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