Program of COCOA 2023
Sunday |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
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08:00 – 08: 30 Registration |
08:00 – 10:00 Topic 2 120 minutes |
08:00 – 10:00 Topic 1 120 minutes |
08:00 – 10:00 Topic 2 120 minutes |
08:00 – 10:00 Topic 1 120 minutes |
08: 00 – 10:00 Supplementary Session Topic 2 and Contributed Lectures
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08:30 -08:45 Welcome speech |
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08:45 – 09:00 Short Break |
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09:00 – 10:30 Topic 1 90 minutes |
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10:30 – 11: 00 |
10:00 – 10:30 |
10:00 – 10:30 |
10:00 – 10: 30 |
10:00 – 10:30 |
10:00 – 10:30 |
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11:00 – 12:30 Topic 2 90 minutes
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10:30 – 12:30 Topic 1 120 minutes
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10:30 – 12:30 Topic 2 120 minutes |
10:30 – 12:30 Topic 1 120 minutes |
10:30 – 12:30 Topic 2 120 minutes |
10:30 – 12:30 Supplementary Session Topic 1 and Contributed Lectures
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Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
Lunch |
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13:00 - 18:00 Install and introduce CoCoA program. Learning CoCoA Language |
14:30 – 16:00 Supplementary Session Topic 1 |
14:30 – 16:00 Supplementary Session Topic 2 |
14:30 – 16:00 Supplementary Session Topic 1 |
14:00 – 18:00 Excursion |
14:30 – 16:00 Supplementary Session Topic 1 |
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16:00 – 16: 15 Coffee Break |
16:00 – 16: 15 Coffee Break |
16:00 – 16: 15 Coffee Break |
16:00 – 16:15 Coffee Break |
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16: 15 – 17:45 Supplementary Session Topic 2
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16: 15 – 17:45 Supplementary Session Topic 1 |
16: 15 – 17:45 Supplementary Session Topic 2 |
16: 15 – 17:45 Supplementary Session Topic 2 |
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18:00-21:00 Welcome Dinner |
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18:00-21:00 Gala Dinner
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19:30-21:30 Poster section
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The main goal of the COCOA School is to introduce the knowledge and the skills of computational algebra. The intensive courses will be accompanied by computer tutorials. The participants will learn how to work with the computer algebra system CoCoA and practice the application of computer algebra calculations in studying current research topics in commutative algebra and algebraic geometry.
The school lasts 7 days. There are two intensive courses by four main speakers, (comprising 14.5 hours of scientific activity each) and two sequences of supplementary sessions by four lecturers (comprising 8 hours of scientific activity each). There will be a poster session for showcasing contemporary and ongoing research by young researchers.
Course 1:
Main Speakers: Prof. Dr. Martin Kreuzer and Prof. Dr. Lorenzo Robbiano
Lecturers: Dr. Le Ngoc Long, Dr. Tran Nguyen Khanh Linh
Topic: Border bases
Abstract: For 0-dimensional polynomial ideals, border bases have developed in the last 20 years into a viable alternative to the more widely known Gröbner bases, sharing many properties and characterizations, but offering several distinct advantages. Starting with an introduction to the basic theory of border bases, the course proceed to specific algorithms for computing them and to applying them to a number of important research topics, leading all they way up to explicit calculations in moduli spaces
Course 2:
Main Speakers: Prof. Jürgen Herzog and Prof. Takayuki Hibi
Lecturers: Dr. Anna Maria Biggati and Dr. Ayesha Asloob Qureshi
Topics: Binomial ideals arising from lattice polytopes
Abstract: In the first part of the talk, after recalling some basic definitions and facts on convex polytopes, the integer decomposition property and normality of lattice polytopes are discussed. Then unimodular coverings together with unimodular triangulations of lattice polytopes are introduced. Especially, the role of Gröbner bases in the modern study of lattice polytopes is emphasized. In the second part of the talk, edge polytopes and edge rings of finite graphs are discussed. The problem when the edge polytope of a finite graph is normal as well as the problem when the toric ideal of an edge ring is generated by quadratic binomials is mainly studied. These problems, whose solutions are provided in the language of finite graphs, were the starting point on the research of edge polytopes and edge rings. Furthermore, a characterization for the edge ring of a bipartite graph to be Koszul is supplied. In the third part of my talk, the study on a special class of binomial ideals, so-called join-meet ideals, which arise from finite lattices is done. In the algebraic study of join-meet ideals, Birkhoff's fundamental structure theorem for finite distributive lattices together with a characterization of distributive lattices due to Dedekind is indispensable. One of the basic facts is that the join-meet ideal of a finite lattice is a prime ideal if and only if the lattice is distributive. An example of a modular lattice whose join-meet ideal is not radical is presented.