Research

My papers are also listed on arXiv and Google Scholar.

Publications and Preprints

10. Intersection complexes and unramified L-factors [pdf] [journal] [arXiv]
    Joint with Yiannis Sakellaridis
    J. Amer. Math. Soc., electronically published on October 5, 2021, 112 pp. (to appear in print).
    
    • Here are some notes, slides (RT, NT) and videos from talks I gave.
      
      • 80 minute video, slides for talk at Columbia Automorphic Forms Seminar, October 9, 2020.
        
      • 90 minute video, notes for talk at Geometric Langlands Office Hours, October 14, 2020.
        
      • 60 minute video for talk at NUS Representation Theory and Number Theory Seminar, October 22, 2020.
        
11. Smooth non-admissible asymptotics for \(SL_2(\mathbb R)\) [pdf]
    Preliminary version (2020) 12 pp.
    
12. On an invariant bilinear form on the space of automorphic forms via asymptotics [pdf] [journal] [arXiv]
    Duke Math. J. 167 (16), 2965-3057 (2018).
    • Here is a video of a talk I gave.
13. On the reductive monoid associated to a parabolic subgroup [pdf] [journal] [arXiv]
    J. Lie Theory 27 (3), 637-655 (2017).
    
14. On a strange invariant bilinear form on the space of automorphic forms [pdf] [journal] [arXiv]
    Joint with Vladimir Drinfeld
    Selecta Math. (N.S.) 22 (4), 1825-1880 (2016).
    
15. Radon inversion formulas over local fields [pdf] [journal] [arXiv]
    Math. Res. Lett. 23 (2), 535–561 (2016).
    
16. A new Fourier transform [pdf] [journal] [arXiv]
    Math. Res. Lett. 22 (5), 1541–1562 (2015).
    

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Undergraduate work:

1. Thin Lehman matrices and their graphs, Electronic Journal of Combinatorics 17 (2010), R165.
   
2. A new infinite family of minimally nonideal matrices, Journal of Combinatorial Theory, Series A 118 (2011), 365-372.
   
3. The zero-divisor graph associated to a semigroup (with L. DeMeyer, L. Greve, and A. Sabbaghi), Communications in Algebra 38 (2010), 3370-3391.