Dr. Julius M. Basilla is recognized of his outstanding work in the area of number theory, which includes development of algorithms for determining the solution of certain Diophantine equations and the development of algorithms that led to understanding further the structure of the ideal class group of quadratic fields. His contributions to class field and the theory of elliptic curves and their applications to cryptography bring these difficult areas within the reach of graduate students and young mathematicians studying these cutting-edge research topics

**Sex: **Male

**Education**

- Sophia University, Chiyoda-ku, Tokyo, Japan, Doctor of Philosophy in Mahematics, 2005 Mr
- Japan Languauge Center, Tokyo University of Foreign Studies, Japan, Certificate in Japanese Language, 2001 S
- University of the Philippines Diliman, Quezon City, Master Science in Mathematics, 2002 Ap
- University of the Philippines Diliman, Quezon City, Bachelor of Science in Mathematics, 1997 Ap

**Field of Specialization**

Mathematics

**Researches**

Basilla, J.M., (2004 Mr) On the solutions of x2-dy2 = + - m

Proceeding of Japan Academy Volume 80 A, No. 5

Basilla, J.M., (2005) On the Sylow 2-subgroup of the ideal class group of quadratic fields and related Diophantine equations

Dissertation, Sophia University, Tokyo, Japan

Basilla, J.M., (1997) A radially and latitudinally evolving newtonian Universe

Undergraduate Thesis, University of the Philippines, Quezon City

Basilla, J.M., Nagata, K., (2004 My) The integral solutions of x2 + dy2=m(0

Personal Computer Literacy Volume 25, No. 5

Basilla, J.M., (2004 D) The quadratic fields with discriminant divisible by exactly three primes and with narrow class number divisible by 8

Proceeding of Japan Academy Volume 80 A, No. 10

Basilla, J.M., Wada, H., (2004 D) On efficient computation of the 2-parts of ideal class groups of quadratic fields

Proceedingof Japan Academy Volume 80 A , No. 10

Basilla, J.M., Wada, H., (2005) On the solutions of x2-dy2 = + - m

Proceeding of Japan Academy Volume 81 A, No. 8

Basilla, J.M., (2002) On the Discrete Logarithm Problems on Elliptic Curves and the Xedni Calculus

Master's Thesis, University of the Philippines, Quezon City

**Papers Presented**

- A geometric proof of algorithms for solving the diophantine equation x2 +dy2 = m , International Congress of Mathematician 2006, Madrid, Spain
- The quadratic fields with discriminant divisible by exactly three primes and with `narrow' class number divisible by 8, 2007 Annual Convention of the Mathematical Society of the Philippines, Boho1 Tropics Resort, Tagbilaran City
- The quadratic fields with discriminant divisible by exactly three primes and with narrow class number divisible by 8, 7th Sino-Philippines Symposium in Mathematics, MMLDC, Antipolo City
- A real-coded genetic algorithm solution to Fiber-Bragg Grating Parameter Synthesis, 7th Sino Philippines Symposium in Mathematics, MMLDC, Antipolo City
- Number representations and applications, 2007 Annual Convention of the Mathematical Society of the Philippines, Bohol Tropics Resort, Tagbilaran City
- On the solutions of the diophantine equation x2-d2 = + - m , Mathematical Society of the Philippines, Annual Convention 2006, Ateneo de Davao, Davao City Philippines
- Computing the 2-part of the ideal class group of a quadratic field , 6th International Symposium on algebra and Computation, Tokyo Metropolitan University Tokyo, Japan
- On Cornacchia's algorithm for solving the diophantine equation x2 + dy2 = m, 6th Taiwan-Philippines Symposium on Analysis, National Sun-Pat Sen University, Kaohsiung, Taiwan,
- On the Integral Solutions of x2 + dy2=m, 2005 Mathematical Society of the Philippines Annual Convention, Ateneo de Naga, Naga, City Philippines
- On computing the 2-part of the ideal class group of a quadratic field, Personal Computer Users Association Convention, Tougai University, Slrinagawa-Ku Tokyo, Japan
- On the Sylow 2-subgroups of the ideal class group of quadratic fields and related Diophantine equations, 39th Workshop on Commutative Algebra, Department of Mathematics, Sophia University, Tokyo, Japan
- A new Algorithm for computing the 2 part of the ideal class group of quadratic fields, Number Theoretic Algorithms and their Application , 13th Convention of Japan Association of Number Theorist, Security University, Yokohama, Japan
- A simple proof of the validity of Cornacchia's algorithm for solving the diophantine equation x2+dy2 = m, Number Theoretic Algorithms and their Application, 11th Convention of Number Theorist, Tokyo University Komaba Campus, Tokyo, Japan
- A new Algorithm for computing the 2 part of the ideal class group of quadratic fields, Number Theoretic Algorithms and their Application , 11th Convention of Number Theorist, Tokyo University, Komaba Campus, Tokyo, Japan
- The quadratic fields with discriminant divisible by exactly two primes and with narrow class number divisible by 8 , Colloquium in Gakushuin University, Tokyo, Japan
- On the AKS primality testing, Colloquium in Waseda University, Japan
- On the Elliptic curve discrete logarith problem and Xedni Calculus, Asian Math Conference
- An invitation to cryptography, Mathematical Society of the Philippines Annual Convention, St. Louis University, Baguio City
- The quadratic fields with discriminant divisible by exactly two primes and with narrow class number divisible by 8 - , 2007 Annual Convention of the Mathematical Society of the Philippines, Bohol Tropics Resort, Tagbilaran City
- On the 2-part of the ideal class group of quadratic fields and related diophantine equations, Mathematical Society of Japan Autumn Convention, Hokkaido University, Sapporo, Japan
- An algorithm for solving x2 + dy2 = m , 37th Workshop on Commutative Algebra, Department of Mathematics, Sophia University, Tokyo, Japan

**Awards**

- CIMPA Grant , Hanoi, Vietnam , 2005 D 26-2006 Ja 6
- Recipient, Travel Grant for Young Mathematicians, International Mathematician Union, 2006
- Du Pont Talent Search for Young Scientist Award, NAST, 2006
- International Publication Award on the paper The quadratic fields with discriminant.., UP, 2005
- International Publication Award for the paper On the solution of x2 - dyZ = ±rn.., University of the Philippines, 2005
- UPIP Faculty Grant Award , , 2005 Jl 1- 2006Je 30
- Monbukagakusho Scholar, Japanese Government, 2001 Ap-2005 Mr
- DOST-SEI Undergraduate Scholarship, , 1993 Je-1997 Ap