CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "www.columbia.edu",cType: 'managed',cRay: '92a2db1c49f71fc7',cH: 'sjBO7MBj4t4e.tfFvrHqa613jGu3JhsVcBs8Pcic9BM-1743623433-1.2.1.1-H6xJ.9a8X_eGcoMF0YHDdqvwEcsFih1B.Q.RbZWkpBXut9BYreKuZSm13cPTrLRf',cUPMDTk: "\/?__cf_chl_tk=Y_I7aGGWEGPwP_UDFwy17tparQmIf8m6qccunsHJXyg-1743623433-1.0.1.1-Hzg8SY4Ft60y9ejAZdQUqPa43XkeYAlpAPFv4AEUJiA",cFPWv: 'g',cITimeS: '1743623433',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/?__cf_chl_f_tk=Y_I7aGGWEGPwP_UDFwy17tparQmIf8m6qccunsHJXyg-1743623433-1.0.1.1-Hzg8SY4Ft60y9ejAZdQUqPa43XkeYAlpAPFv4AEUJiA",md: "ZEc9ldj2XOqEQudeTPlkrs.V9HkqLMbkc7S6t8DWLC4-1743623433-1.2.1.1-_lfqa80pq.CQZJX7yPeej2zhDcdtYUcR_eEo3Mq5Aps_j9pqGxIt.cRtSwztNYVr4Z0E.E8RYxipbant1ymhwzsyyMv2Qey1kHZt1McnMIi.I9CxxtPd6InDggd13mdohwCQt31LsT16CYQVop5nlHdZ9iFKkUoD3HUhQTT0dsU4Rb7zJH0BV70sKw3cXok9TsMssW5yF_fMziYNNhMRwJXSAtBF0.wiS0yXimQwRnzqd9FDNHGNClQXW98JH6JUhguUqHErxczYlCNHQOLK04baD5xxmYm_UMn6so3BKNmnRgodccMTNZnp9KimMN2ELDxBXVDUfCTDx6JV5SViNH9hbU._LKqtflAMIQ5als.EBO2hMQiwKe_oXtODP6oDTkmIza4A6H92IyrKUwRR72_8so2J8_H2c122wLaiUeFR54QX683HaX7jQPLImm_vv_K6RqYjYF8qT3plVNii0nG5YPM9Upw.AdZz66L.JEV9sBJbtNy5.c65R94owLmCH3x5Xy43PSX1GjjzHklQiBOeNz5WhBIaspkyEKpV_KuGtA7YXiwiKughwLvkUAOrescUhUhc6RktfjLaPEQrj7MHxBTXpvfg4sisZXzl9nFckxo5BDX5llqMu.xkarbP5cZKJIxhMavNL9wSYHSGjyGBZnhdE8PklWjBSOw2jYMB0fpU3IYnrdYiDFamM91FVAPJc0uguLK1v04e3.eEuePxNKKFgB3MbFG.aeagI3pUvnsGC3Gvz6g.FRAzXt2LEVVlVgnlIwN4KGsogMEop1EnrY456VlL4LECIhRvSZs4RidIyM.UgDEBEWmtLIzEnyYcFUf9QiQTJ3HMdDc4hXQ5JQ4lpuiaBIZYt8W5aAAVicqlerZX5nApOHQ.tY5VHfFUSi7fpEDAfeGGc7IVk10D74B1BO_vldmiF3DsOTXeTDNmKsF6U7vbO46xkgHk5YgdjKVRTGMNPYbyHXuuqiD8p6yR3OhQoBsyDrPf2vg4KO_LMCuSalT9YlOEg28Pfc9fZdgZJ1zlf03.YgOXuAsCMuhh7xwlKm3ZHk0GFGSE0MnqD5Hm9Pn.u.tyd_hfWYUkPcEk9KqU.2TcCT1MH9bWGXSAy30r4mTSBviZjbHiAanZDKhKV40SmCZs0rPrHwbk0bvRfQA7iC2K3stlgUMcop5Y9_R8S9GvC9h4kYR51PBDLWGdlT0.R3QCWuWZ",mdrd: "XeNWc2dXUiQN2lQL.GHQGfc0e2xlrhXl1XzZErRTLj0-1743623433-1.2.1.1-Mb78qkrXf1Bwh11SRfCN8s4rfbILojixREAHS50spiwcdf2wE7bnqToX1i2eOUogC0KKYwfi4hWvwdf1NZCXGpsS6R6yodD0RfOQu4BeWJYW4xhipQHe4ejxWVjKCsIRX0m63TKkyRSM.QptPM9RLWs4x1u8EusrCCjZiJgainC6JUM4S0mkFvETplYUqIjbSmom_rgtCsNheg1LoOd5pOdEHU38nnwkWwd2Ioqh8z8KmrYxOboNvlyLcBgJ_BQngM0ivHWN692M2aPKplydYlBQuUiGPzNmePbaMufVACDbGsQdwC0fNe4ynfpzfxbezqFtC2GRaQvhtaNPUQ9rvn0MSjNXpG4LBpYu2DkckTuG_nVjMnYTQcnq47SMNvZzjinO1cpK66MR7HaAlxWk8PmBPkAoOVLENXfRnbAMGDJ_lhgLZzp36mKRqPTtZhXYS5FDAwxzR1i3B2RKuzXub4oDCLP8huohE0XmbIZxx60n35WVbncSo0mJiMR2EWErn9whyOSvUEhT2L68nwZQYATbDi3CzIkeXfUJlw3PBaht2lYLm_4_._WuQgmkmnL3eWxQdBGsnS7NizRF9PZjJNtDLlat1vF5O.BVIQanZTBBfuFzWRcGeCRjABPJ.2vLOm4ZF18ZkbejHNKUONaNNKuZEV6oGM60kOS9m_uJqs41QMr5_5LCZ_73.W3GTr.TR7dcs5mCs10lRm39z2u3EA"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=92a2db1c49f71fc7';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/?__cf_chl_rt_tk=Y_I7aGGWEGPwP_UDFwy17tparQmIf8m6qccunsHJXyg-1743623433-1.0.1.1-Hzg8SY4Ft60y9ejAZdQUqPa43XkeYAlpAPFv4AEUJiA" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>