{"id":3,"date":"2014-03-11T20:57:33","date_gmt":"2014-03-11T20:57:33","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/edsaff\/homepage\/"},"modified":"2026-05-17T06:16:04","modified_gmt":"2026-05-17T11:16:04","slug":"homepage","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/edsaff\/","title":{"rendered":"Home Page"},"content":{"rendered":"

<\/a><\/strong><\/h3>\n

Edward Barry Saff<\/strong><\/h3>\n

Distinguished Research Professor, Vanderbilt University<\/strong><\/p>\n

Distinguished Professor of Mathematics, Emeritus, Vanderbilt University<\/strong><\/p>\n

Director, Center for Constructive Approximation<\/strong>
\n1326 Stevenson Center
\nVanderbilt University
\nNashville, TN 37240
\nEmail: edward.b.saff@vanderbilt.edu,\u00a0 Office phone: +1\u00a0 615 779 4128<\/p>\n

Upcoming Conferences\/Programs<\/h2>\n

“Energy and Polarization Problems in Mathematics and Statistics, part I,”\u00a0 Aug 16-19, 2026, Vanderbilt University. Organized by Doug Hardin, Ed Saff and Raffaello Seri.<\/span><\/p>\n

Recent Book<\/h2>\n

Recent Advances in Approximation and Potential Theory; in Honor of Edward Saff, edited by D. Bilyk,\u00a0 E. Iacob, A. Martinez-Finkelshtein, A. M. Stokolos<\/em><\/h5>\n
https:\/\/link.springer.com\/book\/10.1007\/978-3-031-95551-8<\/em><\/h5>\n

Recent Articles<\/h2>\n
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“Universal polar dual pairs of spherical codes found in E_8 and $\\Lambda_ 24$”, <\/span><\/span><\/span><\/span>Authors:<\/span> S. V. Borodachov<\/a>, P. G. Boyvalenkov<\/a>, P. D. Dragnev<\/a>, D. P. Hardin<\/a>, E. B. Saff<\/a>, M. M. Stoyanova, arXiv:2512.25037<\/a><\/span><\/span><\/a><\/p>\n<\/div>\n

“Riesz equilibrium on a ball in the external field of a point charge”, Authors:<\/span> Peter D. Dragnev<\/a>, Ramon Orive<\/a>, Edward B. Saff<\/a>, Franck Wielonsky, <\/a>arXiv:2501.01208<\/a>\u00a0<\/a><\/p>\n

“Bounds on energy and potentials of discrete measures on the sphere” Authors:<\/span> S. Borodachov<\/a>, P. Boyvalenkov<\/a>, P. Dragnev<\/a>, D. Hardin<\/a>, E. Saff<\/a>, M. Stoyanova,\u00a0 \u00a0<\/a>arXiv:2412.07442<\/a><\/p>\n

“Bounds on Discrete Potentials of Spherical (k,k)-Designs” Authors:<\/span> S. Borodachov<\/a>, P. Boyvalenkov<\/a>, P. Dragnev. D. Hardin. E. Saff<\/a>, M. Stoyanova\u00a0 <\/a>arXiv:2411.00290<\/a><\/p>\n

“Riesz Energy with a Radial External Field: When is the Equilibrium Support a Sphere?” (with Djalil Chafa\u00ef<\/a>, Ryan W. Matzke<\/a>, Minh Quan H. Vu<\/a>, Robert S. Womersley<\/a>), https:\/\/arxiv.org\/abs\/2405.00120<\/p>\n

On a problem of E. Meckes for the unitary eigenvalue process on an arc, (with Liudmyla Kryvonos<\/a>), accepted by Analysis and Math Physics journal, https:\/\/arxiv.org\/abs\/2402.11096<\/p>\n

Energy bounds for weighted spherical codes and designs via linear programming, (with Sergiy Borodachov<\/a>, Peter Boyvalenkov<\/a>, Peter Dragnev<\/a>, Douglas Hardin<\/a>, Maya Stoyanova<\/a>) arXiv:2403.07457<\/a><\/p>\n

Universal minima of discrete potentials for sharp spherical codes, (with P. Boyvalenkov, P. Dragnev, D.P. Hardin and M. Stoyanova), accepted for publication in <\/span>Revista Matem\u00e1tica Iberoamericana.\u00a0 https:\/\/arxiv.org\/pdf\/2211.00092.pdf<\/p>\n

On Polarization of Spherical Codes and Designs (with P. Boyvalenkov, P. Dragnev, D.P. Hardin and M. Stoyanova), JMAA (J. Math Analysis and Appl.) , Vol. 524, #1, August 2023, 127065. arXiv:2207.08807<\/a><\/p>\n

Archetype tasks link intratumoral heterogeneity to plasticity and 2cancer hallmarks in small cell lung cancer (with Sarah M. Groves et al), Cell Systems, 2022 Sep 21;13(9):690-710.e17. <\/span>doi: 10.1016\/j.cels.2022.07.006. <\/span> Epub 2022 Aug 17. <\/span><\/p>\n

Point source equilibrium problems with connections to weighted quadrature domains,(with P. Dragnev and A. Legg), Indag. Math. (N.S.)<\/a> 34 <\/a><\/span>(2023<\/a>)<\/span>, no. 2<\/a><\/span>, 200\u2013218. arXiv:2203.09421<\/a>
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Threshold Condensation to Singular Support for a Riesz Equilibrium Problem (with Djalil Chafa\u00ef and Robert S. Womersley), Analysis and Math Phys, Vol. 13, article 19, Jan. 30, 2023.\u00a0 https:\/\/arxiv.org\/abs\/2206.04956<\/p>\n

On the solution of a Riesz equilibrium problem and integral
\nidentities for special functions (with Djalil Chafa\u00ef and Robert S. Womersley),
\nJ. Math. Anal. and App., Volume 515, Issue 1, 1 November 2022, 126367<\/p>\n

Asymptotics of k-nearest neighbor Riesz energies (with D.P. Hardin and O.Vlasiuk) Constructive Approximation journal, DOI:https:\/\/doi.org\/10.1007\/s00365-023-09641-5, April, 2023.\u00a0 https:\/\/arxiv.org\/abs\/2201.00474<\/p>\n

Riesz Energy Problems with External Fields and Related Theory (with P. Dragnev, R. Orive and F. Wielonsky) , Constr. Approx.<\/a> 57 <\/a><\/span>(2023<\/a>)<\/span>, no. 1<\/a><\/span>, 1\u201343. arXiv:2104.03733<\/a>
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Dynamics of particles on a curve with pairwise hyper-singular repulsion (with D. Hardin, R. Shu, E. Tadmor), Discrete Contin. Dyn. Syst.<\/a> 41 <\/a><\/span>(2021<\/a>)<\/span>, no. 12<\/a><\/span>, 5509\u20135536.\u00a0 arXiv:2010.05431<\/a>
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Google Scholar Profile<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Edward Barry Saff Distinguished Research Professor, Vanderbilt University Distinguished Professor of Mathematics, Emeritus, Vanderbilt University Director, Center for Constructive Approximation 1326 Stevenson Center Vanderbilt University Nashville, TN 37240 Email: edward.b.saff@vanderbilt.edu,\u00a0 Office phone: +1\u00a0 615 779 4128 Upcoming Conferences\/Programs “Energy and Polarization Problems in Mathematics and Statistics, part I,”\u00a0 Aug 16-19, 2026, Vanderbilt University. Organized by…<\/p>\n","protected":false},"author":1985,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-3","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/pages\/3","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/users\/1985"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/comments?post=3"}],"version-history":[{"count":206,"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/pages\/3\/revisions"}],"predecessor-version":[{"id":607,"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/pages\/3\/revisions\/607"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/media?parent=3"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/edsaff\/wp-json\/wp\/v2\/tags?post=3"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}