Address:

University of California at Irvine,
Department of Mathematics,
510H Rowland Hall
Irvine, CA 92697
Tel: (949) 824-8778
E-mail: lxiao [at] math [at] uci [dot] edu

Fields of Interest:

Employment:

Education:

  • 2005.9-2009.6       Ph.D., Massachusetts Institute of Technology, MA (Advisor: Kiran S. Kedlaya)
  • 2001.9-2005.7       B.S. in Mathematics, Peking University, China

Awards and grants:

  • CORCL faculty research grant, UC Irvine (2014).
  • Simons Foundation Collaboration Grants (Fall 2013 - Summer 2018).
  • Newton International Fellowship 2009 (not taken).
  • International Mathematics Olympiad: Gold medal, 2001.

Papers and Preprints:

See separate webpage.

Conference Talks:

  • Ekedahl-Oort stratification and classicality of overconvergent automorphic forms, \textit{Arithmetic Geometry and Automorphic Form}, Morningside Center, China, August 2012.
  • Global triangulation over eigenvarieties, \textit{Second Annual Upstate Number Theory Conference Second Annual Upstate Number Theory Conference}, Rochester University, April 2012.
  • On family versions of some arithmetic conjectures, Arithmetic geometry and representation theory, Institute for Advanced Study, Hong Kong University of Science and Technology, December 2011.
  • Computing log-characteristic cycles using ramification theory, Atkin Memorial Lecture and Conference, Chicago, April 2011.
  • Computing log-characteristic cycles using ramification theory, AMS Special sessions, Iowa, March 2011.
  • Computing log-characteristic cycles using ramification theory, Midwest Number Theory Conference for Graduate Students and Recent PhD's 2010, Michigan, November 2010.
  • Computing log-characteristic cycles using ramification theory, Berkovich spaces and p-adic differential equations, Strasbourg, November 2010.
  • Non-archimedean differential modules and ramification theory, Journées de Géométrie Arithmétique de Rennes (presenting as a poster), Rennes, July 2009

Seminar Talks:

  • Slopes of modular forms, University of California at Irvine, May 2014.
  • Galois representations and torsion in the cohomology of Hilbert modular varieties, University of California at San Diego, April 2014.
  • Slopes of the eigencurve over boundary disks, University of Chicago, February 2014.
  • Slopes of the eigencurve over boundary disks, Northwestern University, February 2014.
  • Supersingular loci and Tate conjecture for some Shimura varieties mod p, M.I.T., February 2014.
  • Galois representations and torsion in the cohomology of Hilbert modular varieties, Boston University, September 2013.
  • Cycles on the special fiber of Hilbert modular varieties, University of Connecticut at Storrs, September 2013.
  • Goren-Oort stratification of Hilbert modular varieties and Tate conjecture, University of California at Los Angeles, May 2013.
  • Goren-Oort stratification of Hilbert modular varieties and Tate conjecture, University of California at San Diego, May 2013.
  • Goren-Oort stratification of Hilbert modular varieties and Tate conjecture, Caltech, April 2013.
  • Goren-Oort stratification of Hilbert modular varieties and Tate conjecture, University of California at Berkeley, April 2013.
  • Goren-Oort stratification of Hilbert modular varieties, University of California at Irvine, April 2013.
  • Goren-Oort stratification of Hilbert modular varieties, University of Illinois at Chicago, March 2013.
  • Goren-Oort stratification of Hilbert modular varieties and Tate conjecture, Princeton University, March 2013
  • Goren-Oort stratification of Hilbert modular varieties, Michigan State University, Feburary 2013.
  • Goren-Oort stratification of Hilbert modular varieties, University of Chicago, December 2012.
  • On the parity conjecture for Selmer groups of modular forms, Purdue University, February 2012.
  • On the parity conjecture for Selmer groups of modular forms, Northwestern University, February 2012.
  • On the parity conjecture for Selmer groups of modular forms, University of Texas at Austin, February 2012.
  • On the parity conjecture for Selmer groups of modular forms, University of Indiana at Bloomington, January 2012.
  • On the parity conjecture for Selmer groups of modular forms, University of California at Irvine, January 2012.
  • Computing log-characteristic cycles using ramification theory, Boston College, December 2011.
  • On the parity conjecture for Selmer groups of modular forms, University of Minnesota, December 2011.
  • On the parity conjecture for Selmer groups of modular forms, Iowa State University, December 2011.
  • On the parity conjecture for Selmer groups of modular forms, MIT, November 2011.
  • Global triangulation on the eigencurve, Boston University, November 2011.
  • On the parity conjecture for Selmer groups of modular forms, University of Illinois at Chicago, November 2011.
  • On family versions of some arithmetic conjectures, University of Chicago, November 2011.
  • Lecture series: Euler Systems, Morningside Center, China, Summer 2011.
  • Computing log-characteristic cycles using ramification theory, University of Wisconsin at Madison, April 2011.
  • Cohomology of (φ,Γ)-modules and application, Beijing Normal University, China, September 2010.
  • Lecture series: Introduction to p-adic Hodge Theory, Morningside Center, China, Summer 2010.
  • Ramification theory and p-adic differential modules, Northwestern University, May 2010.
  • Slope filtration d'après Kedlaya, University of Chicago, May 2010.
  • Ramification theory and p-adic differential modules, Nottingham University, May 2009.
  • Ramification theory and p-adic differential modules, Columbia University, February 2009.
  • Ramification theory and its application to algebraic geometry, MIT STAGE, October 2008.
  • Ramification theory for local fields with imperfect residue field, MIT STAGE, November 2007.
  • Semistable reduction in p-adic cohomology, MIT STAGE, March 2007.
  • Conductors of Galois representations à la Colmez, MIT STAGE, November 2006.
  • p-adic modular forms (after Katz), MIT STAGE, September 2006.
  • An introduction to algebraic fundamental groups, MIT BAGS, April 2006.
  • p-divisible groups, MIT STAGE, March 2006.

Teaching:

  • Fall 2014, Math 5230 Graduate Algebraic Number Theory, University of Connecticut, Storrs.
  • Spring 2014, Math 232C Graduate Algebraic Number Theory, University of California at Irvine.
  • Winter 2014, Math 232B Graduate Algebraic Number Theory, University of California at Irvine.
  • Fall 2013, Math 232A Graduate Algebraic Number Theory, University of California at Irvine.
  • Spring 2013, Math 121B Linear Algebra, University of California at Irvine.
  • Winter 2013, 25400 Basic Algebra I, and 25500 Basic Algebra II, University of Chicago.
  • Spring 2012, 25500 Basic Algebra II, and 25600 Basic Algebra III, University of Chicago.
  • Fall 2011, 19620 Linear Algebra, University of Chicago.
  • Spring 2011, 25500 Basic Algebra II, and 25600 Basic Algebra II, University of Chicago
  • Winter 2010, 19900 Introduction to Analysis and Linear Algebra, and 25400 Basic Algebra I, University of Chicago.
  • Spring 2010, 16300 Honors Calculus III, University of Chicago.
  • Winter 2009, 16200 Honors Calculus II, and 26200 Point Set Topology, University of Chicago.
  • Fall 2008, Recitation for 18.01 Calculus, MIT.
  • Spring 2007, Recitation for 18.03 Differential Equations, MIT.

Advising Experience:

  • MIT Undergraduate Research Opportunity Program, Fall 2008: Hansheng Diao.
  • MIT Research Science Institute, Summer 2008: Edwards Miles, Sung-hun Song.
  • Co-advising PhD student: Rufei Ren (UC Irvine).
  • UC Irvine Undergraduate Research, Spring 2014: Craig Steinke.

Last update: April 2014