@Article{CAM-12-4,
author = {},
title = {北京国际数学研究中心近期活动},
journal = {CAM-Net Digest},
year = {2015},
volume = {12},
number = {4},
pages = {4--4},
abstract = {<p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif;"><span style="font-size: 16px;">１</span><span style="font-size: 16px;">. BICMR-CNRS Lectures in Mathematics - Integral Formulas and Serre Duality&nbsp;for the Cauchy-Riemann Equation<br/><br/>Speaker(s)Christine Laurent, Université Joseph Fourier, Institut Fourier<br/>DateFrom 2015-04-27 To 2015-05-08<br/>VenueRoom 29 at Quan Zhai, BICMR<br/><br/>Speaker</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">Christine Laurent, Université Joseph Fourier, Institut Fourier<br/><br/>Sponsored by</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">BCIMR, CNRS, Mount Everest Project<br/><br/>Time</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">10:00-12:00, From 2015-04-27 to 2015-04-30, 2015-05-05 to 2015-05-08<br/><br/>Venue</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">Room 29 at Quan Zhai, BICMR<br/><br/>Abstract</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">The Cauchy-Riemann equation is one of the most important tools in&nbsp;complex analysis. Different approaches are possible to study this equation,&nbsp;here we will focus on the theory of integral representations developped by&nbsp;Grauert, Lieb, Henkin in the 70’s for the local study and use the Grauert’s&nbsp;bumping method to derive global results from the local ones.<br/><br/>The obstruction to the solvability of the Cauchy-Riemann equation on a complex&nbsp;manifold is given by the Dolbeault cohomology groups. We will study these groups&nbsp;in several settings: for smooth forms, for Lp form or for currents. The vanishing&nbsp;of a Dolbeault cohomology group in some setting is equivalent to the solvability&nbsp;of the Cauchy-Riemann equation in the same setting, the finiteness says that the&nbsp;obstruction is rather small.<br/><br/>For some problems, it is natural to introduce support conditions in the study of&nbsp;the Cauchy-Riemann equation, the case of compact supports is of great importance.&nbsp;<br/>Serre duality will give some relation between the usual Dolbeaut cohomology and&nbsp;the Dolbeault cohomology with compact support.<br/><br/>Applications to the extension of CR functions and to the solvability of the&nbsp;Cauchy-Riemann equation with prescribe support will be given.<br/><br/>2. BICMR-CNRS Lectures in Mathematics--Entire Holomorphic Curves and Algebraic Differential Equations<br/><br/>Speaker(s)Jean-Pierre Demailly, Université Joseph Fourier,Institut Fourier<br/>DateFrom 2015-04-07 To 2015-06-18<br/>VenueRoom 77201 at #78 courtyard, Beijing International Center for Mathematical&nbsp;<br/>Research/Room 29 at Quan Zhai, BICMR<br/><br/>Speaker</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">Jean-Pierre Demailly, Université Joseph Fourier, Institut Fourier<br/><br/>Sponsored by</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">BCIMR, CNRS, Mount Everest Project<br/><br/>Time</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">&nbsp;Every Tuesday &amp; Thursday, 14:00-16:00, From 2015-04-7 to 2015-06-18<br/><br/>Venue: Classroom 77201(2015-04-07 to 2015-06-11), Classroom Quan29 (2015-06-16 to 2015-06-18)<br/><br/>Abstract</span><span style="font-size: 16px;">：</span><span style="font-size: 16px;">The geometry of projective algebraic varieties is intimately&nbsp;related to positivity or negativity properties of their curvature tensor. In the&nbsp;introduction, we will first recall some basic concepts of complex differential geometry:&nbsp;<br/>complex manifolds, Dolbeault cohomology, vector bundles, connections, Chern classes,&nbsp;holomorphic Morse inequalities. These fundamental concepts will then be used to investigate&nbsp;the existence of entire holomorphic curves drawn in projective algebraic varieties. This&nbsp;problem is related to deep conjectures concerning number theory (Diophantine equations) and,in a more algebraic setting, to curvature properties of jet bundles. The ultimate goal will&nbsp;be to prove a recent result of the lecturer in the direction of the Green-Griffiths-Lang&nbsp;conjecture, according to which every entire curve drawn in a variety of general type&nbsp;satisfies algebraic differential equations.</span></span></p>},
issn = {},
doi = {https://doi.org/2015-CAM-14911},
url = {https://global-sci.com/article/76671/%E5%8C%97%E4%BA%AC%E5%9B%BD%E9%99%85%E6%95%B0%E5%AD%A6%E7%A0%94%E7%A9%B6%E4%B8%AD%E5%BF%83%E8%BF%91%E6%9C%9F%E6%B4%BB%E5%8A%A8}
}