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❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧ ❢❛❝✉❧t②✳✈❛❧♣♦✳❡❞✉✴❧♣✉❞✇❡❧❧ ❱❛❧♣❛r❛✐s♦ ❙②♠♣♦s✐✉♠ ♦♥ ❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❛♥❞ ❈r❡❛t✐✈❡ ❊①♣r❡ss✐♦♥ ▼❛② ✶✹✱ ✷✵✷✵ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ■♠❛❣❡ ❝r❡❞✐t✿ ❤tt♣s✿✴✴♣❤✐❧✳❝❞❝✳❣♦✈✴❞❡t❛✐❧s✳❛s♣①❄♣✐❞❂✷✸✸✶✷ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ❖✉ts✐❞❡ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❲♦r❧❞ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ P❡rs♦♥❛❧ ❉✐s❝♦✈❡r② ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ P❡rs♦♥❛❧ ❉✐s❝♦✈❡r② I’ve discovered just how much nature there is to explore and appreciate even though we are in the middle of a giant city. I’m better at baking than I thought, and I’m only getting better while this goes on. ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ P❡rs♦♥❛❧ ❉✐s❝♦✈❡r② I am excited that I may be able to attend more conferences than I ever thought I would because they are going virtual. I’ve come to realize just how much I appreciate my office, my campus, and my face-to-face colleagues and students. ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❚❤❡ ❚✐♠❡ ♦❢ ❈♦r♦♥❛ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ P❡rs♦♥❛❧ ❉✐s❝♦✈❡r② I got to teach my 4 year old to read! Watching someone learn to read is AWESOME. I’ve realized anew how much I really do enjoy my kids, and also how beautiful the inquiring mind is. ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❛t ❱❛❧♣♦ ❙❖❯❘❈❊ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❛t ❱❛❧♣♦ ❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❛t ❱❛❧♣♦ ❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ ❛t ❱❛❧♣♦ ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❲❤✐❝❤ ♣❡r♠✉t❛t✐♦♥s ❤❛✈❡ ♥♦ ♦r ❄ ❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❲❤✐❝❤ ♣❡r♠✉t❛t✐♦♥s ❤❛✈❡ ♥♦ ♦r ❄ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❲❤✐❝❤ ♣❡r♠✉t❛t✐♦♥s ❤❛✈❡ ♥♦ ♦r ❄ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s ❲❤✐❝❤ ♣❡r♠✉t❛t✐♦♥s ❤❛✈❡ ♥♦ ♦r ❄ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s P❡r♠✉t❛t✐♦♥s t❤❛t ❤❛✈❡ ♥♦ ♦r ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s P❡r♠✉t❛t✐♦♥s t❤❛t ❤❛✈❡ ♥♦ ♦r ❚❤❡♦r❡♠ ✭❙✐♠❡♦♥ ❛♥❞ ❙❝❤♠✐❞t✱ ✶✾✽✺✮ ❚❤❡r❡ ❛r❡ ✷ n − ✶ ♣❡r♠✉t❛t✐♦♥s ♦❢ s✐③❡ n ✇✐t❤ ♥♦ ♦r ✳ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧

❍♦✇ ♠❛♥② ❡①♣❡❝t❡❞✳✳✳ ❛s❝❡♥ts❄ ❞❡s❝❡♥ts❄ ♣❡❛❦s❄ ✈❛❧❧❡②s❄ ❯♥❞❡r❣r❛❞✉❛t❡ ❘❡s❡❛r❝❤ P❡r♠✉t❛t✐♦♥s ❉✐s❝♦✈❡r② ✐♥ t❤❡ ❉✐s❝✐♣❧✐♥❡✿ P❡r♠✉t❛t✐♦♥s P❡r♠✉t❛t✐♦♥s t❤❛t ❤❛✈❡ ♥♦ ♦r ❚❤❡♦r❡♠ ✭❙✐♠❡♦♥ ❛♥❞ ❙❝❤♠✐❞t✱ ✶✾✽✺✮ ❚❤❡r❡ ❛r❡ ✷ n − ✶ ♣❡r♠✉t❛t✐♦♥s ♦❢ s✐③❡ n ✇✐t❤ ♥♦ ♦r ✳ ❉✐s❝♦✈❡r②✱ ■♥s✐❞❡ ❛♥❞ ❖✉t ▲❛r❛ P✉❞✇❡❧❧