Events for 02/01/2024 from all calendars

Seminar on Banach and Metric Space Geometry

Time: 10:00AM - 11:00AM

Location: BLOC 302

Speaker: Hung Viet Chu, Texas A&M University

Title: Higher Order Tsirelson Spaces and their Modified Version are Isomorphic

Abstract: In this talk, we sketch the proof that the Tsirelson space $T_\xi$ is naturally isomorphic to its modified version $T^M_\xi$ for each countable ordinal $\xi$. We begin by recalling the definition of Schreier families $\mathcal{S}_\xi$, where $\xi$ is a countable ordinal, and their modified version $\mathcal{S}^M_\xi$. These families are defined by transfinite induction on $\xi$. In the case of a successor ordinal $\xi$, i.e., $\xi = \gamma+1$, the family $\mathcal{S}_\xi$ is the collection of unions of sets $E_1< E_2 < \cdots < E_d$ in $\mathcal{S}_\gamma$ with $\min E_1\geqslant d$, where $E_i < E_j$ means that $\max E_i < \min E_j$. On the other hand, the modified version $\mathcal{S}^M_\xi$ only requires the sets $E_i$ to be disjoint instead of being consecutive. From these definitions, we know that $\mathcal{S}_\xi \subset \mathcal{S}^M_\xi$. Our first result shows that $\mathcal{S}_\xi$ is actually equal to $\mathcal{S}^M_\xi$ for each countable ordinal $\xi$, thus answering a question by Argyros and Tolias. This result together with certain tree analysis of the norming sets of $T_\xi$ and $^M_\xi$ give us their isomorphism. As an application, we show that the algebra of linear bounded operators on $T_\xi$ has $2^{\mathfrak c}$ closed ideals. The speaker is thankful to Dr. Schlumprecht for his excellent guidance in this joint work.

Noncommutative Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Hao Zhuang, Washington University in St. Louis

Title: Invariant Morse-Bott-Smale complex, the Witten deformation and Lie groupoids

Abstract: In this talk, we will first introduce an invariant Morse-Bott-Smale chain complex for closed $T^l$-manifolds with a special type of $T^l$-invariant Morse-Bott functions. Then, we will establish a quasi-isomorphism between the invariant Morse-Bott-Smale complex and the Witten instanton complex. Finally, if time permits, we will explain an ongoing project, which is a generalization of Mohsen’s Witten deformation via Lie groupoids to our $T^l$-invariant Morse-Bott functions.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. Reza Ovissipour, Texas A&M University

Title: Mathematics for the Agri-food Systems

Abstract: Mathematics for Agri-food Systems is the strategic application of mathematical principles and techniques to address challenges and optimize diverse facets within agriculture and the food supply chain. This discipline plays a pivotal role in elevating efficiency, productivity, and sustainability throughout agri-food systems. Its application spans various critical domains, encompassing statistical analysis, precision agriculture, modeling, optimization, traceability, blockchain, crop and livestock management, food safety risks, big data management, genetics, and decision support systems. The integration of mathematics into different facets of agri-food systems facilitates precise statistical analysis, enabling evidence-based decision-making. This interdisciplinary approach to mathematics in agri-food systems will be thoroughly explored during the seminar with an emphasis on its significance in food safety, big data management, precision agriculture, optimization, bioreactor scaling up, kinetics of changes, and the implementation of blockchain for traceability. The seminar will discuss how mathematical methodologies contribute to the advancement and sustainability of agri-food systems.