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<HEAD><TITLE>Ngo Bao Chau</TITLE></HEAD>   
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	<H1>Ngô Bảo Châu   </H1>		
	Francis and Rose Yuen <br> Distinguished Service Professor  <br><br>

	<a href="http://www.math.uchicago.edu/">Department of Mathematics</a><br>
	5734 University Avenue<br> 
	Chicago, IL 60637-1514, USA <br>
	Office: Eckhart 303 <br>
	Email: <a href="mailto:ngo@uchicago.edu">ngo@uchicago.edu</a><br>
	Phone: +1 773-702-7385 <br>

<br>		


<H3>Preprints </H3>
<ul>
	<li> Hankel transform, Langlands functoriality and functional equation of automorphic L-functions [<a href="takagi.pdf">takagi.pdf</a>]
	<li>On the Hitchin morphism for higher dimensional varieties, joint work with T.H. Chen [<a href="Chen-Ngo.pdf">Chen-Ngo.pdf</a>]
	<li> Weierstrass preparation theorem and singularities in the space of non-degenerate arcs, 
				[<a href="Weierstrass.pdf">Weierstrass.pdf</a>]
	</ul>

<H3>Recent publications</H3>

	<ul>

	<li> Perverse sheaves and fundamental lemmas, published in the Proceedings of the PCMI 201 [<a href="PCMI.pdf">PCMI.pdf</a>]</li>
	<li> On a conjecture of Braverman anh Kazhdan, with S. Cheng , published in IRMN	[<a href="BKGLn.pdf">BKGLn.pdf</a>]</li>
	<li> On the formal arc space of a reductive monoid, with A. Bouthier and Y. Sakellaridis [<a href="BNY.pdf">BNY.pdf</a>]</li>
	<li> Average size of 2-Selmer groups of elliptic curves over function fields, with Le Hung and Ho Phu Quoc [<a href="bcq.pdf">bcq.pdf</a>]</li> 
	<li>On a certain sum of L-functions 
		[<a href="PS.pdf">PS.pdf</a>]</li>
	<li>Geometrization of the trace formula, with E. Frenkel
		[<a href="geom.pdf">geom.pdf</a>]</li>
	<li>Formule des traces et fonctorialité: le début d'un programme, with Frenkel and Langlands
		[<a href="quebec.pdf">quebec.pdf</a>]  </li>
	<li>Kloosterman sheaves for reductive groups, with J. Heinloth and Z. Yun 
		[<a href="Kloosterman.pdf">Kloosterman.pdf</a>] </li>
	<li>Endoscopy theory of automorphic forms, ICM 2010 report
		[<a href="ICM.pdf">ICM.pdf</a>]</li>
	<li>Le lemme fondamental pour les algèbres de Lie 
		[<a href="LF.pdf">LF.pdf</a>]</li> 
	<li>	<a href="Eprints.html">more</a></li>
	</ul>

<H3 >Selected presentations</H3>

	<ul>
	<li>Leonardo Da Vinci Lecture 2013 :&nbsp; Arithmetic of certain integrable systems [<a 		href="Milan.pdf">Milan.pdf</a>]<br></li>
	<li>ICM in Hyderabad 2010 : Endoscopy theory of automorphic forms [<a 		href="ICM2010-talk.pdf">ICM2010-talk.pdf</a>]<br></li>
	</ul>


	<H3>Teaching</H3>
		<ul>
		<li> 2016: Representation theory of p-adic reductive groups [<a href="Rep-p-adic.pdf">notes</a>] </li>
		<li> 2015: Elementary Number Theory </li>
		<li> 2015: Introduction to Drinfeld's shtuka </li>
		<li> 2014: Geometry of the Hitchin fibration </li>
		<li> 2013: Algebraic Number Theory </li>
		<li> 2012: Algebraic Number Theory </li>
		<li> 2011: Automorphic forms on GL(2) </li>
		</ul>

	<H3>PhD students</H3>
	<ul>
	<li> Alexis Bouthier graduated in 2014 in Orsay, now is a Maître de Conférence in
		Université de Pierre et Marie Curie. 
		This is a <a href="http://arxiv.org/pdf/1409.1275v3.pdf">paper</a>
		extracted from his PhD thesis prepared under the co-supervision of G. Laumon and me.
		With Sakellaridis, we worked out a geometric interpretation of the basic function 
		 of the	local factor of automorphic L-function [<a href="BNY.pdf">BNY.pdf</a>].  </li>

	<li> Shuyang Cheng graduated in 2016 in Chicago, now is a postdoc in the University of Michgan at Ann Arbor. 
		This is a
		<a href="http://arxiv.org/pdf/1410.0415v3.pdf">paper</a> extracted from his PhD thesis. 
		We also worked together on a conjecture of Braverman 
		and Kazhdan on gamma sheaves over finite reductive groups [<a href="https://arxiv.org/pdf/1602.05688.pdf">BK.pdf</a>].</li>

	<li> Hồ Phú Quốc graduated in 2017, now is a postdoc in IST Vienna. In this 
		<a href="https://arxiv.org/pdf/1512.04490.pdf">paper</a>, he proved a theorem of stability 
		on cohomology of configuration spaces for smooth irreducible algebraic varieties. With Lê 
		Hùng Việt Bảo, we worked out a version of the Bhargava-Shankar theorem for function 
		fields [<a href="bcq.pdf">bcq.pdf</a>].</li> 

	<li> Daniel Johnstone graduated in 2017, now is a postdoc in the University of Minnesota. 
		He works on the generalization of the  
		<a href= "https://arxiv.org/pdf/1611.06291.pdf"> Gelfand-Graev character formula </a>.
	<li> Jingren Chi graduated in 2018. His thesis can be found <a href="https://arxiv.org/pdf/1805.08770.pdf">here</a>. 
	<li> Phạm Ngọc Hoàng Minh 
	<li> Trịnh Minh Tâm
	<li> Xiao Wang 
	<li> Kostas Psaromiligkos
	<li> Aaron Slipper
	<li> Thomas Hameister	
	</ul>

<H3> Editorial board</H3>

	<ul>
  	<li>Grundlehren der mathematischen Wissenschaften</li>
  	<li>Compositio Mathematica</li>
  	<li>Acta Mathematica Vietnamica</li>
  	<li>Vietnam Journal of Mathematics</li>
	</ul>

<a href="cv-2018.pdf"><H3>Vitae </H3> </a>

<hr style="width: 100%; solid  height: 1px;">
updated on May 25, 2018<br>

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