**April 2017**

**Numerical Computations with the Selberg trace formula **

(Seminar, PMI POSTECH, Pohang, Korea)

**Numerical Computations with the Selberg trace formula **

(Seminar, KAIST, Daejeon, Korea)

**January 2017**

**Numerical Computations with the Selberg trace formula **

(JMM MAA Invited paper session on L-functions and other animals, Atlanta, GA, USA)

**November 2016**

**Effective equidistribution of rational points on expanding horospheres**

(Oxford Number Theory Seminar, University of Oxford, UK)

**June 2016 **

**Effective equidistribution of primitive rational points on expanding horospheres**

(London Number Theory Seminar, King’s College, UK)

**March 2016**

**Effective equidistribution of primitive rational points on expanding horospheres**

(British Mathematical Colloquium, University of Bristol, UK)

**Abstract:** link

**February 2016**

**The Selberg trace formula as a Dirichlet series**

(London Number Theory Seminar, UCL, UK)

**January 2016**

**The Selberg trace formula as a Dirichlet series**

**(POSTECH 2016: 2016 Korea-Japan Joint Number Theory Seminar, POSTECH, South Korea)**

**The Selberg trace formula as a Dirichlet series and applications**

(Number Theory and Function Fields at the Crossroads 2016, University of Exeter, UK)

**November 2015**

**The Selberg trace formula as a Dirichlet series**

(AMS Fall Eastern Sectional Meeting, Rutgers University, USA)

**Abstract:** link

**GL(3) Maass forms and the Kuznetsov trace formula**

(Computational Aspects of L-functions, ICERM, USA)

**Abstract:** In this talk, we describe a method to determine whether there exists a genuine Maass forms for SL(3, \Z) with Casimir eigenvalues in a small neighborhood of a given pair of numbers, using the Kuznetsov trace formula. This is an ongoing joint project with Andrew Booker.

**October 2015**

**The Selberg trace formula as a Dirichlet series**

(Linfoot seminar, University of Bristol, Bristol, UK)

**Abstract:** We explore an idea of Conrey and Li of expressing the Selberg trace formula as a Dirichlet series. We describe two applications, including an interpretation of the Selberg eigenvalue conjecture in terms of quadratic twists of certain Dirichlet series, and a formula for an arithmetically weighted sum of the complete symmetric square L-functions associated to cuspidal Maass newforms of squarefree level N>1. This is a joint work with Andrew Booker.

**July 2015**

**Spectral methods of automorphic forms on SL(2) **(five lectures)

(Morningside Center of Mathematics, 2015 Workshop on Number Theory 16 July – 25 July)

**Abstract:** The spectral theory of non-holomorphic automorphic forms for the Poincare upper half plane began with Maass and Selberg. Maass forms were first studied by Maass in 1949. Selberg introduced his trace formula as a tool to prove the existence of infinitely many even Maass forms, in 1956. The spectral theory of automorphic forms continues to grow extensively. Selberg trace formula and Bruggeman-Kuznetsov trace formula have been studied and then generalized to the higher rank groups. They have played important roles in analytic number theory to understand automorphic forms and L-functions, and also in other fields.

In these lecture, we study a portion of the spectral methods of automorphic forms on SL(2), particularly the Selberg trace formula, Bruggeman-Kuznetsov trace formula and their applications to L-functions.

**May 2015**

**The Selberg trace formula as a Dirichlet series**

(POSTECH, PMI Number Theory Seminar, 11 May)

**December 2014**

**Shifted Multiple Dirichlet Series and moments of Rankin-Selberg -functions**

(NCTS, NCTS-PMI Joint Workshop in Number theory, 23 Dec)

**Abstract:** In this talk, we develop certain aspects of the theory of shifted multiple Dirichlet series and study their meromorphic continuations. These continuations are used to obtain explicit spectral first and second moment formulas for Rankin-Selberg L-functions of automorphic forms.

This is a joint work with Jeff Hoffstein.

**Shifted Multiple Dirichlet Series and moments of Rankin-Selberg -functions**

(Banff International Research Station, Families of automorphic forms and trace formula, 4 Dec)

**November 2014**

**Second moments of -functions and shifted Dirichlet series **

(University of Bristol, Linfoot seminar, 19 Nov)