Giới thiệu về ideal đơn thức ngẫu nhiên

Người báo cáo: Phạm Việt Hùng

Thời gian: 9:30 -- 11:00, 11 tháng 10 năm 2023.

Địa điểm: Phòng 612 Nhà A6 Viện Toán học

Tóm tắt: Mô hình monomial ideal ngẫu nhiên bắt đầu được đề xuất và nghiên cứu từ 2017 bởi nhóm nghiên cứu Jesus De Loera, Lily Silverstein, Dane Wilburne và các cộng sự để nghiên cứu các thống kê cho các đặc trưng của ideal đơn thức ngẫu nhiên và áp dụng phương pháp xác suất trong đại số giao hoán. Trong báo cáo này, chúng tôi sẽ trình bày ý tưởng về mô hình lấy ngẫu nhiên, các kết quả ban đầu cũng như một số kết quả cập nhật.

Tài liệu tham khảo:

  1. J. A. De Loera, S. Petrović, L. Silverstein, D. Stasi, and D. Wilburne, “Random monomial ideals”, J. Algebra 519 (2019), 440–473.
  2. D. Erman and J. Yang, “Random flag complexes and asymptotic syzygies”, Algebra Number Theory 12:9 (2018), 2151–2166.
  3. Lily Silverstein. Dane Wilburne. Jay Yang. "ASYMPTOTIC DEGREE OF RANDOM MONOMIAL IDEALS." J. Commut. Algebra 15 (1) 99 - 114, Spring 2023.
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