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.

Thesis Defence
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Character Values at Special Elements in Complex Classical Groups
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: -

Colloquium
Speaker: Sutanu Roy, IIT Bombay
Title: On the path correspondences of quantum graphs
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: In this talk we will describe a theory of paths for quantum graphs. In the spirit of the edge correspondence of Brannan–Hamidi–Ismert–Nelson–Wasilewski, we associate to each quantum graph a sequence of path correspondences modelling its quantum paths of every length. These assemble into a subproduct system over the centre of the underlying vertex algebra, and I will illustrate the construction on classical, complete, and trivial quantum graphs. This is based on a joint work in progress with Sourav Khatua.

Student Seminar
Speaker: Ankita Parashar, IIT Bombay
Host: Suman Kumar Sahoo
Title: From Symmetry to Representation theory
Time, day and date: 5:30:00 PM – 6:30:00 PM, Wednesday, August 05
Venue: Ramanujan Hall
Abstract: Symmetry appears everywhere in mathematics, from the rotations of a square and a sphere to the hidden structures behind Fourier analysis and number theory. Representation theory provides a powerful language to study these symmetries by translating groups into matrices and linear transformations. In this talk, we will explore how simple geometric symmetries lead to the idea of representations, and their surprising connections to Fourier series and modular forms, which are key objects in the two subjects: Fourier Analysis and Number theory.

Statistics and Probability Seminar
Speaker: Raghavendra Tripathi, NYU Abu Dhabi
Host: Parthanil Roy
Title: Efficient sampling from almost all monotone sets
Time, day and date: 11:00:00 AM – 12:00:00 PM, Thursday, August 06
Venue: Conference Room
Abstract: Sampling from the uniform measure on a monotone subset of Boolean hypercube arises in several contexts. For example, sampling a configuration in bond percolation with left to right crossing, or sampling a Knapsack. One popular and oft used method to sample from such sets is to restrict the random walk on the full hypercube to the monotone set. The random walk on the full hypercube mixes in $O(nlogn)$ time.Ding and Mossel (2014) conjectured that restricted chain on any monotone set with fixed positive measure also mixes in $O(nlogn)$ time and proved an upper bound $O(n^3)$. This was recently improved to $O(n^2)$ by proving a sharp Poincare inequality. We prove that for almost all monotone subsets, the log-Sobolev constant is order $n$ which in turn implies the Ding and Mossel’s conjecture for almost all monotone sets. This talk is based on joint work with Patrick O. Santos and Pierre Youssef.

Deep Learning in Finance – Lecture 2
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Machine Learning Methods for Financial Model Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 06
Venue: Ramanujan Hall
Abstract: This presentation introduced machine learning methods for the calibration of financial models, focusing on the recovery of unknown model parameters from observed market data. We began by formulating model calibration as an inverse problem in which parameters are estimated so that theoretical option prices closely match market prices. After reviewing the mathematical optimization framework, we showed how machine learning can replace repeated numerical optimization by directly learning the inverse mapping from market prices to model parameters, enabling fast real-time calibration. Samuelson's geometric Brownian motion model
was then presented as a fundamental example, together with its stochastic differential equation, probabilistic properties, and explicit maximum likelihood estimators for drift and volatility. To account for changing market conditions, we introduced sliding-window estimation, which produces time-dependent parameter estimates capable of identifying volatility clustering, market regimes, and trend changes. Finally, the limitations of constant-volatility models motivated the introduction of the Heston stochastic volatility model, whose additional parameters provide a more realistic description of financial markets. Throughout the presentation, interactive implementations demonstrated how modern machine learning techniques can efficiently estimate model parameters, visualize their evolution over time, and support practical applications in option pricing, hedging, and quantitative risk management.

Combinatorics Seminar
Speaker: Raghavendra Tripathi, NYU Abu Dhabi
Host: Parthanil Roy
Title: Counting the Erdos matrices
Time, day and date: 3:00:00 PM – 4:00:00 PM, Friday, August 07
Venue: Conference Room
Abstract: Marcus and Ree (1959) showed that any n x n doubly stochastic matrix satisfies
\[
\max_{P \in S_n} Trace(AP^T) \leq \|A\|_F^2,
\]
where $S_n$ is the set of permutation matrices of size $n$ and $\|A\|_F$ is the Frobenius norm of $A$. Erdos asked to characterize those matrices which saturate the above inequality. The set of all such matrices in dimension $3$ was obtained in 2023 by Bouthat, Mashregi and Morneau-Gurin. Surprisingly, there are only 6 such matrices in dimension 3. I subsequently proved that in each dimension there are only finitely many such matrices and it naturally leads to the question—can we find the asymptotic for the number of such matrices? The exact numbers are known only in dimensions upto 6. We show that the number of Erdos matrices in dimension n is asymptotically $2^{n^2}$. We further show that one can construct an Erdos matrix corresponding to every d-regular bipartite graphs.

Analysis Seminar
Speaker: Dr. Subhankar Mahapatra, IIT Ropar
Host: Sourav Pal
Title: De Branges Spaces of Entire Functions: Functional Model and Sampling Theory
Time, day and date: 4:15:00 PM – 5:15:00 PM, Friday, August 07
Venue: Online (https://meet.google.com/cqv-doha-gfc)
Abstract: https://drive.google.com/drive/folders/1XKWgYpYHmsRa6d-pyyHchxHEky-uQ9Ey