Conference Talks

Abstract: A functional calculus serves to be quite useful in vector lattices. The Daniell functional calculus has been introduced by Grobler to study stochastic processes in vector lattices. In this talk, we will introduce the various basic concepts in vector lattices and show that the Daniell functional calculus is merely the pointwise functional calculus in continuous functions spaces. Joint work with Vladimir Troitsky. 


Abstract: The study of vector lattices and their relationship with stochastic processes has been an active area of research in recent years. The concept of sup-completion is a powerful tool in this field due to its properties of extending the notion of supremum to partially ordered sets that may not have a natural upper bound. In this talk, we will briefly introduce the field of vector lattices and provide a representation of the sup-completion using the Maeda-Ogasawara theorem. This representation will essentially reduce the sup-completion to studying the properties of continuous functions on the Stone space of the vector lattice. Joint work with Vladimir Troitsky. 


Abstract: A network game is a game over a graph where each vertex is associated with a player and the adjacent vertices of a vertex in the graph represent the neighbors of each player. In a network game with binary decisions, players might prefer one strategy over the other based on the number of neighbors that are choosing it. A network game is said to be at equilibrium when every player in the network reaches a decision with which they are all satisfied. A fundamental question is if a given network game will ever reach an equilibrium. It has been proved in a recent paper that there exists an equilibrium in every network game consisting purely of either coordinating or anti-coordinating players. However, the results for when both types of players coexist in a network are unknown. In this talk, we will use a linear-threshold model to establish the conditions for an equilibrium to exist in various types of networks which contain both coordinating and anti-coordinating players.

Seminar Talks

Abstract: Summing operators are a class of linear operators in functional analysis that play a fundamental role in the study of Banach spaces and probability. In this series of talks, we will introduce the concept of a p-summing operator, and explore their relation with various topics in functional analysis, including Schatten-Von Neumann Classes, p-integral operators, and Type and Cotype in Banach spaces. We will discuss the properties of different types of summing operators, such as p-summing and p-integral operators, and demonstrate how they can be used to derive estimates for the norms of operators on Banach spaces. We will also examine how summing operators can be applied in the study of probability and Banach lattices.


Abstract: In this talk, we will explore the fascinating field of network game theory. Network game theory studies the interactions and strategies of rational agents in interconnected networks, such as social networks, transportation networks, and communication networks. We will discuss various models used to analyze network games, such as network formation games, and evolutionary games. This talk will provide a glimpse into the exciting and rapidly growing field of network game theory, and its potential to shed light on complex interactions in a wide range of real-world settings.