Analysis seminar
Speaker: Sushil Singla, University of Regina, Canada
Host: Santanu Dey
Title: Representations of noncommutative cubes and prisms
Time, day and date: 3:45:00 PM - 4:45:00 PM, Tuesday, August 04
Venue: Ramanujan Hall
Abstract: In this talk, I will describe certain noncommutative realizations of three classical geometric objects: cubes, polydiscs, and prisms. I will establish the connection of representations of discrete groups with the noncommutative extreme points of the noncommutative state space of the operator systems generated by the canonical unitaries that correspond to the generators of the group. Using this connection, I will be shedding light on the noncommutative geometry of noncommutative dcubes and k-prisms via the representations of the operator system determined by the canonical generators of the free product of two cyclic groups of order 2 and k, or d cyclic groups of order 2. By way of the duality of the categories NCConv and OpSys of noncommutative convex sets and operator systems, respectively, I will also establish an analysis of tensor products of the operator system under consideration.
Finally, I will apply classical dilation theorems of Halmos and Mirman to give a complete description of the maximal noncommutative triangular prism in terms of joint unitary dilations. This is joint work with D. Farenick, R. Maleki, and S. Medina Varela, and has been accepted for publication in J. Noncommut. Geom. The preprint of the article is available on Arxiv:2601.16902.

Deep Learning in Finance – Lecture 1
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Deep Learning for Stock Price Prediction: Convolutional Networks, Recurrent Neural Networks and Transformers
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 04
Venue: Ramanujan Hall
Abstract: This presentation introduced modern deep learning methods for stock price prediction, emphasizing three major neural network architectures: Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Transformers. We began by discussing the challenges posed by financial time series, including temporal dependence, nonlinearity, nonstationarity, and market noise, which make stock prediction substantially more difficult than standard regression problems. CNNs were presented as effective tools for extracting local temporal patterns through one-dimensional convolutions and pooling operations, while RNNs, particularly those based on LSTM and GRU cells, were shown to model long-term temporal dependencies using recurrent hidden states. Finally, Transformers were introduced as the current state-of-the-art architecture, employing self-attention mechanisms to capture global interactions among all observations in the input sequence while allowing highly parallel training. Throughout the presentation, practical implementations were discussed, including interactive programs for training these models on financial data, selecting hyperparameters, visualizing training losses, and forecasting future stock prices. Together, these architectures illustrate the evolution of deep learning methods from local feature extraction to sequential memory and, ultimately, to global attention mechanisms for financial time-series prediction.