Double coverings and integral local system cohomology of hyperplane arrangements

Người báo cáo: Sakumi Sugawara (Hokkaido University)


Time: 9:00 - 10:00 (VN time), 11:00-12:00 (Japan time) 16th February

Venue: Room 507, A6, Institute of Mathematics

Online (Zoom):

https://us06web.zoom.us/j/82191500949?pwd=UVlmYXFOMGFrQS9FY3Nja1labWRmZz09

Meeting ID: 821 9150 0949

Passcode: 123456

Abstract: It is a central question in the topology of hyperplane arrangements whether several topological invariants are combinatorially determined, for example, the rank of twisted cohomology groups of the complement, and the torsions in the homology of Milnor fibers or covering spaces. In this talk, we give a formula on the 2-torsion of double coverings, which refines the formula conjectured by Papadima-Suciu. We also discuss the recent study on integral local system cohomology groups of arrangements. This is partially joint work with Suguru Ishibashi (Arise analytics, inc.) and Masahiko Yoshinaga (Osaka University)

8.1.30PHP Version205msRequest Duration4MBMemory UsageGET xemina-chi-tiet/{alias}Route
    • Booting (37.22ms)
    • Application (167ms)
    • 1 x Application (81.8%)
      167ms
      1 x Booting (18.19%)
      37.22ms
      7 templates were rendered
      • client.pages.seminar.seminar_detail (resources/views/client/pages/seminar/seminar_detail.blade.php)1blade
        Params
        0
        serminar
      • client.layout.app (resources/views/client/layout/app.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.head (resources/views/client/layouts/head.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.header (resources/views/client/layouts/header.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.navbar (resources/views/client/layouts/navbar.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.column_left (resources/views/client/layouts/column_left.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.footer (resources/views/client/layouts/footer.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      uri
      GET xemina-chi-tiet/{alias}
      middleware
      web, locale
      controller
      App\Http\Controllers\SeminarController@view_seminar_detail
      namespace
      prefix
      where
      as
      seminar.detail
      file
      app/Http/Controllers/SeminarController.php:38-61
      36 statements were executed, 14 of which were duplicated, 22 unique67.36ms
      • select * from `serminars` where `ser_alias` = 'double-coverings-and-integral-local-system-cohomology-of-hyperplane-arrangements' limit 1
        4.24ms/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Bindings
        • 0. double-coverings-and-integral-local-system-cohomology-of-hyperplane-arrangements
        Backtrace
        • 15. /app/Http/Controllers/SeminarController.php:40
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `members` where `members`.`id` in (531)
        1.01ms/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/SeminarController.php:40
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `serminar_rooms` where `serminar_rooms`.`id` in (36)
        780μs/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/SeminarController.php:40
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `pages`
        2.1ms/app/Repositories/Pages/PagesRepository.php:30beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Pages/PagesRepository.php:30
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:33
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `pages`
        1.85ms/app/Repositories/Pages/PagesRepository.php:30beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Pages/PagesRepository.php:30
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:73
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `parent_id` = 0 order by `order` asc
        810μs/app/Repositories/Department/DepartmentRepository.php:17beta_math_vn
        Metadata
        Bindings
        • 0. 0
        Backtrace
        • 14. /app/Repositories/Department/DepartmentRepository.php:17
        • 15. view::41329013d802ceb5f40c0b002e8af12e76ed34df:91
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `departments`.`parent_id` in (12, 13, 14, 15, 16) order by `order` asc
        1.1ms/app/Repositories/Department/DepartmentRepository.php:17beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Department/DepartmentRepository.php:17
        • 20. view::41329013d802ceb5f40c0b002e8af12e76ed34df:91
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `departments`.`parent_id` = 1 and `departments`.`parent_id` is not null order by `order` asc
        780μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 2 and `departments`.`parent_id` is not null order by `order` asc
        790μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 2
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 3 and `departments`.`parent_id` is not null order by `order` asc
        950μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 4 and `departments`.`parent_id` is not null order by `order` asc
        840μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 4
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 5 and `departments`.`parent_id` is not null order by `order` asc
        860μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 5
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 6 and `departments`.`parent_id` is not null order by `order` asc
        950μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 6
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 7 and `departments`.`parent_id` is not null order by `order` asc
        870μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 7
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 8 and `departments`.`parent_id` is not null order by `order` asc
        940μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 8
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 9 and `departments`.`parent_id` is not null order by `order` asc
        4.02msview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 9
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 17 and `departments`.`parent_id` is not null order by `order` asc
        1.08msview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 17
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 10 and `departments`.`parent_id` is not null order by `order` asc
        960μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 10
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `cadres`
        1ms/app/Repositories/Department/DepartmentRepository.php:37beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Department/DepartmentRepository.php:37
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:144
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `posts_category`
        1.3ms/app/Repositories/Posts/PostsRepository.php:48beta_math_vn
        Metadata
        Backtrace
        • 15. /app/Repositories/Posts/PostsRepository.php:48
        • 16. view::41329013d802ceb5f40c0b002e8af12e76ed34df:186
        • 18. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `posts` where `hot` = 1 and `posts`.`deleted_at` is null order by `date_create` desc limit 3
        9.18ms/app/Repositories/Posts/PostsRepository.php:19beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Repositories/Posts/PostsRepository.php:19
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:15
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `conferences` where date(`date_show`) <= '2025-12-31' and ((date(`date_create`) >= '2025-01-01' and date(`date_create`) <= '2025-12-31') or (date(`date_end`) >= '2025-01-01' and date(`date_end`) <= '2025-12-31') or (date(`date_create`) <= '2025-01-01' and date(`date_end`) >= '2025-12-31')) limit 3
        4.26ms/app/Repositories/Conferences/ConferencesRepository.php:39beta_math_vn
        Metadata
        Bindings
        • 0. 2025-12-31
        • 1. 2025-01-01
        • 2. 2025-12-31
        • 3. 2025-01-01
        • 4. 2025-12-31
        • 5. 2025-01-01
        • 6. 2025-12-31
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:39
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:43
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `prints` where `pr_hot` = '1' order by `created_at` desc limit 3
        5.61ms/app/Repositories/Pages/PagesRepository.php:156beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Repositories/Pages/PagesRepository.php:156
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:74
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select `members`.*, `same_authorsables`.`same_authors_id` as `pivot_same_authors_id`, `same_authorsables`.`members_id` as `pivot_members_id`, `same_authorsables`.`same_authors_type` as `pivot_same_authors_type` from `members` inner join `same_authorsables` on `members`.`id` = `same_authorsables`.`members_id` where `same_authorsables`.`same_authors_id` in (1134, 1135, 1137) and `same_authorsables`.`same_authors_type` = 'App\Models\Prints'
        3.09ms/app/Repositories/Pages/PagesRepository.php:156beta_math_vn
        Metadata
        Bindings
        • 0. App\Models\Prints
        Backtrace
        • 18. /app/Repositories/Pages/PagesRepository.php:156
        • 19. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:74
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1137 order by `id` asc
        1.83ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1137
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (305, 306, 671)
        1.36ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1137 order by `id` asc
        1.42ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1137
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (305, 306, 671)
        1.47ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1135 order by `id` asc
        1.81ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1135
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (138, 161, 252)
        850μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1135 order by `id` asc
        1.76ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1135
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (138, 161, 252)
        710μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1134 order by `id` asc
        2.28ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1134
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (181, 667, 668, 669, 670)
        1ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1134 order by `id` asc
        1.83ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1134
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (181, 667, 668, 669, 670)
        1.67ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      App\Models\SameAuthorsables
      22
      App\Models\Prints
      3
      App\Models\Conference
      3
      App\Models\Posts
      3
      App\Models\PostsCategory
      5
      App\Models\Cadres
      7
      App\Models\Department
      16
      App\Models\Pages
      54
      App\Models\SerminarRoom
      1
      App\Models\Members
      34
      App\Models\Serminars
      1
          _token
          K0GYtEU0SAGKm1fO260b8RNUMbPxS4plp0LJupq9
          _previous
          array:1 [ "url" => "https://beta.math.ac.vn/xemina-chi-tiet/double-coverings-and-integral-local-sy...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /xemina-chi-tiet/double-coverings-and-integral-local-system-cohomology-of-hyperplane-arrangements
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:15 [ "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "connection" => array:1 [ 0 => "keep-alive" ] "host" => array:1 [ 0 => "beta.math.ac.vn" ] ]
          request_server
          0 of 0
          array:41 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CONNECTION" => "keep-alive" "HTTP_HOST" => "beta.math.ac.vn" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "beta.math.ac.vn" "SERVER_PORT" => "443" "SERVER_ADDR" => "119.17.215.180" "REMOTE_PORT" => "63744" "REMOTE_ADDR" => "18.218.183.7" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/1.1" "DOCUMENT_ROOT" => "/var/www/math.ac.vn/html/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/xemina-chi-tiet/double-coverings-and-integral-local-system-cohomology-of-hyperplane-arrangements" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/math.ac.vn/html/public/index.php" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1743721936.0512 "REQUEST_TIME" => 1743721936 ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Thu, 03 Apr 2025 23:12:16 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjJCK21yODFJQnU5RE5ZTWpBMExZQlE9PSIsInZhbHVlIjoiUG1idEhLVFE4Vm1TSW45dFdMSkxCQ21IZVZoUUlMQlovUUhRUE5EeGRuUGFVWXpIdlJjWmd6dFR0TUlvcEZtMlQ3RzByWXBDNmNoZWVGSy93Uy9zd0xZd3VHNzdpRGg4YkdyMkJmQVhFZ0o5LytlUG9lUEJ3UjhkcGJXR0w0MGkiLCJtYWMiOiI3OGJjNzI1MTk1OGQzOTNjY2NmNDQxMjgwYWQwMDZiNDE0MmY5MGVkZDNjMGRiMmRjYzM4OTQ5YjJhMWRlY2RhIiwidGFnIjoiIn0%3D; expires=Fri, 04-Apr-2025 01:12:16 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IjJCK21yODFJQnU5RE5ZTWpBMExZQlE9PSIsInZhbHVlIjoiUG1idEhLVFE4Vm1TSW45dFdMSkxCQ21IZVZoUUlMQlovUUhRUE5EeGRuUGFVWXpIdlJjWmd6dFR0TUlvcEZtMlQ3RzByW" 1 => "laravel_session=eyJpdiI6IlNxMEY0YzNtTjlpYjZvY2RneXNsN3c9PSIsInZhbHVlIjoicDQ5WVFod1QwSzcxaTkyU1haRlFtYXhzRmdGOXJkeEtOWDUyamxxdVU2NmtTYmttcWNwaGxyb0szd1g5Nzg3OHUyNUhGRWxPU3Z4VW9JR3BZZWFDQXV1eEptKzBwSGc5VUt0Ymw0T2s4TW56cUo5THZ2dWdPNnhZWlk0Q2cwZkciLCJtYWMiOiI4ZmEyODA2ODM2NjM3YTAxOWU3MTI1ZWQzMzg0MzA3NDQwNzU0MzI0NDNkZTQ4YmRhNDU4ZjA3MjEwYmZjYzNiIiwidGFnIjoiIn0%3D; expires=Fri, 04-Apr-2025 01:12:16 GMT; Max-Age=7200; path=/; httponly; samesite=laxlaravel_session=eyJpdiI6IlNxMEY0YzNtTjlpYjZvY2RneXNsN3c9PSIsInZhbHVlIjoicDQ5WVFod1QwSzcxaTkyU1haRlFtYXhzRmdGOXJkeEtOWDUyamxxdVU2NmtTYmttcWNwaGxyb0szd1g5Nzg3OHUy" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjJCK21yODFJQnU5RE5ZTWpBMExZQlE9PSIsInZhbHVlIjoiUG1idEhLVFE4Vm1TSW45dFdMSkxCQ21IZVZoUUlMQlovUUhRUE5EeGRuUGFVWXpIdlJjWmd6dFR0TUlvcEZtMlQ3RzByWXBDNmNoZWVGSy93Uy9zd0xZd3VHNzdpRGg4YkdyMkJmQVhFZ0o5LytlUG9lUEJ3UjhkcGJXR0w0MGkiLCJtYWMiOiI3OGJjNzI1MTk1OGQzOTNjY2NmNDQxMjgwYWQwMDZiNDE0MmY5MGVkZDNjMGRiMmRjYzM4OTQ5YjJhMWRlY2RhIiwidGFnIjoiIn0%3D; expires=Fri, 04-Apr-2025 01:12:16 GMT; path=/XSRF-TOKEN=eyJpdiI6IjJCK21yODFJQnU5RE5ZTWpBMExZQlE9PSIsInZhbHVlIjoiUG1idEhLVFE4Vm1TSW45dFdMSkxCQ21IZVZoUUlMQlovUUhRUE5EeGRuUGFVWXpIdlJjWmd6dFR0TUlvcEZtMlQ3RzByW" 1 => "laravel_session=eyJpdiI6IlNxMEY0YzNtTjlpYjZvY2RneXNsN3c9PSIsInZhbHVlIjoicDQ5WVFod1QwSzcxaTkyU1haRlFtYXhzRmdGOXJkeEtOWDUyamxxdVU2NmtTYmttcWNwaGxyb0szd1g5Nzg3OHUyNUhGRWxPU3Z4VW9JR3BZZWFDQXV1eEptKzBwSGc5VUt0Ymw0T2s4TW56cUo5THZ2dWdPNnhZWlk0Q2cwZkciLCJtYWMiOiI4ZmEyODA2ODM2NjM3YTAxOWU3MTI1ZWQzMzg0MzA3NDQwNzU0MzI0NDNkZTQ4YmRhNDU4ZjA3MjEwYmZjYzNiIiwidGFnIjoiIn0%3D; expires=Fri, 04-Apr-2025 01:12:16 GMT; path=/; httponlylaravel_session=eyJpdiI6IlNxMEY0YzNtTjlpYjZvY2RneXNsN3c9PSIsInZhbHVlIjoicDQ5WVFod1QwSzcxaTkyU1haRlFtYXhzRmdGOXJkeEtOWDUyamxxdVU2NmtTYmttcWNwaGxyb0szd1g5Nzg3OHUy" ] ]
          session_attributes
          0 of 0
          array:4 [ "_token" => "K0GYtEU0SAGKm1fO260b8RNUMbPxS4plp0LJupq9" "_previous" => array:1 [ "url" => "https://beta.math.ac.vn/xemina-chi-tiet/double-coverings-and-integral-local-system-cohomology-of-hyperplane-arrangements" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]