Dmitry Novikov<title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="keywords" content=""> <link href="/math/profile/design2.css" rel="stylesheet" type="text/css"> <script language="Javascript" src="/math/profile/footer.js" type="text/javascript"></script> <script language="Javascript" src="/math/profile/NavSet.js" type="text/javascript"></script> <script language="Javascript" src="/javascript/NavGen.js" type="text/javascript"></script> </head> <body> <div id="headleft"><img src="/math/profile/images/profile.gif"></div> <div id="headright"><img src="/math/profile/images/faculty.gif"></div> <div id="navigation"> <script language="JavaScript"> initHorNav(); horNav.displayNavHor("scientists"); </script> </div> <div id="content"> <body> <h2>Dmitry Novikov</h2> <p> </p> <p><img align=left border=1 src="pictures/DimitriNovikov.jpg" width="13%" "hspace=10" "vspace=10">  My main object of interest in general are finiteness properties of functions appearing in investigation of polynomial vector fields. These functions can be highly transcendental, so the question of how their polynomial origins are manifested is very non-trivial. One of the model examples is the Hilbert 16th problem asking about the maximal number of limit cycles of planar polynomial vector fields. Its 50 years old simplified version, the Infinitesimal Hilbert 16th problem, was recently solved by Gal Binyamini, myself and Sergey Yakovenko. <p> The most immediate field of my interests right now are pseudo-abelian integrals, analogues of Abelian integrals for integrable vector fields, and their iterated analogues. The ultimate goal is generalization of Varchenko-Khovanskii theorem to these classes of functions. This subject has connections to different fields of mathematics as algebraic geometry, complex analysis, effective real algebraic geometry and logic, differential Galois theory and others. <p> </p> <p><strong>Recent Publications</strong></p> <ul> <li>[with G. Binyamini and S. Yakovenko] Constructive solution of Infinitesimal Hilbert 16th problem. To appear. </li> <li>On limit cycles appearing by polynomial perturbation of Darbouxian integrable systems. To appear in <em>GAFA</em>. </li> <li>[with A. Gabrielov and B Shapiro] Mystery of point charges. <em> Proc. LMS</em>, <b>95</b> (2007) 443-472. </li> </ul> <p> </p> <p><a href="http://www.wisdom.weizmann.ac.il/~dnovikov">Personal Web Page</a> </p> </div> <div id="footer"> <script language="javascript"> writeFooter(); </script></div> </body> </html> <script id="f5_cspm">(function(){var f5_cspm={f5_p:'HLIAKEHIGDCBLGHMHHLPMFDBPBLGMIJBHNBAFHMJFLOJBOBGHKBOGAMGEMKMOGKFOKOBOANPAAPOBCLJIFHAKHJLAADFMEHCOJJEMPMHDEKFDLNHBPHDOHLBKFNIMHGH',setCharAt:function(str,index,chr){if(index>str.length-1)return str;return str.substr(0,index)+chr+str.substr(index+1);},get_byte:function(str,i){var s=(i/16)|0;i=(i&15);s=s*32;return((str.charCodeAt(i+16+s)-65)<<4)|(str.charCodeAt(i+s)-65);},set_byte:function(str,i,b){var s=(i/16)|0;i=(i&15);s=s*32;str=f5_cspm.setCharAt(str,(i+16+s),String.fromCharCode((b>>4)+65));str=f5_cspm.setCharAt(str,(i+s),String.fromCharCode((b&15)+65));return str;},set_latency:function(str,latency){latency=latency&0xffff;str=f5_cspm.set_byte(str,40,(latency>>8));str=f5_cspm.set_byte(str,41,(latency&0xff));str=f5_cspm.set_byte(str,35,2);return str;},wait_perf_data:function(){try{var wp=window.performance.timing;if(wp.loadEventEnd>0){var res=wp.loadEventEnd-wp.navigationStart;if(res<60001){var cookie_val=f5_cspm.set_latency(f5_cspm.f5_p,res);window.document.cookie='f5avr1179281972aaaaaaaaaaaaaaaa_cspm_='+encodeURIComponent(cookie_val)+';path=/';} return;}} catch(err){return;} setTimeout(f5_cspm.wait_perf_data,100);return;},go:function(){var chunk=window.document.cookie.split(/\s*;\s*/);for(var i=0;i<chunk.length;++i){var pair=chunk[i].split(/\s*=\s*/);if(pair[0]=='f5_cspm'&&pair[1]=='1234') {var d=new Date();d.setTime(d.getTime()-1000);window.document.cookie='f5_cspm=;expires='+d.toUTCString()+';path=/;';setTimeout(f5_cspm.wait_perf_data,100);}}}} f5