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AIMS
  • Home
  • Research
    • Computer Algebra Software
    • Artificial Intelligence
    • Arithmetic Geometry
    • Machine Learning in Mathematics
    • Computational Linguistics
    • Hyperelliptic Isogeny Based Cryptography
      • Abelian Varieties and Cryptography
    • Galois Theory: A database approach
      • Gal-1
      • Invariants
    • Homomorphic Encryption
    • Cybersecurity and cryptography
      • Financial Cyber Security
    • NeuroSymbolic AI
      • ML and Invariant Theory
      • Equivariant Neural Networks
    • Mathematics Education
  • Conferences & Seminars
    • Seminars
      • Artificial Intelligence Seminar
      • Arithmetic Geometry Seminar
    • Quantum Computer Algebra
      • QCA 2026
        • Registration QCA 2025
        • Program QCA 2025
        • Participants QCA 2025
        • SS-01
        • SS-02
        • SS-03
      • Quantum Resources
      • QCA Board
      • Organizing Special Sessions
      • QCA Forms
    • Isogeny based post-quantum cryptography
      • Talks
      • Accommodations
      • Proceedings
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    • Seville 24
      • Participants
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      • Participants
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        • Editorial Board
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        • Submissions
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      • NATO Proceedings
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    • Ervin Ruci
    • Jurgen Mezinaj
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  • More
    • Home
    • Research
      • Computer Algebra Software
      • Artificial Intelligence
      • Arithmetic Geometry
      • Machine Learning in Mathematics
      • Computational Linguistics
      • Hyperelliptic Isogeny Based Cryptography
        • Abelian Varieties and Cryptography
      • Galois Theory: A database approach
        • Gal-1
        • Invariants
      • Homomorphic Encryption
      • Cybersecurity and cryptography
        • Financial Cyber Security
      • NeuroSymbolic AI
        • ML and Invariant Theory
        • Equivariant Neural Networks
      • Mathematics Education
    • Conferences & Seminars
      • Seminars
        • Artificial Intelligence Seminar
        • Arithmetic Geometry Seminar
      • Quantum Computer Algebra
        • QCA 2026
          • Registration QCA 2025
          • Program QCA 2025
          • Participants QCA 2025
          • SS-01
          • SS-02
          • SS-03
        • Quantum Resources
        • QCA Board
        • Organizing Special Sessions
        • QCA Forms
      • Isogeny based post-quantum cryptography
        • Talks
        • Accommodations
        • Proceedings
      • Machine Learning
      • Seville 24
        • Participants
      • Milwaukee 2024
      • Quantum 2023
      • Boston-23
      • Algebra 2022
        • Algebra 2022: Talks
        • Participants
        • Special Issue
        • Activities
      • ACA 2010
      • ACA 2007
      • Moscow 2005
    • Publications
      • Journals
        • Albanian Journal of Mathematics
          • Editorial Board
          • Archives
          • Submissions
      • Books and Editorial
        • Textbooks
        • ML-Cont-Math
          • Contemporary Math (2025)
        • NATO Proceedings
      • Preprints
        • 2024-03
    • About us
      • Bylaws
      • Administration
    • Admissions
      • Admission criteria for Undergraduates
      • Admission tests
      • Application forms
      • Tuition and scholarships
      • Registration
        • Schedule
    • Education & Training
      • Academic programs
      • RISAT Courses
        • Abstract Algebra
        • Cryptosystems in automotive industry
        • MAT 151: Linear Algebra
        • Calculus II
        • Calculus III
        • Machine Learning with Pytorch
        • Computer Algebra
      • Summer Schools
      • Graduate Certificates
    • People
      • Elira Shaska
      • Ervin Ruci
      • Jurgen Mezinaj
      • Tony Shaska
        • Research
        • Teaching
        • Papers
        • Talks
        • Students
        • CV
        • Interviews and Media
    • Email
Seville

European Congress of Mathematics

Galois Theory and Arithmetic

Seville, July 15-19, 2024
Organizers 

  • Sara Areas de Reyna, University of Seville 

  • Tony Shaska, Oakland University

Deadline for submitting abstracts 

All abstracts must be submitted .........

List of participants (not yet complete)

Topics and motivation

Overview

The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th century. 


The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the Inverse Problem of Galois Theory). What are the implications for the structure and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).


All the above provides the  general theme of this mini-symposia: the beauty and power of group theory, and how it applies to problems of arithmetic via the basic principle of Galois. 


This conference continues a major line of work about covers of the projective line (and other curves), their fields of definition and parameter spaces, and associated questions about arithmetic fundamental groups. This is intimately tied up with the Inverse Problem of Galois Theory, and uses methods of algebraic geometry, group theory and number theory. Here is a brief summary of some highlights in the area:


  • The classification of finite simple groups was announced around 1980; Fried, Matzat, Thompson and others begin to explore applications to the Inverse Galois Problem. \item Thompson (1984) realizes the monster, the largest sporadic simple group, as a Galois group over the rationals. All other sporadic simple groups follow, with one exception ($M_{23}$). More generally, Malle, Matzat, Fried, Thompson, Voelklein and others construct covers of the projective line defined over the rationals, by using rigidity, Hurwitz spaces and the braid group, in order to realize simple (and related) groups as Galois groups over the rationals. One is still far from realizing all simple groups.

  • Harbater  and Raynaud win the Cole Prize in 1995 for solving Abhyankar's Conjecture on unramified covers of affine curves in positive characteristic. \item The Guralnick-Thompson Conjecture on monodromy groups of genus zero covers of the  projective line: Proof  completed by Frohard and Magaard in 1999, building on work of Aschbacher, Guralnick, Liebeck, Thompson and other group-theoretists. 

  • The MSRI semester  Galois groups and fundamental groups, fall '99, organized by Fried, Harbater, Ihara, Thompson and others, defines the area, its methods, goals and open problems.

The mini-symposia in Seville will be a continuation of our modest efforts to revive the Inverse Galois group, which started in 2022  with an online conference.  If you are interested in attending the conference in Seville or want to be kept updated with our efforts please fill the form below. 

Institute of Artificial Intelligence  and Mathematical Sciences

Webpage: https://www.risat.org/index.html