## Vijaykumar Singh

PhD student, Claude Shannon Institute,

School of Mathematical Sciences,

University College Dublin

PhD supervisor: Gary McGuire

Email: Vijaykumar dot Singh at ucdconnect dot ie

My areas of interest Arithmetic Geometry (Dessins D'Enfant) and Algebraic Geometry : Isogeny classes of abelian varieties over finite fields, Number theory, coding theory and Cryptography.

### Curriculum Vitae

My CV

### Publications

Vijaykumar Singh,Gary McGuire, "The Intersection of Two Fermat Hyper-surfaces in P3 via Computation of Quotient Curves", submitted. available here

Vijaykumar Singh, Alexey Zaytsev, Gary McGuire, "On The Characteristic Polynomials of Frobenius of Supersingular Abelian Varieties Of Dimension up
to 7 over Finite Fields", accepted at the conference YACC 2010. available here

Safia Haloui, Vijaykumar Singh, "The characteristic polynomials of abelian varieties of dimensions 4 over finite fields", submitted. arXiv .

Vijaykumar Singh "The Grothendieck Theory of Dessins of d'Enfants" Chennai Mathematical Institute, 30 p. available here

### Work In Progress

Vijaykumar Singh, Alexey Zaytsev, "On Zeta Function of Towers on Function Fields".

### Talks

Child's Drawing, University College Dublin, March 2011

Explicit Honda-Tate Theorem for Supersingular Abelian varieties, University College Dublin, Nov 2010.

On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields, Yet Another Conference on Cryptography, Porquerolles, October 2010. available here

Supersingular Weil-$q$ numbers, Institut de mathematiques de Luminy, May 2010.

$L$-series, University College Dublin, March 2010.

Frobenius of Supersingular Abelian Varieties of dimension $1,\dots 7$, Feb 2010.

Intersection of Fermat Hypersurfaces in $\mathbb{P_{\mathbb{F}_p}}^{3}$ using quotient curves,University College Dublin, Nov 2009.

Duering's Lifting Theorem, Claude Shannon Institute, March 2009.

Algebraic Geometry in Error Correcting Codes, Claude Shannon Institute, Jan 2008.

Complex Multiplication for Elliptic Curves, Claude Shannon Institute, April 2007.

McEliece Cryptosystems, SETS, Feb 2007.

Grothendieck Theory of Dessins d'Enfants, Institute Of Mathematical Sciences, June 2006.

Whitney Embedding theorem, Chennai Mathematical Institute, December 2005.