{"id":3612,"date":"2023-09-08T15:56:06","date_gmt":"2023-09-08T13:56:06","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/blog\/research-groups\/antonella-peruccas-research-group\/"},"modified":"2025-08-28T09:23:07","modified_gmt":"2025-08-28T07:23:07","slug":"number-theory-and-arithmetic-geometry","status":"publish","type":"research-groups","link":"https:\/\/www.uni.lu\/fstm-en\/research-groups\/number-theory-and-arithmetic-geometry\/","title":{"rendered":"Number Theory and Arithmetic Geometry"},"content":{"rendered":"
\n \n
\n \n \n Overview<\/span>\n \n \n <\/svg>\n <\/button>\n\n
    \n
  • \n \n \n \n <\/svg>\n Overview<\/span>\n <\/a>\n<\/li>\n
  • \n \n \n \n <\/svg>\n Research<\/span>\n <\/a>\n<\/li>\n
  • \n \n \n \n <\/svg>\n People<\/span>\n <\/a>\n<\/li>\n
  • \n \n \n \n <\/svg>\n Join us<\/span>\n <\/a>\n<\/li>\n <\/ul>\n <\/nav>\n<\/div>\n<\/div>\n\n
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    \n
    \n \n
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    \n<\/span>\n\n\n

    \nInvestigating numbers<\/h1>\n<\/div>\n<\/header>\n
    \n \n\"perucca-board\"\n <\/figure>\n
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    The group members explore many facets of modern number theory (algebraic, analytic, and computational aspects), arithmetic geometry and cryptography. They represent a broad spectrum of number theory and they are involved in multiple research projects. <\/p>\n\n\n

      \n\n<\/ul>\n<\/div>\n<\/div>\n <\/div>\n<\/section><\/div>\n<\/div>\n\n
      \n \n
      \n

      \nKummer theory and the reductions of algebraic groups<\/h2>\n\n\n\n
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      \n \n\"\"\n <\/figure><\/section><\/div>\n\n\n\n
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      \n<\/h3>\n\n\n\n

      We study algebraic groups (for example, elliptic curves) defined over number fields. In particular, we develop Kummer theory for number fields and we consider problems related to the reductions (for example, Artin\u2019s Conjecture on primitive roots). <\/p>\n<\/div>\n\n\n\n

      \n
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      \n<\/h3>\n\n\n
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      • \n \n
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        <\/div><\/div>\n<\/li><\/ul>\n\n<\/div>\n<\/div>\n<\/div>\n\n\n\n
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          \n \n
        • \n \n \nPublications Team Antonella Perucca<\/span><\/use><\/svg><\/a>\n<\/li>\n\n
        • \n \n \nPublications Team Gabor Wiese<\/span><\/use><\/svg><\/a>\n<\/li>\n<\/ul><\/div>\n\n\n\n
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            <\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n\n\n
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            \nHeads of Group<\/h2>\n
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            • \n
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              \n \n\"Assoc.\n <\/figure>\n <\/div>\n
              \n

              Assoc. Prof Antonella PERUCCA<\/h3>\n

              Associate professor in Mathematics<\/p>\n

              \n \n \n Learn more<\/span>\n <\/span>\n <\/use><\/svg> <\/a>\n<\/div>\n <\/div>\n <\/div>\n<\/div>\n<\/div><\/li>
            • \n
              \n
              \n
              \n \n\"Prof\n <\/figure>\n <\/div>\n
              \n

              Prof Gabor WIESE<\/h3>\n

              Full professor in Mathematics<\/p>\n

              \n \n \n Learn more<\/span>\n <\/span>\n <\/use><\/svg> <\/a>\n<\/div>\n <\/div>\n <\/div>\n<\/div>\n<\/div><\/li><\/ul>\n\n<\/div>\n\n<\/div><\/section>\n\n\n\n
              \n

              \nThis group is part of:<\/h3>\n\n\n
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              • \n \n \n
                \n \n\"Faculty <\/figure>\n\n\nFaculty of Science, Technology and Medicine (FSTM)<\/span>\n\n<\/use><\/svg><\/span>\n<\/a>\n<\/li>
              • \n \n \n
                \n \n\"\"\n <\/figure>\n\n\nDepartment of Mathematics<\/span>\n\n<\/use><\/svg><\/span>\n<\/a>\n<\/li><\/ul>\n<\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"

                Members of our group study number theory (algebraic, analytic, and computational aspects) and arithmetic geometry.<\/p>\n","protected":false},"author":115,"featured_media":3611,"parent":0,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Number Theory and Arithmetic Geometry ","uluxPrePostTitle":"Research Group","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"field-of-interest":[294],"organisation":[65,29],"authorship":[115,112,215],"acf":[],"yoast_head":"\nNumber Theory and Arithmetic Geometry - 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