In the framework of "the 2025 VIASM Activity on Algebraic Topology", the Vietnam Institute of Advanced Study in Mathematics organized on December 8, 2023, the Workshop on New Trends in Algebraic Topology at the International Center for Interdisciplinary Science and Education (ICISE).
Mr. Nguyen Dinh Hien, Vice Rector of Quy Nhon University, delivered the opening speech
Prof. Dr. Sci. Nguyen Huu Viet Hung delivered the opening speech at the Winter School
The school features the participation of many renowned scientists in the field of Topology and Algebra, along with approximately 40 attendees, including students, postgraduate students, lecturers, and researchers from Hanoi, Ho Chi Minh City, and other provinces.
The Winter School comprises three courses by experts from Sorbonne Paris Nord University, France; the University of Sheffield, England; and University of Roma Tor Vergata, Italy. This lecture series focuses on introducing some modern research directions in Topology and recent advancements.
Prof. Paolo Salvatore, University of Roma Tor Vergata, Italy
In the morning session on December 4th, the Winter School began with a lecture series by Professor Paolo Salvatore from the University of Roma Tor Vergata, Italy, on “Introduction to Operads”. This lecture series introduces the theory of operads. Operads describe multi-input operations, meaning operations with multiple inputs. Operads play an increasingly important role in modern mathematics and have numerous applications in algebra, geometry, and mathematical physics. The lecture series explores some examples, especially the E_n operad, which describes the degree of higher homotopy commutativity. The lectures introduce the Koszul duality of operads in algebra and the theory of stable homotopy algebras, and discuss a recent result on the stable Koszul duality of E_n operads achieved by Professor Salvatore and Michael Ching.
Prof. Neil Strickland, University of Sheffield, England
Starting the afternoon session on December 4th, Professor Neil Strickland from the University of Sheffield lectured on 'Chromatic Cohomology of Finite Groups.' This lecture series presents K-theory and Morava E-theory and their applications to the study of stable homotopy of finite groups, including symmetric and general linear groups. The topics covered in the course include general stable homotopy, formal groups, Lazard rings, Quillen's theorem, character groups, Tate's nilpotence theorem, and Chern approximation
Prof. Gregory Ginot, University of Sorbonne Paris Nord, France
On the third day of the Winter School, Professor Gregory Ginot from Sorbonne Paris Nord University commenced a lecture series on 'Introduction to Persistence Homology and Its Applications.' This series presents some ideas of algebraic topology applied to data science, specifically focusing on the theory of persistent homology. In broad terms, this is the application of simplicial complexes and persistent homology to compute invariants of filtered spaces and datasets. The lectures explain fundamental constructions, the concept of a barcode representing invariants of filtered spaces, and the distances between them, emphasizing constructions derived from data analysis.
The Winter School concluded with a Workshop on New trends in Algebraic Topology held at the ICISE. The workshop included 6 presentations from researchers: Dr. Lorenzo Guerra (University of Roma Tor Vergata, Italy), Prof. Huynh Mui (University of Natural Sciences - Hanoi National University), Prof. Jean Lannes (University of Paris 7, France), Assoc. Prof. Dr. Nguyen Dang Ho Hai (University of Sciences, Hue University), Prof. Sarah Whitehouse (University of Sheffield, England) and Msc. Nguyen Duc Nga (Phenikaa University).
In addition to the academic activities, a day was dedicated to a field trip for lecturers and students to explore places in Quy Nhon such as Banh It Tower, and the Quang Trung Museum.
The Winter School concluded successfully with the enthusiastic and thoughtful support from the local organizing committee.
Some photos of the winter school:
