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:
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Slopes of modular forms.
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Special fibers of Shimura varieties.
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p-adic automorphic forms.
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p-adic Hodge theory and (φ,Γ)-modules.
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Iwasawa theory for non-ordinary modular forms.
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Theory of nonarchimedean differential modules and its application to ramification theory.
Employment:
- 2009.9-2013.2 Dickson Instructor, University of Chicago.
- 2013.3-2014.6 Assistant Professor, University of California at Irvine.
- 2014.8-present Assistant Professor, University of Connecticut at Storrs.
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:
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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.
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Slopes of the eigencurve
over boundary disks,
University of Chicago, February 2014.
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Slopes of the eigencurve
over boundary disks,
Northwestern University, February 2014.
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Supersingular loci and Tate conjecture for some Shimura varieties mod p, M.I.T., February 2014.
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Galois representations and torsion in the cohomology of Hilbert
modular varieties, Boston University, September 2013.
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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