Παρασκευή, 27 Ιουλίου 2012

Projects

- Algorithmic implementations of Endomorphism rings of supersingular Drinfeld Modules. Mainly written reports. (August 2005)
- Algorithmic implementations of Brauer invariants. Mainly written reports. (September 2005)
- Junior member of FP6 Research and Training Network "Galois Theory and Explicit Methods" (GTEM). Written reports and implementations in Magma and SAGE. (October 2006 to October 2010)- Toolkit for security tests for Elliptic Curve Cryptography, written both in C++ (using NTL) and Magma. Part of Brainpool for EU passport standards. (December 2006)
- Website construction in PHP. Created http://www.tzimakos.gr in PHP. (January 1998 to present)
- AutoWikiBrowser, Wikipedia specialised browser that uses .NET. Developer. Contributions in C# and Visual Basic for plugins (October 2007 to present)

Δευτέρα, 23 Ιουλίου 2012

Undergraduate Courses


Here is a list of the courses I have attended as an undergraduate student in the University of Crete (1997-2003). The maximum grade is ten (10), the passing grade is five (5) and the scaling is the following: 8.5-10 excellent, 6.5-8.49 very good, 5-6.49 good. The grade point average (GPA) of graduation is computed according to the Ministerial Decree F-141/B3/2166 (FEK 308/18-6-87) for all Greek Universities.
 
Computer Programming
10
Algebra I
9
English I
7.5
English II
7.5
English III
7.5
Calculus I
7.5
Introduction to Set Theory
7.5
Linear Algebra I
7
English IV
6.5
Probability Theory
6
Introduction to Analysis II
6
Introduction to Analysis I
5
Calculus II
5
Calculus III
5
Analytical Geometry - Complex Numbers
5
Physics I
5
  
Theory of Recursive Functions
10
Number Theory
9
Special Topics: Computation Theory
9
Mathematics Education
7
Discrete Mathematics
5

Topics in Analysis: The Problem Seminar
9
Ordinary Differential Equations
7.5
  
Topics in Algebra: Cryptology
10
Rings and Modules Theory
10
Topics in Algebra: Symbolic Computation
9.5
Topics in Algebra: Applied Algebra
8.5
Topics in Algebra: Quadratic Number Fields
8
Linear Algebra II
7.5
Group Theory
7.5
Fields Theory
7.5
Topics in Algebra: Linear Algebra & Modules
6
  
Topics in Applied Mathematics: Algorithms and Complexity Theory
9.5
Topics in Probability and Statistics: Descriptive Statistics
8
Numerical Analysis
6.5
  
Introduction to Pedagogy
8
School Pedagogy
8
Supportive and Compensative Education
6.5
  
Algebra I (Graduate)
9
Numerical Analysis (Graduate)
8
Algebraic Geometry (Graduate)
7
Coding (Graduate)
7
Functional Analysis (Graduate)
6
  
On-job training in Education
8.5
  
Diploma Thesis
9

Teaching Experience (short version)


As undergraduate and graduate student at the Univ. of Crete I worked as an assistant to the following courses.

  • 2 semesters Algebra I
  • 1 semester Linear Algebra I
  • 1 semester Introduction to Computing
  • 1 semester Applied Algebra
  • 2 semesters Number Theory
  • 1 semester Rings and Modules Theory
  • 1 semester Group Theory
  • 2 semesters Cryptology
  • 1 semester Symbolic Computations


    During my phD I assisted the following courses:
  • 1 semester Analysis II at the University of Duisburg-Essen
  • 2 semesters Algebra I at the Carl von Ossietzky University of Oldenburg
  • 1 semester Algorithmic Number Theory at the Carl von Ossietzky University of Oldenburg
  • Talks


    2011

    Semiautomated editing in Wikipedia: The AutoWikiBrowser case (in English, 18 slides)
    (abstract missing)
    DLP: From RSA to ECDLP and HCDLP (in German and English, 26 slides)
    We discuss the difficulty of the discrete logarithm problem in various finite fields. We also examine various attacks on ECDLP and focus on the isogeny attack.
    2009
    The discrete logarithm problem on isogenous hyperelliptic curves of genus 2 (in English, 53 slides)
    In 2005, Jao, Miller, and Venkatesan proved that the DLP of elliptic curves with the same endomorhism ring is random reducible under the GRH. In this talk, we discuss a possible generalization of this result to hyperelliptic curves of genus 2 (and 3) defined over a finite field and show the difficulties involved. First, we explain the role of the endomorphism rings of the Jacobian and the polarization. Following the work of Jao, Miller and Venkatesan, we construct isogeny graphs for genus 2 curves. Specifically, we discuss the connection between isogenies and ideal classes in the Jacobian of these curves. This project is research in progress and we describe the current status of this research.
    The DLP on Curves with the same endomorphism ring: The genus 2 case (in English and partially in German, 49 slides)
    We try to extend the result we presented in our last talk for higher genus curves. We give some background on the arithmetic of curves of high genus and discuss the discrete logarithm problem (DLP) in the divisor class group for curves over finite fields with Jacobian varieties having the same ring of endomorphisms. We strict ourselves to the genus 2 case with Jacobian of CM type and we present the work we have done so far. Finally, we explain which phenomena can occur for curves of genus 3.
    The DLP on Curves with the same endomorphism ring: The genus 1 case (in English, 48 slides)
    We consider elliptic curves with the same order over a finite filed and the same endomorphism ring. We ask whether the discrete logarithm problem has the same complexity. We present a result of Jao, Miller and Venkatesan who proved that the answer to our question is positive  under Generalised Riemann Hypothesis. Possible generalisations on curves of higher genus will be discussed in a second talk.
    The DLP on Elliptic and Hyperelliptic Curves with the same endomorphism ring (in English, 39 slides)
    We ask whether the discrete logarithm problem (DLP) in the divisor class group has the same complexity for all curves over finite fields with Jacobian varieties having the same ring of endomorphisms. We present a result of Jao, Miller and Venkatesan who proved that the answer to our question is positive for elliptic curves. We try to use the same methods to extend the result to the genus 2 case in the case that the Jacobian is of CM type and we present the work we have done so far. Finally, we explain which phenomena can occur for curves of genus 3.
    2008
    Iwasawa's theorem (in English, 15 pages)
    We prove the Iwasava's Theorem, which describes the behaviour of the class number in an extension of a finite field.
    [dvi] [ps] [pdf]
    Arithmetic of Quaternion Algebras: Orders and Ideals (in English, 17 pages)
    The basics on the arithmetic on quaternion algebras is introduced: (maximal) orders, (principal) ideals, (reduced) norm/discriminant, ideal classes, etc.
    [dvi] [ps] [pdf]
    The DLP on Elliptic Curves with the same order (in English, 20 pages)
    We ask whether the discrete logarithm problem (DLP) has the same difficulty for all curves with the same order over a finite field. We present the result of Jao, Miller and Venkatesan who proved that the answer to our question is positive if you limit ourselves to curves with the same endomorphism ring.
    [ps] [pdf]
    2007
    The Tensor Product Theorem (in English, 11 pages)
    The Tensor Product Theorem from Flath asserts that if A is the adele ring of a global field F and G is a reductive algebraic group over F, then G(A) decomposes into a "restricted tensor product" of representations of the groups G(Fυ). We give a proof of the theorem.
    [dvi] [ps] [pdf]
    2006
    Modular forms of weight 1 (in English, 22 pages)
    We study modular forms and Galois representations over finite and fields and over the complex numbers. We give the proof of an important theorem from Serre and Deligne that in every modular form of weight 1 we can attach a linear representation. This representation is unique up to isomorphism.
    [dvi] [ps] [pdf]
    2004
    Primes of the form x2 + ny2 (in English, 24 pages)
    We study ring class fields of orders in imaginary quadratic fields to determine which primes are of the form x2 + ny2, where x, y integers, for arbitrary n. We give certain examples how our result works in practice.
    [dvi] [ps] [pdf]
    Optimal linear codes over GF(4) (in Greek, 18 pages)
    A central problem in coding theory is that of finding the smallest length for which there exists a linear code of dimension k and minimum distance d, over a filed of q elements. We consider here the problem for quaternary codes (q = 4), solving the problem for k < 5 for all values of d.
    [doc] [ps] [pdf]
    2003
    Primality test (Algorithms and Complexity) (in Greek, 26 pages)
    We consider the primality problem, to decide whether a number is prime or composite. In this survey we show that PRIMES is in coNP and in NP. Then we try a probabilistic approach and we show that PRIMES is in coRP and in ZPP. Finally we present one of the most significant results of the last years: that PRIMES is in P.
    Last update: Aug 31, 2005
    [doc] [mdi] [pdf]
    Smooth numbers and the quadratic sieve (in Greek, 12 pages)
    With the help of Analytic Number Theory we consider the problem of optimizing the bound used in the quadratic sieve to factorise numbers.
    [doc] [ps] [pdf]
    The main linear coding theory problem (in Greek, 27 pages)
    Central problem in coding theory is that of constructing optimal codes for a variable (length, dimension, minimum distance), over a field of q elements, while keeping the other two constant. Here we present one version of the problem, with the help of Finite Geometries, and all the known results until now.
    Last update: Jan 14, 2004
    [doc] [ps] [pdf]
    2002
    A lecture on Groebner bases (in Greek, 12 pages)
    We study the methods of the Groebner bases in order to solve problems concerning polynomial ideals with algorithmic or computable methods.
    [doc] [ps] [pdf] [html]

    Conferences/Summer Schools


    20114-7/8Wikimania 2011HaifaIsrael
    201129/4Intercity Number Theory SeminarRijksuniversiteit GroningenThe Netherlands
    201018-19/11North German Algebraic Geometry Seminar (NoGAGS)OldenburgGermany
    201018-22/10Workshop on Elliptic Curve Computation (ECC 2010)Microsoft Research in Redmond, WAUSA
    201017-18/6North German Algebraic Geometry Seminar (NoGAGS)HannoverGermany
    201017-21/5GTEM - Workshop on Computational Number Theory and Arithmetic GeometryLeuven-HeverleeBelgium
    200913/11Intercity Number Theory SeminarRijksuniversiteit GroningenThe Netherlands
    200919-20/11North German Algebraic Geometry Seminar (NoGAGS)BerlinGermany
    200911-12/9Workshop on Factoring Large IntegersBochumGermany
    200924-26/813th Workshop on Elliptic Curve Cryptography (ECC 2009)CalgaryCanada
    200919-22/8Summer school on Elliptic Curve CryptographyCalgaryCanada
    20099/7Festkolloquium und Oberseminar zu Ehren von  Prof. Dr. Dr. h.c. Gerhard FreyIEM, University of Duisburg-Essen, EssenGermany
    20098/5Intercity Number Theory SeminarRijksuniversiteit GroningenThe Netherlands
    20094-6/5Workshop on Pairings in Arithmetic Geometry and CryptographyIEM, University of Duisburg-Essen, EssenGermany
    200822-24/912th Workshop on Elliptic Curve Cryptography (ECC 2008)UtrechtThe Netherlands
    200827/7-5/8German-Israel Minerva Summer School 2008: Arithmetic Geometry and Public Key CryptographyTel AvivIsrael
    200822-23/4Workshop on Factoring Large Numbers, Discrete Logarithms and Cryptanalytical HardwareIEM, University of Duisburg-Essen, EssenGermany
    200822-23/1Workshop on Arithmetic GeometryIEM, University of Duisburg-Essen, EssenGermany
    20075-7/911th Workshop on Elliptic Curve Cryptography (ECC 2007)DublinIreland
    20073-4/9Tutorial on Elliptic and Hyperelliptic Curve Cryptography 2007DublinIreland
    200519-21/99th Workshop on Elliptic Curve Cryptography (ECC 2005)CopenhagenDenmark
    200512-16/9FICS-Summer School on "Elliptic Curves in Cryptography"CopenhagenDenmark
    200523-29/7Number Fields and Curves over Finite FieldsAnogia Academic Village, CreteGreece
    200530/5-3/6Anogia Algorithmica '05Anogia Academic Village, CreteGreece
    200420-22/98th Workshop on Elliptic Curve Cryptography (ECC 2004)BochumGermany
    200413-17/9Summer School on "Elliptic Curves in Cryptography"BochumGermany
    200408-10/7From Arithmetic to Cryptology, Conference on the occasion of Gerhard Frey's 60th birthdayUniversity of Duisburg-Essen, Essen CampusGermany
    200318-25/2, 10-13/6Lectures on Cryptography by G. FreyUniversity of Crete, HeraklionGreece
    200320-27/8Lectures on Cryptography by R.A. MollinUniversity of Crete, HeraklionGreece
    200215-27/7Summer School in Mathematics 2002HeraklionGreece
    200117-22/73rd Panhellenic Logic SymposiumAnogia Academic Village, CreteGreece

    Τρίτη, 10 Ιουλίου 2012

    Wikimania Takes Manhattan

     Wikimania Takes Manhattan was a special pre-Wikimania 2012 weekend in New York City, organized by Wikimedia NYC as a welcome for international visitors eager to experience the Big Apple and self-proclaimed "Capital of the World".

    Activities took place from July 4th (Independence Day) to the morning of Monday July 9.