(click on each title to show descriptions of the research)
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Beilinson's Conjectures
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Beilinson's conjectures are deep conjectures relating higher regulators of pure motives to non-critical values of motivic
L-functions. Instead of working on the general conjectures, I mainly work on examples of Beilinson's conjectures for automorphic motives using
the tools from motives, Hodge theory and automorphic representations
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1. In my Ph.D. thesis, I proved an identity relating the motivic classes constructed in [LSZ] and non-critical values of the motivic L-functions associated to
cuspidal automorphic representations of GU(2,1).
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Kudla Program
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Inspired by the ideas from theta correspondence, Kudla and his collaborators built up the theory of geometric theta series and arithmetic theta series and used those theta series to construct
cohomology classes (Kudla-Millson Theory) and algebraic cycles (arithmetic theta lifting). I mainly work on the motivic aspect of the Kudla program, with the aim of applying it to Beilinson's conjectures.
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Relative Langlands Program
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The relative Langlands program aims to explore the relations between period integrals, special values of automorphic L-functions and Langlands functoriality. I mainly
work on regularization of period integrals and its applications.
1. I proved a formula relating regularized periods of cuspidal Eisenstein series to cuspidal intertwining periods for
linear models. Using this formula, I proved
a formula relating regularized periods of discrete Eisenstein series to discrete intertwining periods for GL2n/GLn ✕ GLn.
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