞŵĂƟĐƐ ^DƐ͘ ĂŶĚDŽůĞĐƵůĂƌŝŽůŽŐLJ͕ĂƐǁĞůůĂƐĂWŚŝŶ DĂƚŚĞŵĂƟĐƐ͘ŌĞƌƚǁŽƉŽƐƚͲĚŽĐƐĂƚƚŚĞ ƌ:ĞīƌĞLJ'ĂůŬŽǁƐŬŝͲ>ĞĐƚƵƌĞƌŝŶWƵƌĞ ŽƵƌĂŶƚ/ŶƐƟƚƵƚĞŽĨƚŚĞEĞǁzŽƌŬhŶŝǀĞƌƐŝƚLJ DĂƚŚĞŵĂƟĐƐ ĂŶĚ/ŵƉĞƌŝĂůŽůůĞŐĞ>ŽŶĚŽŶ/ŶŽǁůŽŽŬ DLJŵĂŝŶĞdžƉĞƌƟƐĞŝƐŝŶƚŚĞŵĞƚŚŽĚƐŽĨ ĨŽƌǁĂƌĚƚŽƌĞƐĞĂƌĐŚŝŶŐ͕ƚĞĂĐŚŝŶŐĂŶĚǁŽƌŬŝŶŐ ŵŝĐƌŽůŽĐĂůĂŶĂůLJƐŝƐĂŶĚ/ƵƐĞƚŚĞƐĞƚŽŽůƐ Ăƚh>͘ ƚŽƵŶĚĞƌƐƚĂŶĚƚŚĞŚŝŐŚĞŶĞƌŐLJďĞŚĂǀŝŽƌŽĨ ĞŝŐĞŶǀĂůƵĞƐĂŶĚĞŝŐĞŶĨƵŶĐƟŽŶƐĨŽƌƉĂƌƟĂů WƌŽĨĞƐƐŽƌsůĂĚŝŵŝƌŽŬĐŚŝƚƐĞƌͲWƌŽĨĞƐƐŽƌŽĨ ĚŝīĞƌĞŶƟĂůŽƉĞƌĂƚŽƌƐ͘DŝĐƌŽůŽĐĂůŵĞƚŚŽĚƐ WƵƌĞDĂƚŚĞŵĂƟĐƐ ĚĞĐŽŵƉŽƐĞĨƵŶĐƟŽŶƐŝŶƚŽƉŝĞĐĞƐǁŚŝĐŚ sůĂĚŝŵŝƌŝƐĂŶƵŵďĞƌƚŚĞŽƌŝƐƚ͕ǁŽƌŬŝŶŐŽŶ ůŽĐĂůŝnjĞŝŶďŽƚŚƉŽƐŝƟŽŶĂŶĚŵŽŵĞŶƚƵŵĂŶĚ ĞůůŝƉƟĐĐƵƌǀĞƐ͕:ĂĐŽďŝĂŶƐĂŶĚƋƵĞƐƟŽŶƐ ĞdžƉůŽŝƚƚŚĞĨĂĐƚƚŚĂƚWƐďĞŚĂǀĞĚŝīĞƌĞŶƚůLJ ƌĞůĂƚĞĚƚŽƚŚĞŝƌĐŚͲ^ǁŝŶŶĞƌƚŽŶͲLJĞƌ in various regions of phase space. They

45 NEW ACADEMIC STAFF

ĐĂŶŽŌĞŶďĞƵƐĞĚƚŽŵĂŬĞƚŚĞŚĞƵƌŝƐƟĐŽĨ ƌ^ŚĂŶĞŽŽƉĞƌͲ>ĞĐƚƵƌĞƌŝŶƉƉůŝĞĚ ͚ƋƵĂŶƚƵŵͲĐůĂƐƐŝĐĂůĐŽƌƌĞƐƉŽŶĚĞŶĐĞ͛ƉƌĞĐŝƐĞ͘ DĂƚŚĞŵĂƟĐƐ DLJƌĞƐĞĂƌĐŚŝŶƚĞƌĞƐƚƐůŝĞŝŶƚŚĞŵĂƚŚĞŵĂƟĐĂů ƌ>ŽƌĞŶnjŽ&ŽƐĐŽůŽͲ>ĞĐƚƵƌĞƌŝŶWƵƌĞ ĂŶĂůLJƐŝƐŽĨŵƵůƟͲƐĐĂůĞƉĂƌƟĂůĚŝĞƌĞŶƟĂů DĂƚŚĞŵĂƟĐƐ ĞƋƵĂƟŽŶƐ;WƐͿƚŚĂƚĂƌŝƐĞŝŶƚŚĞƐƚƵĚLJŽĨ DLJǁŽƌŬŝƐŵŽƟǀĂƚĞĚďLJŐĞŽŵĞƚƌŝĐ ǁĂǀĞƉŚĞŶŽŵĞŶĂĚƵĞƚŽƐĐĂůĞŝŶƚĞƌĂĐƟŽŶƐŝŶ ƋƵĞƐƟŽŶƐ͕ŝƚŝƐŽŌĞŶŝŶƐƉŝƌĞĚďLJƚŚĞŽƌĞƟĐĂů ŚŝŐŚůLJŚĞƚĞƌŽŐĞŶĞŽƵƐĐŽŵƉŽƐŝƚĞŵĞĚŝĂ͘dŚĞ ƉŚLJƐŝĐƐĂŶĚƌĞůŝĞƐŽŶƌĞĮŶĞĚĂŶĂůLJƟĐƚŽŽůƐ ŵƵůƟͲƐĐĂůĞWƐŽĨŝŶƚĞƌĞƐƚĂƌĞŐĞŶĞƌĂůůLJƚŽŽ ƚŽƐƚƵĚLJƉĂƌƟĂůĚŝīĞƌĞŶƟĂůĞƋƵĂƟŽŶƐŽŶ ĐŽŵƉůŝĐĂƚĞĚĨŽƌƉƌĂĐƟĐĂůƉƵƌƉŽƐĞƐĂŶĚĞǀĞŶ ŐĞŽŵĞƚƌŝĐƐƉĂĐĞƐ͘ ĚŝƌĞĐƚŶƵŵĞƌŝĐĂůƐŝŵƵůĂƟŽŶƐǁŽƵůĚďĞŽǀĞƌůLJ /ĂŵĐƵƌƌĞŶƚůLJŝŶƚĞƌĞƐƚĞĚŝŶƚŚĞƐƚƵĚLJ ĐŽƐƚůLJĂŶĚŝŶĞĐŝĞŶƚ͘dŚĞŐŽĂůŽĨŵLJǁŽƌŬ ŽĨZŝĞŵĂŶŶŝĂŶŵĂŶŝĨŽůĚƐǁŝƚŚƐƉĞĐŝĂů ŝƐƚŽƌĞƉůĂĐĞƚŚĞƐĞWƐǁŝƚŚƐŝŵƉůŝĞĚĂŶĚ ŚŽůŽŶŽŵLJ͕ƐŽŵĞŽĨƚŚĞŵŽƐƚŝŵƉŽƌƚĂŶƚ ĐŽŶƚƌŽůůĂďůLJĂĐĐƵƌĂƚĞĂƉƉƌŽdžŝŵĂƚĞŵŽĚĞůƐ ŐĞŽŵĞƚƌŝĐƐƚƌƵĐƚƵƌĞƐŝŶĚŝīĞƌĞŶƟĂů ƚŚĂƚĂƌĞƉƌĂĐƟĐĂůůLJƵƐĞĨƵů͘^ƵĐŚĂƉƉƌŽdžŝŵĂƚĞ ŐĞŽŵĞƚƌLJ͘^ƉĞĐŝĂůŚŽůŽŶŽŵLJŵĂŶŝĨŽůĚƐ ŵŽĚĞůƐĂƌĞĚĞƚĞƌŵŝŶĞĚďLJĂŶĂƐLJŵƉƚŽƟĐ ƉƌŽǀŝĚĞĞdžĂŵƉůĞƐŽĨŝŶƐƚĞŝŶŵĂŶŝĨŽůĚƐ͕ŝŶ ĂŶĂůLJƐŝƐŽĨƚŚĞŽƌŝŐŝŶĂůŵƵůƟͲƐĐĂůĞWŝŶ ƉĂƌƟĐƵůĂƌZŝĐĐŝͲŇĂƚŽŶĞƐ͘dŚĞůĂƩĞƌĂƌĞƚŚĞ ƚĞƌŵƐŽĨĞdžƚƌĞŵĂůƉŚLJƐŝĐĂůĂŶĚͬŽƌŐĞŽŵĞƚƌŝĐ ZŝĞŵĂŶŶŝĂŶĂŶĂůŽŐƵĞƐŽĨƚŚĞƐŽůƵƟŽŶƐŽĨ ƉĂƌĂŵĞƚĞƌƐ͘dLJƉŝĐĂůůLJ͕/ǁŽƌŬǁŝƚŚĞƋƵĂƟŽŶƐ ŝŶƐƚĞŝŶ͛ƐĞƋƵĂƟŽŶƐŽĨ'ĞŶĞƌĂůZĞůĂƟǀŝƚLJǁŝƚŚ ƚŚĂƚĂƌŝƐĞŝŶƚŚĞƐƚƵĚLJŽĨĐŽƵƐƟĐ͕ůĂƐƟĐ͕ ǀĂŶŝƐŚŝŶŐĐŽƐŵŽůŽŐŝĐĂůĐŽŶƐƚĂŶƚ͘/ŶĨĂĐƚ͕Ăůů ĂŶĚůĞĐƚƌŽŵĂŐŶĞƟĐǁĂǀĞƐ͘ ĐƵƌƌĞŶƚůLJŬŶŽǁŶĞdžĂŵƉůĞƐŽĨĐŽŵƉĂĐƚZŝĐĐŝͲ ŇĂƚŵĂŶŝĨŽůĚƐŚĂǀĞƐƉĞĐŝĂůŚŽůŽŶŽŵLJ͊ ƌ/ĂŶWĞƚƌŽǁͲ>ĞĐƚƵƌĞƌŝŶWƵƌĞ DĂƚŚĞŵĂƟĐƐ ƌ>ƵŝƐ'ĂƌĐŝĂDĂƌƟŶĞnjͲ>ĞĐƚƵƌĞƌŝŶWƵƌĞ DLJƌĞƐĞĂƌĐŚŝƐŝŶŶƵŵďĞƌƚŚĞŽƌLJ͕ǁŚŝĐŚŝƐ DĂƚŚĞŵĂƟĐƐ ƚŚĞƐƚƵĚLJŽĨƚŚĞƉƌŽƉĞƌƟĞƐŽĨƚŚĞŝŶƚĞŐĞƌƐ͘ /ĂŵĂƉƵƌĞŵĂƚŚĞŵĂƟĐŝĂŶĨŽĐƵƐŝŶŐŽŶ DŽƌĞƐƉĞĐŝĮĐĂůůLJ͕ŵLJĚŽŵĂŝŶŽĨĞdžƉĞƌƟƐĞ ŶƵŵďĞƌƚŚĞŽƌLJĂŶĚĂƵƚŽŵŽƌƉŚŝĐĨŽƌŵƐ͘/Ăŵ ŝƐĂŶĂůLJƟĐŶƵŵďĞƌƚŚĞŽƌLJ͕ǁŚŝĐŚƚĞŶĚƐƚŽ ŝŶƚĞƌĞƐƚĞĚŝŶƚŚĞŐĞŽŵĞƚƌLJĂŶĚĐŽŚŽŵŽůŽŐLJ ĂƐŬƋƵĞƐƟŽŶƐĂďŽƵƚƚŚĞŝŶƚĞŐĞƌƐĐŽŶĐĞƌŶŝŶŐ ŽĨůŽĐĂůůLJƐLJŵŵĞƚƌŝĐƐƉĂĐĞƐĂŶĚĂƉƉůŝĐĂƟŽŶƐ ĐŽƵŶƟŶŐŽƌĞƐƟŵĂƟŽŶ͘&ŽƌĞdžĂŵƉůĞ͕ŽŶĞ ƚŽǀĂůƵĞƐŽĨ>ͲĨƵŶĐƟŽŶƐ͘ ĨĂŵŽƵƐƵŶƐŽůǀĞĚƋƵĞƐƟŽŶŝŶĂŶĂůLJƟĐŶƵŵďĞƌ ƚŚĞŽƌLJŝƐƚŚĞ'ŽůĚďĂĐŚƉƌŽďůĞŵ͗,ŽǁŵĂŶLJ ƌDĂŚŝƌ,ĂĚnjŝĐͲƐƐŽĐŝĂƚĞWƌŽĨĞƐƐŽƌŝŶ ǁĂLJƐĐĂŶŽŶĞǁƌŝƚĞĂƉŽƐŝƟǀĞĞǀĞŶŝŶƚĞŐĞƌ WƵƌĞDĂƚŚĞŵĂƟĐƐ ĂƐĂƐƵŵŽĨƚǁŽƉƌŝŵĞƐ;ŝŶƉĂƌƟĐƵůĂƌ͕ŝƐƚŚĞƌĞ DLJƌĞƐĞĂƌĐŚŝƐŝŶƚŚĞĮĞůĚŽĨŶŽŶůŝŶĞĂƌƉĂƌƟĂů ĂůǁĂLJƐĂƚůĞĂƐƚŽŶĞǁĂLJͿ͍DLJĨĂǀŽƌŝƚĞƚŚŝŶŐ ĚŝīĞƌĞŶƟĂůĞƋƵĂƟŽŶƐ͕ǁŝƚŚĞŵƉŚĂƐŝƐŽŶ ŝŶŵĂƚŚĞŵĂƟĐƐŝƐǁŚĞŶƚǁŽĂƉƌŝŽƌŝĚŝīĞƌĞŶƚ ƌŝŐŽƌŽƵƐƵŶĚĞƌƐƚĂŶĚŝŶŐŽĨƚŚĞƋƵĂůŝƚĂƟǀĞ ĂƌĞĂƐ͕ƐƵĐŚĂƐĂƌŝƚŚŵĞƟĐĂŶĚĂŶĂůLJƐŝƐ͕ĐŽŵĞ ĚLJŶĂŵŝĐƉƌŽƉĞƌƟĞƐŽĨƚŚĞŝƌƐŽůƵƟŽŶƐ͘/ǁŽƌŬ ƚŽŐĞƚŚĞƌŝŶĂŶƵŶĞdžƉĞĐƚĞĚǁĂLJ͘ǀĞŶŵŽƌĞ ŽŶŵĂƚŚĞŵĂƟĐĂůƉƌŽďůĞŵƐĐŽŵŝŶŐĨƌŽŵ ƐƉĞĐŝĮĐĂůůLJ͕/ĂŵŝŶƚĞƌĞƐƚĞĚŝŶƚŚĞĂŶĂůLJƟĐ ŇƵŝĚŵĞĐŚĂŶŝĐƐ͕ŬŝŶĞƟĐƚŚĞŽƌLJ͕ĂŶĚŐĞŶĞƌĂů ƚŚĞŽƌLJŽĨĂƵƚŽŵŽƌƉŚŝĐĨŽƌŵƐ͕ǁŚŝĐŚĂƌĞ ƌĞůĂƟǀŝƚLJƚŚĞŽƌLJ͘ ƚŚĞĨƵŶĚĂŵĞŶƚĂůŽďũĞĐƚƐŝŶƚŚĞ>ĂŶŐůĂŶĚƐ ƉƌŽŐƌĂŵ͕ĂǁŝĚĞͲƌĂŶŐŝŶŐǁĞďŽĨĐŽŶũĞĐƚƵƌĞƐ ƚŚĂƚĚƌŝǀĞƐĂůĂƌŐĞƉĂƌƚŽĨŵŽĚĞƌŶƌĞƐĞĂƌĐŚŝŶ ŶƵŵďĞƌƚŚĞŽƌLJ͘

46 ALUMNI CAREERS

ůƵŵŶŝĂƌĞĞƌƐĚǀŝĐĞ dŚĞĞƉĂƌƚŵĞŶƚŝƐŬĞĞŶƚŽǁĞůĐŽŵĞĂůƵŵŶŝƚŽŝƚƐĐĂƌĞĞƌƐĞǀĞŶƚƐĂŶĚĨĂŝƌƐĨŽƌŽƵƌĐƵƌƌĞŶƚ ƐƚƵĚĞŶƚƐ͘dŚŝƐŝŶĐůƵĚĞƐĂůƵŵŶŝǁŚŽŚĂǀĞŐŽŶĞŽŶƚŽĐŽŵƉůĞƚĞĨƵƌƚŚĞƌƐƚƵĚLJ͘

/ĨLJŽƵĂƌĞŝŶƚĞƌĞƐƚĞĚŝŶƚŚŝƐƉŽƐƐŝďŝůŝƚLJ͕ƉůĞĂƐĞĐŽŶƚĂĐƚWƌŽĨĞƐƐŽƌ,ĞůĞŶtŝůƐŽŶĂƚ ŚĞůĞŶ͘ǁŝůƐŽŶΛƵĐů͘ĂĐ͘ƵŬ͘ tĞĂůƐŽĞŶĐŽƵƌĂŐĞLJŽƵƚŽũŽŝŶƚŚĞh>ůƵŵŶŝKŶůŝŶĞŽŵŵƵŶŝƚLJ;ƵĐů͘ĂĐ͘ƵŬͬĂůƵŵŶŝͿƚŽƐƚĂLJ ƵƉƚŽĚĂƚĞǁŝƚŚƚŚĞůĂƚĞƐƚŶĞǁƐ͕ǀŝĞǁƐ͕ĞǀĞŶƚƐ͕ƐƉĞĐŝĂůŽīĞƌƐĂŶĚĞdžĐůƵƐŝǀĞŽƉƉŽƌƚƵŶŝƟĞƐĨƌŽŵ h>͕ĂŶĚƐƚĂLJĐŽŶŶĞĐƚĞĚǁŝƚŚLJŽƵƌĨĞůůŽǁĂůƵŵŶŝ͘

ŽŶƚƌŝďƵƟŶŐƚŽƚŚĞĞDŽƌŐĂŶƐƐŽĐŝĂƟŽŶEĞǁƐůĞƩĞƌ tĞǁŽƵůĚǁĞůĐŽŵĞŶĞǁƐĂŶĚĐŽŶƚƌŝďƵƟŽŶƐĨŽƌƚŚĞŶĞdžƚŶĞǁƐůĞƩĞƌ͕ƚŽďĞƐĞŶƚƚŽ͗

WƌŽĨĞƐƐŽƌdĞĚ:ŽŚŶƐŽŶ͕dŚĞĞDŽƌŐĂŶƐƐŽĐŝĂƟŽŶ͕ĞƉĂƌƚŵĞŶƚŽĨDĂƚŚĞŵĂƟĐƐ͕ hŶŝǀĞƌƐŝƚLJŽůůĞŐĞ>ŽŶĚŽŶ͕'ŽǁĞƌ^ƚƌĞĞƚ͕>ŽŶĚŽŶtϭϲd

ŵĂŝů͗ĞĚŝƚŽƌͺŶĞǁƐůĞƩĞƌΛŵĂƚŚ͘ƵĐů͘ĂĐ͘ƵŬ

47 IN MEMORIAM - PROFESSOR YAROSLAV KURYLEV

WƌŽĨĞƐƐŽƌzĂƌŽƐůĂǀ;^ůĂǀĂͿ<ƵƌLJůĞǀ

48 IN MEMORIAM - PROFESSOR YAROSLAV KURYLEV

WƌŽĨĞƐƐŽƌzĂƌŽƐůĂǀ;^ůĂǀĂͿ<ƵƌLJůĞǀ͕ĚŝĞĚŽŶϭϵ ^ůĂǀĂŵŽǀĞĚƚŽhŶŝǀĞƌƐŝƚLJŽůůĞŐĞ>ŽŶĚŽŶ :ĂŶƵĂƌLJϮϬϭϵĂŐĞĚϲϲ͘ ŝŶϮϬϬϳ͘,ĞƌĞŵĂŝŶĞĚĐƌĞĂƟǀĞƵŶƟůŚŝƐ ƵŶƟŵĞůLJĚĞĂƚŚ͘ZĞĐĞŶƚůLJ͕ŝŶĂƐĞƌŝĞƐŽĨ ^ůĂǀĂ<ƵƌLJůĞǀǁĂƐŽŶĞŽĨƚŚĞůĞĂĚŝŶŐ ĂƌƟĐůĞƐǁŝƚŚŽƐŝĂŶĚ>ĂƐƐĂƐ͕ŚĞďƌŽƵŐŚƚƚŽ ƌĞƐĞĂƌĐŚĞƌƐǁŚŽůĂŝĚƚŚĞĨŽƵŶĚĂƟŽŶƐŽĨƚŚĞ ĂĐŽŶĐůƵƐŝŽŶĂůŽŶŐͲƚĞƌŵƉƌŽũĞĐƚŽĨŚŝƐ͕Ă ƚŚĞŽƌLJŽĨŵƵůƟͲĚŝŵĞŶƐŝŽŶĂůŝŶǀĞƌƐĞƉƌŽďůĞŵƐ ƐƚĂďŝůŝƚLJƚŚĞŽƌLJĨŽƌŝŶǀĞƌƐĞďŽƵŶĚĂƌLJƐƉĞĐƚƌĂů ŝŶƚŚĞůĂƚĞϭϵϴϬΖƐĂŶĚĞĂƌůLJϭϵϵϬΖƐ͘ƵƌŝŶŐƚŚŝƐ ƉƌŽďůĞŵƐ͘dŚŝƐŝƐĂƚŽƵƌĚĞĨŽƌĐĞƚŚĂƚƌĞƋƵŝƌĞĚ ƉĞƌŝŽĚ͕ŚĞǁĂƐĂƌĞƐĞĂƌĐŚĞƌĂƚƚŚĞ>ĞŶŝŶŐƌĂĚ ƚŚĞĂƵƚŚŽƌƐƚŽĞƐƚĂďůŝƐŚ͕ĨŽƌŝŶƐƚĂŶĐĞ͕Ă ;^ƚ͘WĞƚĞƌƐďƵƌŐͿĞƉĂƌƚŵĞŶƚŽĨ^ƚĞŬůŽǀ ƉƌĞĐŝƐĞƋƵĂŶƟĮĐĂƟŽŶŽĨŚLJƉĞƌďŽůŝĐƵŶŝƋƵĞ DĂƚŚĞŵĂƟĐĂů/ŶƐƟƚƵƚĞ͕ŚĂǀŝŶŐŽďƚĂŝŶĞĚŚŝƐ ĐŽŶƟŶƵĂƟŽŶ͘ WŚƚŚĞƌĞŝŶϭϵϳϵ͘ ŶŽƚŚĞƌŚŝŐŚůLJƐŝŐŶŝĮĐĂŶƚƌĞĐĞŶƚŝŶŶŽǀĂƟŽŶ ,ŝƐƐĞŵŝŶĂůƌĞƐƵůƚǁŝƚŚĞůŝƐŚĞǀƐĂLJƐƚŚĂƚ ďLJŚŝŵ͕>ĂƐƐĂƐĂŶĚhŚůŵĂŶŶŝƐĂƚĞĐŚŶŝƋƵĞ ĂĐŽŵƉĂĐƚZŝĞŵĂŶŶŝĂŶŵĂŶŝĨŽůĚǁŝƚŚ ƚŚĂƚůĞĂĚƐƚŽĂƐŽůƵƟŽŶŽĨŝŶǀĞƌƐĞƉƌŽďůĞŵƐ ďŽƵŶĚĂƌLJŝƐĚĞƚĞƌŵŝŶĞĚ͕ƵƉƚŽĂŶŝƐŽŵĞƚƌLJ͕ ĨŽƌŶŽŶͲůŝŶĞĂƌŚLJƉĞƌďŽůŝĐĞƋƵĂƟŽŶƐ͘ ďLJŝƚƐŝƌŝĐŚůĞƚĞŝŐĞŶǀĂůƵĞƐƚŽŐĞƚŚĞƌǁŝƚŚ ^ƚƌŝŬŝŶŐůLJ͕ƚŚĞŝƌƌĞƐƵůƚĐŽǀĞƌƐĂůĂƌŐĞ ƚŚĞŶŽƌŵĂůĚĞƌŝǀĂƟǀĞƐŽĨƚŚĞĐŽƌƌĞƐƉŽŶĚŝŶŐ ĐůĂƐƐŽĨŐĞŽŵĞƚƌŝĐƐĞƫŶŐƐĨŽƌǁŚŝĐŚƚŚĞ ĞŝŐĞŶĨƵŶĐƟŽŶƐ͘dŚŝƐƌĞƐƵůƚŐŝǀĞƐĂǁĂLJƚŽ ĐŽƌƌĞƐƉŽŶĚŝŶŐƉƌŽďůĞŵƐĨŽƌůŝŶĞĂƌĞƋƵĂƟŽŶƐ ƐĞĞŝŶƐŝĚĞƚŚĞŵĂŶŝĨŽůĚŐŝǀĞŶŝŶĨŽƌŵĂƟŽŶŽŶ ĂƌĞŽƉĞŶ͘tŚŝůĞƚŚĞŝƌǁŽƌŬǁĂƐƉƵďůŝƐŚĞĚ ŝƚƐďŽƵŶĚĂƌLJ͕ĂŶĚŝƚĐĂŶďĞĂůƐŽǀŝĞǁĞĚĂƐĂ ŽŶůLJůĂƐƚLJĞĂƌŝŶ/ŶǀĞŶƟŽŶĞƐDĂƚŚĞŵĂƟĐĂĞ͕ ŵĂƚŚĞŵĂƟĐĂůŵŽĚĞůĨŽƌĂƉƉůŝĞĚƉƌŽďůĞŵƐ several researchers have already started ĂƌŝƐŝŶŐ͕ĨŽƌĞdžĂŵƉůĞ͕ŝŶŐĞŽƉŚLJƐŝĐĂůŝŵĂŐŝŶŐ͘ ĂƉƉůLJŝŶŐŝƚƚŽǀĂƌŝŽƵƐĞƋƵĂƟŽŶƐĂƌŝƐŝŶŐŝŶ physics. ^ůĂǀĂĐŽŶƟŶƵĞĚŵĂŬŝŶŐŵĂũŽƌĐŽŶƚƌŝďƵƟŽŶƐ ƚŽŝŶǀĞƌƐĞƉƌŽďůĞŵƐƚŚƌŽƵŐŚŽƵƚŚŝƐĐĂƌĞĞƌ͘,Ğ ^ůĂǀĂǁĂƐǁŝĚĞůLJƌĞĂĚĂŶĚ͕ďĞLJŽŶĚ ŵŽǀĞĚƚŽ>ŽƵŐŚďŽƌŽƵŐŚhŶŝǀĞƌƐŝƚLJŝŶϭϵϵϱ ŵĂƚŚĞŵĂƟĐƐ͕ĞŶũŽLJĞĚĐŽŶǀĞƌƐĂƟŽŶƐŽŶ ĂŶĚďĞĐĂŵĞƉƌŽĨĞƐƐŽƌƚŚĞƌĞŝŶϭϵϵϴ͘ƵƌŝŶŐ ŚŝƐƚŽƌLJ͕ĂƌƚƐĂŶĚĐƵůƚƵƌĞ͘,ĞǁĂƐĂŶŽƵƚƐŝĚĞͲ ŚŝƐƟŵĞĂƚ>ŽƵŐŚďŽƌŽƵŐŚŚĞǁƌŽƚĞƚŚĞŬ ƚŚĞͲďŽdžƚŚŝŶŬĞƌĂŶĚƐƉƌĞĂĚŚŝƐĞŶƚŚƵƐŝĂƐŵ Η/ŶǀĞƌƐĞďŽƵŶĚĂƌLJƐƉĞĐƚƌĂůƉƌŽďůĞŵƐΗ͕ũŽŝŶƚůLJ ƚŽŽƚŚĞƌƐ͘/ƚǁĂƐĂůǁĂLJƐĞdžĐŝƟŶŐƚŽďĞĂƌŽƵŶĚ ǁŝƚŚ<ĂƚĐŚĂůŽǀĂŶĚ>ĂƐƐĂƐ͕ǁŚŝĐŚŝƐŶŽǁĂ Śŝŵ͘ ĐůĂƐƐŝĐĂůƌĞĨĞƌĞŶĐĞŝŶŝŶǀĞƌƐĞƉƌŽďůĞŵƐ͘ >ĂƵƌŝKŬƐĂŶĞŶ ,ĞĂůƐŽƐƚƵĚŝĞĚĐŽƵŶƚĞƌͲĞdžĂŵƉůĞƐƚŽŝŶǀĞƌƐĞ ƉƌŽďůĞŵƐŝŶƚŚĞƐĞŶƐĞŽĨĐůŽĂŬŝŶŐ͘dŚŝƐŝƐƚŚĞ ŵĂƚŚĞŵĂƟĐĂůĂŶĂůLJƐŝƐŽĨƐƉĞĐŝĂůŵĂƚĞƌŝĂůƐƚŚĂƚ ĐĂŶďĞƵƐĞĚƚŽĐŽĂƚĂŶŽďũĞĐƚƐŽƚŚĂƚůŝŐŚƚŐŽĞƐ ĂƌŽƵŶĚŝƚ͕ƚŚĞŽďũĞĐƚƚŚƵƐďĞĐŽŵŝŶŐŝŶǀŝƐŝďůĞ͘ &ŽƌĞdžĂŵƉůĞ͕ŚŝƐǁŽƌŬŽŶĞůĞĐƚƌŽŵĂŐŶĞƟĐ ǁŽƌŵŚŽůĞƐǁŝƚŚ'ƌĞĞŶůĞĂĨ͕>ĂƐƐĂƐĂŶĚ hŚůŵĂŶŶǁĂƐĨĞĂƚƵƌĞĚŝŶEĂƚƵƌĞũŽƵƌŶĂů͘

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