Mathematics

11/20/2024

**11 a.m.**

Title: Manin's Universal Quantum Groups under 2-cocycle Twists

Abstract: We examine 2-cocycle twists of a family of infinite-dimensional Hopf algebras, known as Manin’s universal quantum groups, denoted by aut(A), which Manin showed, universally coact on connected graded quadratic algebras, A. In this talk, we consider aut(A) under a more general setting, namely, when A is a finitely generated algebra subject to m- homogeneous relations and show how aut(A) can be twisted by 2-cocycles. This is joint work with H. Huang, V. C. Nguyen, C. Ure, K. B. Vashaw, and X. Wang under an AIM SQuaRE grant.

11/13/2024

**11 a.m.**

Title: Labeled Graph C*-Algebras and Desingularization
Abstract: Given a directed graph E and a labeling L, one forms the la-
beled graph C*-algebra by taking a weakly left-resolving labeled space
(E;L; B) and considering a universal generating family of partial isome-
tries and projections. In this talk we will introduce concepts in the area
of labeled graph C*-algebras and define what is meant by singularities
in a labeled graph. In addition, we will discuss some ideas on how
to define a process in which one can build a "larger" desingularized
labeled space.

Title: Measuring Diversity in Classifier Ensembles

Abstract: With the advent of classifier ensembles came an interesting observation: when the individual predictors of a classifier ensemble make differing predictions, the ensemble’s performance may increase.  Many researchers understand the induction of diversity in these ensembles on an intuitive level.  However, there is no universally accepted measure for the diversity of a set of classifiers.  In this talk, we’ll discuss a few proposed measures of classifier diversity and look at a few experiments to illustrate the relationship between these measures and ensemble performance.  

Title: An introduction to finite element methods

Abstract: The finite element method (FEM) is a numerical approximation technique that is used extensively for engineering to approximate solutions of partial differential equations.  In this presentation, the FEM will be introduced and applied to a simple model problem.  Some details about the derivation, implementation, and convergence will be discussed.

An Introduction to Spatial Statistics and Kriging

Abstract: From weather forecasting to mining, geographical information systems (GIS) have become one of the mainstays of spatial prediction. This talk will introduce the underlying “engine”, called kriging, of GIS prediction, from the basic spatial model formulation to some of the more exotic multivariate spatial-temporal models, and present relevant examples.  

Title: Introduction to Calculus of Variations

Abstract: Calculus of Variations concern with finding the optimal solution to functionals of certain forms.  In this talk we will visit several famous classical problems, some have demonstrations to help analyzing the best solution.

Title: Bose-Einstein condensation of an ideal gas

Abstract: A Bose-Einstein condensate is a state of matter that arises, under certain conditions, in a gas consisting of bosons and represents an exotic quantum phenomenon. It was theoretically predicted by Bose and Einstein in 1924 but was long regarded as a mathematical curiosity with no practical applications. However, since the experimental observation of such a condensate in 1995, Bose-Einstein condensation has become a field of significant research interest. Although the phenomenon is thought to be well understood from a physical perspective, its mathematically rigorous description remains incomplete. In this talk, we discuss a mathematically precise treatment of Bose-Einstein condensation in the simplified case of an ideal Bose gas confined to a box.

Title: Introduction to Deep Reinforcement Learning

Abstract:Deep Reinforcement Learning (DRL) is an exciting field that merges reinforcement learning with deep neural networks, enabling agents to learn through dynamic interactions with their environment. Unlike traditional methods that rely on static datasets, DRL allows agents to adapt and maximize rewards over time. This seminar will cover the fundamental concepts of DRL, including agents, actions, rewards, and policies. We’ll also explore case studies, like DRL’s success in mastering Atari games, highlighting how these methods drive advancements in fields such as robotics, game AI, and autonomous systems.

Title:  On some Banach Function Spaces

Abstract:  In the first part of the talk, I will present a short introduction to the theory of Banach function spaces. The second part will be devoted to Cesaro spaces and their non-trivial generalization to spaces on general measure spaces. 

Title: Graduate students’ role in the Emporium and SI leaders

Abstract: A talk will overview the graduate students’ role in the Emporium and SI leaders. Q&A session will follow the presentation.

Title: A complete characterization of monotonicity equivalence for continuous-time Markov processes

Abstract: A research article and abstract titled above can be found at https://arxiv.org/abs/2408.10840.

Instead we cover background materials, starting from Markov chains and continuous-time Markov processes on discrete state spaces. Then we introduce two notions of monotonicity for them, and discuss why we care about them in the context of exact Markov chain Monte Carlo (MCMC) sampling algorithms.