Cotype zeta functions of nilpotent groups. In preparation.

Zeta Functions of Classical Groups and Class Two Nilpotent Groups,  PhD Thesis, (2019). CUNY Academic Works. (PDF, last updated October, 2019).  Section 1.2 and Chapter 3 differ from version here.

Counting subgroups of fixed order in finite abelian groups, with A. Sehgal. 2018, arXiv preprint arXiv:1806.03774. Pulbished in the Journal of Discrete Mathematical Sciences and Cryptography, 24(1), pp.263-276.

Emergent structures in Neural Networks. ANC Journal Club. Jan 25th, 2023. Video. 

Solutions to selected exercises in “Finite Groups: An Introduction by Jean-Pierre Serre." PDF.  (Last update: December, 2019)

All the unique converses from Hecke’s theory of holomorphic modular forms and Dirichlet series. April, 2017. PDF.

The first non-vanishing coefficients of “nice” Dirichlet series. February, 2017. PDF.

Point evaluations of the GLn Eisenstein series. March 2016. PDF.

Notes on nontriviality criteria for the tame Kernel of imaginary quadratic fields. August, 2015. PDF.

The Mordell-Weil Theorem for Elliptic Curves over Q. Pre-PhD Diploma thesis, ICTP, Trieste, 2012. PDF; Talk Slides.

Artinian Rings and Modules. B.Sc. Thesis. Addis Ababa Univesity, 2011. PDF. 

From Summer 2016 to Spring 2019,  I co-organized the Automorphic Forms and L-functions Student Seminar at the Graduate Center, CUNY. 

*Emergent structures in Neural Networks. Video. ANC Journal Club. Jan 25th, 2023. 

*The Algebra Seminar, Binghamton University, Binghamton, NY. August 31st and Sept 4th, 2021.  

*UCI Number Theory Seminar, University of California, Irvine. April 1st, 2021.

*Joint Algebra/Arithmetic seminar, Binghamton University, Binghamton, NY. February 23rd, and March 16th, 2021.

 *Joint Algebra/Arithmetic seminar, Binghamton University, Binghamton, NY.  September 08, 2020 and September 15, 2020.

Zassenhaus Groups and Friends Conference 2020,  Hofstra University Hempstead, NY,  held online, May 29th - 30th and June 5th - 6th, 2020.

*The Algebra Seminar, Binghamton University, Binghamton, NY. February 25, 2019.  

*The Arithmetic Seminar, Binghamton University, Binghamton, NY. February 4 & 11, 2019.  

*The Arithmetic Seminar, Binghamton University, Binghamton, NY. November 5, 2019.

Binghamton University Graduate Conference in Algebra and Topology (BUGCAT), Binghamton, NY. November 2-3, 2019.

*The Arithmetic Seminar, Binghamton University, Binghamton, NY. October 22, 2019. 

*No theory seminar, Binghamton University, Binghamton, NY. October 21, 2019.

*The Algebra Seminar, Binghamton University, Binghamton, NY. October 15, 2019. 

*Fall Eastern Sectional Meeting. Special Session on What's New in Group Theory? Binghamton University, Binghamton, NY. October 12-13, 2019. 

UNCG Summer School in Computational Number Theory and Algebra: Computational Aspects of Buildings, the University of North Carolina at Greensboro, June 24-28, 2019. 

*Analytic and Combinatorial Number Theory: The Legacy of Ramanujan: A conference in honor of Bruce C. Berndt's 80th birthday, at the University of Illinois at Urbana-Champaign: June 6-9, 2019.

*Fifth Annual Graduate Student Conference in Algebra, Geometry, and Topology at Temple University, Philadelphia, PA: June 1-2, 2019

NSF-CBMS Conference: L-functions and Multiplicative Number Theory. A conference featuring a series of ten lectures by K. Soundararajan (Stanford).  University of Mississippi, May 20-24, 2019. 

*Ninth Annual Upstate Number Theory Conference, Cornell University, Ithaca, NY: April 27–28, 2019

*33rd Automorphic Forms Workshop, Duquesne University, Pittsburgh, PA: March 6 - 10, 2019

*Study group in number theory, the Graduate Center, March 1st, 2019

Joint Mathematics Meetings, Baltimore Convention Center, Baltimore, MD: January 16-19, 2019

Representations of Finite and Algebraic Groups, MSRI Summer school, Berkeley, CA, April 9-13, 2018

*Interesting Functions for Arithmetic Groups, GC CUNY, September 14th, 2017

Automorphic Forms and the Langlands Program,  MSRI Summer school, Berkeley, CA, July 24 - August 04, 2017

*Galois Representations of the Absolute Galois Group of Number Fields, GC CUNY, July 13th, 2017

*Hecke's Correspondence for Siegel Modular Forms, GC CUNY,  May 12th, 2017

Abstract: We will discuss Siegel modular forms which are generalizations of elliptic modular forms to higher genus and their properties. We then see K. Imai's generalization of Hecke's correspondence to that between Siegel modular cusp forms of genus two and two variable Dirichlet series with functional equations.

*Hecke's Theory of Holomorphic Modular forms, GC CUNY, April 28th, 2017

Abstract: We will discuss Hecke’s main correspondence theorem between Dirichlet series with functional equations and modular forms of some weight and apply it to show how finding the number of Dirichlet series with a given signature (λ, k, γ) is equivalent to determining the dimension of M_0(λ, k, γ), the space of entire automorphic forms with respect to G(λ) of same signature.  

*Whittaker Models and Automorphic Forms, part II, GC CUNY, March 24th, 2017

Abstract: We will discuss the Whittaker function approach of constructing the standard L-function of an automorphic cuspidal representation and also local functional equation of a local zeta integral and global functional equation of a partial L-function.

*Whittaker Models and Automorphic Forms, part I, GC CUNY, March 17th, 2017

Abstract:We will discuss how the uniqueness of Whittaker models(local multiplicity one theorem) leads to the proof of the multiplicity one theorem and also to the functional equations of the standard L-function of an automorphic cuspidal representation of GL(2).

*Classical Automorphic Forms and Representations, GC CUNY, February 17th, 2017

Abstract: We will define automorphic forms as elements of the space of functions A(Γ\G, χ, ω) and relate this notion of an automorphic form to the classical notions of modular forms and Maass forms. 

*Basic Representation Theory II: Classification of (g,K)-modules for GL(2,R), GC CUNY, November 7th, 2016

Abstract: Continuing the discussion on admissible representations, (g,K)-modules and infinitesimal equivalence, we will prove a complete explicit list of the irreducible admissible (g,K)-modules when g=gl(2,R) and K=SO(2).

*Basic Representation Theory I, GC CUNY, October 24th, 2016

Abstract: In the next two talks, we will discuss section 2.4 on representation theory notions we will use for the study of automorphic forms. This will include smooth vectors, K-finite vectors, admissible representations, (g,K)-modules and infinitesimal equivalence. Although the discussion is for G=GL(n,R), if time permits, we will see how we can generalize each time to the context of an arbitrary reductive group. 

*Basic Lie Theory II(continued from last), GC CUNY, September 19th, 2016

Abstract: The talk will be on Section 2.2 of Bump's Automorphic Forms and Representations. The goal is to discuss the Lie theory notions we need to reinterpret the raising operator, the lowering operator and the Laplace-Beltrami operator as elements in the universal enveloping algebra of the Lie algebra gl(2,R) of GL(2,R). 

*Basic Lie Theory I, GC CUNY, September 12th, 2016

Abstract: The talk will be on Section 2.2 of Bump's Automorphic Forms and Representations. The goal is to discuss the Lie theory notions we need to reinterpret the raising operator, the lowering operator and the Laplace-Beltrami operator as elements in the universal enveloping algebra of the Lie algebra gl(2,R) of GL(2,R). 

*Maass Forms, July 15th, GC CUNY, 2016

Abstract: After introducing Maass forms of weight zero as in section 1.9, we will show that the non-holomorphic Eisenstein series is a Maass form and define an L-series associated to the forms so we can prove analytic continuation and find a functional equation for them. The construction of a Maass cusp form on \Gamma_0(D) will be best understood after seeing a discussion of Langland's functionality or base change.

*Hecke Operators, GC CUNY, June 24th, 2016

Abstract: After a brief overview of of congruence modular forms, congruence cusp forms, the Peterson inner product, Hecke operators and the Hecke algebra on the space of modular forms on SL(2,Z), we will show how the commutativity of the Hecke algebra leads to an Euler product for L-functions arising from modular forms. Exercises will be mentioned in passing.

*Group cohomology, Prof. L. Szpiro’s course at The Graduate Center, CUNY, December, 2015

Abstract: After motivating the topic, I will define the cohomology of groups in two ways: one using co-chains and another using a projective resolution and then prove their equivalence. Then if there is time I will consider computing lower cohomology groups when the group is finite and also discuss various interpretations of the lower dimensional group cohomologies. 

*Generators and Relations of K2OF, Oral exam talk, The Graduate Center, CUNY. September 2015. Talk Outline (Oral exam committee: Professors Lucien  Szpiro, Abhijit Champanerkar and Gautam Chinta).

*Representations of integers as sums of squares and algebraic K-Theory, informal Graduate Student Number Theory Seminar, CUNY, The Graduate Center. May 2015.

Abstract:  I plan to go over the following topics, mainly from Rosenberg's "Algebraic K-theory and Its applications" and Milnor's "Introduction to Algebraic K-theory":  K0 and K1 of rings and categories: examples and applications; Relative K0, relative K1 and Milnor's K2: examples and applications. 

*Grothendieck Topologies, Prof. L. Szpiro’s course, at The GC, CUNY. March 2015. PDF Abstract.

*Towards a construction of the sheaf of algebraic functions on Spec A, Prof. L. Szpiro’s course at The GC, CUNY. December 2014. PDF notes.