ECC2016 Computational Algebraic Number Theory School
This school
Ravzan Barbulescu
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Omer Kucuksakalli
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Université Pierre et Marie Curie, Laboratoire IMJ-PRG, Paris, France |
Middle East Technical University (METU), Ankara, Turkey |
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Maike Massierer
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Benjamin Smith
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University of New South Wales (UNSW), Sydney, Australia |
Équipe-Projet GRACE, INRIA Saclay–Île-de-France and Laboratoire d'informatique (LIX), École polytechnique, Paris, France |
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Peter Stevenhagen
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Osmanbey Uzunkol
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Leiden University, Leiden, Netherlands |
Mathematical and Computational Sciences, Tubitak, Gebze, Turkey |
Date |
Time |
Talk/Event |
Media |
Sept 1 |
09:00 - 09:45 |
Peter Stevenhagen, "Overview - The history of Algebraic Number Theory" |
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09:45 - 10:00 |
Break |
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10:00 - 10:45 |
Razvan Barbulescu, "Overview - Algebraic Number Theory in Cryptography" |
[SLIDES] | |
10:45 - 11:00 |
Coffee/Tea Break |
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11:00 - 11:45 |
Omer Kucuksakalli, Part I: "Rings and fields, field extensions, modules, free abelian groups, algebraic numbers, conjugates and discriminants, algebraic integers, integral bases, norms and traces, ring of integers." |
[SLIDES] | |
11:45 - 12:00 |
Break |
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12:00 - 12:45 |
Omer Kucuksakalli, Part II: "Rings and fields, field extensions, modules, free abelian groups, algebraic numbers, conjugates and discriminants, algebraic integers, integral bases, norms and traces, ring of integers." |
[SLIDES] | |
12:45 - 14:00 |
Lunch |
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14:00 - 14:45 |
Osmanbey Uzunkol, Part I: "Examples of number fields: quadratic fields, cubic fields, cyclotomic fields. Prime ideal decomposition. Class group. Generalization to arbitrary orders." |
[SLIDES] | |
14:45 - 15:00 |
Break |
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15:00 - 15:45 |
Osmanbey Uzunkol, Part II: "Examples of number fields: quadratic fields, cubic fields, cyclotomic fields. Prime ideal decomposition. Class group. Generalization to arbitrary orders." |
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15:45 - 16:00 |
Coffee/Tea Break |
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16:00 - 17:45 |
Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106" |
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Sept 2 |
09:00 - 09:45 |
Peter Stevenhagen, Part I: "Finiteness of class group and Dirichlet's unit theorem" |
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09:45 - 10:00 |
Break |
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10:00 - 10:45 |
Peter Stevenhagen, Part II: "Finiteness of class group and Dirichlet's unit theorem" |
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10:45 - 11:00 |
Coffee/Tea Break |
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11:00 - 11:45 |
Razvan Barbulescu, "The computation of class groups and units" |
[SLIDES] | |
11:45 - 12:00 |
Break |
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12:00 - 12:45 |
Peter Stevenhagen, "Quadratic orders" |
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12:45 - 14:00 |
Lunch |
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14:00 - 15:45 |
Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106" |
[FILES] | |
15:45 - 16:00 |
Coffee/Tea Break |
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16:00 - 20:00 |
Social Event - Downtown City Tour |
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Sept 3 |
09:00 - 09:45 |
Peter Stevenhagen, Part I: "Class field theory; the rational and imaginary quadratic base fields. Complex multiplication" |
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09:45 - 10:00 |
Break |
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10:00 - 10:45 |
Peter Stevenhagen, Part II: "Class field theory; the rational and imaginary quadratic base fields. Complex multiplication" |
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10:45 - 11:00 |
Coffee/Tea Break |
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11:00 - 11:45 |
Osmanbey Uzunkol, Part I: "Generating various class fields by modular functions" |
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11:45 - 12:00 |
Break |
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12:00 - 12:45 |
Osmanbey Uzunkol, Part II: "Generating various class fields by modular functions" |
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12:45 - 14:00 |
Lunch |
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14:00 - 14:45 |
Benjamin Smith, Part I: "Constructing elliptic curves over finite fields with "known" Frobenius" |
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14:45 - 15:00 |
Break |
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15:00 - 15:45 |
Benjamin Smith, Part II: "Constructing elliptic curves over finite fields with "known" Frobenius" |
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15:45 - 16:00 |
Coffee/Tea Break |
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16:00 - 17:45 |
Maike Massierer and Omer Kucuksakalli and Razvan Barbulescu, "Computer Algebra Lab Session @ Room F106" |
[FILES] | |
Sept 4 |
09:00 - 09:45 |
Benjamin Smith, Part I: "Point counting for elliptic curves over finite fields" |
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09:45 - 10:00 |
Break |
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10:00 - 10:45 |
Benjamin Smith, Part II: "Point counting for elliptic curves over finite fields" |
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10:45 - 11:00 |
Coffee/Tea Break |
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11:00 - 11:45 |
Razvan Barbulescu, Part I: "Variants of NFS for fields of p^n elements when n>1" |
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11:45 - 12:00 |
Break |
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12:00 - 12:45 |
Razvan Barbulescu, Part II: "Variants of NFS for fields of p^n elements when n>1" |
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12:45 - 14:00 |
Lunch |
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14:00 - 14:45 |
Maike Massierer, Part I: "Recent advances in Index Calculus methods" |
[SLIDES] | |
14:45 - 15:00 |
Break |
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15:00 - 15:45 |
Maike Massierer, Part II: "Recent advances in Index Calculus methods" |
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15:45 - 16:00 |
Coffee/Tea Break |
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16:00 - |
Closing remarks, open problems (Chair: Peter Stevenhagen) |
The school will take place at Auditorium A011 F001, Yasar University, Selcuk Yasar Campus, Izmir, Turkey. The auditorium can accommodate a maximum of 154 60 persons. The auditorium is equipped with air-conditioning, overhead projectors, boards, desk per seat, WIFI, HD broadcast to Internet infrastructure, and sound system.