2020, Sep 29 
Slides 
Institute for Advanced Study Postdoc member short talk 
2020, Aug 21 
Slides 
University of Ottawa Quantum Groups, Representation Theory, Superalgebras, and Tensor Categories : an online conference 
2020, July 21 
Notes 
Institute for Advanced Study Basic Notions Seminar in Number Theory 
2020, Apr 30 
Slides Video 
Princeton University and Institute for Advanced Study Joint Number Theory Seminar 
2019, Nov 13  Slides  Yale University Colloquium, Department of Mathematics 
2019, Oct 4 Oct 11 Oct 18 Oct 25 Nov 1 
Lecture notes 
Rutgers University Working group on symmetric functions and applications My seminar series title: Whittaker functions and (non)symmetric polynomials 
2019, Sep 25  Video 
Institute for Advanced Study Postdoc member short talk 
2019, Mar 6  Slides
(Parts 1 & 2) Video 1 Video 2 
Simons Center for Geometry and Physics Twoparts overview lecture in workshop: Automorphic Structures in String Theory 
2018, Dec 18 
Chalmers University of Technology Algebraic Geometry and Number Theory Seminar 

2018, Dec 7 
Rutgers University Lie Groups/Quantum Mathematics Seminar 

2018, Nov 28 
Stanford University Quantum Groups Learning Seminar 

2018, Jun 25 
ETH, Zürich Poster. Automorphic forms on reductive groups and their covers A conference in honour of Solomon Friedberg 

2017, Dec 20 
Chalmers University of Technology Algebraic Geometry and Number Theory Seminar 

2017, Jul 18 
Korea Institute for Advanced Study (KIAS) Four lectures during the program: Arithmetic Geometry and Quantum Field Theory 

Automorphic String AmplitudesAutomorphic forms arise naturally when studying scattering amplitudes in toroidal compactifications of string theory. In this talk, I will summarize the conditions on fourgraviton amplitudes from the literature required by Uduality, supersymmetry and string perturbation theory, which are satisfied by certain Eisenstein series on exceptional Lie groups. Physical information, such as instanton effects, are encoded in their Fourier coefficients on parabolic subgroups, which are, in general, difficult to compute. I will demonstrate a method for evaluating certain Fourier coefficients of interest in string theory. Based on arXiv:1511.04265, arXiv:1412.5625 and work in progress. 

2017, Jan 30  Slides  Oxford UniversityString theory seminar 
2016, Dec 6  Slides  Albert Einstein Institute, PotsdamSeminar 
2016, Nov 15  Slides  ULB, BrusselsHEP seminar 
2016, Nov 3  Slides  DAMTP, CambridgeString Theory Seminar 
2016, Oct 11  Slides  Paris (IPhT, Saclay)Séminaire de matrices, cordes et géométries aléatoires 
2016, Oct 5  Slides  Stanford (SITP)SITP seminar 
Eisenstein series attached to small automorphic representationsIn this talk we study certain Fourier coefficients of Eisenstein series attached to small automorphic representations motivated by open problems in string theory. Whittaker coefficients on the Borel subgroup can be computed using the CasselmanShalika formula and Langlands' constant term formula, but no similar tools are available for Fourier coefficients on other parabolic subgroups. We therefore demonstrate a method to compute parabolic Fourier coefficients of Eisenstein series in terms of known Whittaker coefficients on the Borel and show how they simplify for small automorphic representations. This is joint work with Dmitry Gourevitch, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi. 

2016, Oct 4  Slides  Stanford (math department)Representation theory seminar 
2016, Sep 30  Slides  Rutgers Lie Group/Quantum Mathematics Seminar 
2016, Sep 14  Slides Video 
Simons Center, Stony Brook Program: Automorphic forms, mock modular forms and string theory 
Small automorphic representationsIn this talk we study maximal parabolic Fourier coefficients of automorphic forms in small automorphic representations motivated by string theory. We start with an introduction to how automorphic forms enter in string theory scattering amplitudes, discussing the moduli space of string theory compactified on tori, Uduality, and the differential equations for the automorphic forms that arise from supersymmetry. We see that the scattering amplitudes may be described using certain Eisenstein series in the minimal and nexttominimal representations, and that physical information may be extracted from them by Fourier expansions. For higher rank groups we show how to compute maximal parabolic Fourier coefficients in terms of Whittaker vectors for the minimal and ntm representations for SL(3) and SL(4) using methods from Ginzburg and MillerSahi. We test similar relations for $E_6$, $E_7$ and $E_8$ by comparing the factorization of global (adelic) Whittaker vectors with known local spherical vectors. Based on arXiv:1412.5625 [math.NT] and arXiv:1511.04265 [math.NT] 

2016, Jan 26  Slides  Rutgers Number Theory Seminar 
Instantons and Automorphic RepresentationsThe low energy expansion of fourgraviton scattering amplitudes in string theory on toroidal compactifications is given by automorphic forms on the moduli space attached to certain automorphic representations. These automorphic forms contain all perturbative corrections in the string coupling constant as well as nonperturbative, instanton corrections. Physical information, such as the instanton measure, can be extracted by studying their Fourier coefficients on certain parabolic subgroups of the underlying group G corresponding to taking different limits on the moduli space. Building on recent work by MillerSahi and Ginzburg, we present a method for calculating such Fourier coefficients by associating them with nilpotent orbits which are deeply connected to automorphic representations. We provide evidence that, for the minimal representation related to 1/2 BPS corrections, the above Fourier coefficients are determined by single, Gtranslated, maximally degenerate Whittaker vectors and propose a generalization for 1/4 BPS. Based on arXiv:1412.5625 [math.NT] 

2015, June 22  Poster session  Strings 2015, Bangalore 
2015, June 11  Gongshow  Advanced Strings School 2015, Bangalore 
2015, Mar 17  Albert Einstein Institute, Potsdam Seminar  
2015, Mar 10  Chalmers, Gothenburg Fundamental physics group seminar 