09:20 to 10:00 
Rajesh Gopakumar (ICTS, India), Kyewon Koh Park (KIAS, South Korea) and Sanoli Gun (IMSc, India) 
Inaugural Talk 


10:10 to 10:40 
HyangSook Lee (Ewha Womans University, Seoul, South Korea) 
Latticed based Cryptography and its Applications Since the first use of lattices in the Knapsack cipher system in 1982 for cryptographic purposes, latticebased cryptography has begun to draw attention to its potential cryptographic applications. Above all, with the fact that latticebased problems are resistant to attacks by quantum computers, latticebased cryptosystems are considerd as one of main post quantum cryptography. Since then, Fully Homomorphic Encryption (FHE) has been also developed based on the Ideal lattice, and the entire cryptographic community has begun to pay attention to the lattice, and applications of various techniques are being studied. In this presentation, we introduce latticebased cryptography and its applications.



10:50 to 11:20 
Cheryl Praeger (University of Western Australia, Australia) 
Importance of Women in Mathematics Associations (ONLINE) The first such association was AWM, the Association for Women in Mathematics, established 50 years ago in the USA. National associations and regional associations were established over the ensuing decades: the Australian one, Women in Mathematics Special Interest Group (WIMSIG) of the Australian Mathematical Society (AustMS), WIMSIG established only in 2012. I will speak about links between these associations and the International Mathematical Union, in particular the role of the IMU in acknowledging, including, and promoting women in mathematics.



11:40 to 12:10 
Punita Batra (HRI, Allahabad, India) 
Modules of loopToroidal Lie algebras I will talk about Integrable modules of looptoroidal Lie algebras with finite dimensional weight spaces, when a part of the center acts nontrivially on the modules.



12:20 to 12:50 
Phan Ha Duong (Vietnam Academy of Science and Technology, Vietnam) 
Community Detection in Directed Graphs using Stationary Distribution and Hitting Times Methods Community detection has been extensively developed using various algorithms. One of the most powerful algorithms for undirected graphs is Walktrap, which determines the distance between vertices by employing random walk and evaluates clusters using modularity based on vertex degrees. Although several directions have been explored to extend this method to directed graphs, none of them have been effective. In this paper, we investigate the Walktrap algorithm and the spectral method and extend them to directed graphs. We propose a novel approach in which the distance between vertices is defined using hitting time, and modularity is computed based on the stationary distribution of a random walk. These definitions are highly effective, as algorithms for hitting time and stationary distribution have been developed, allowing for good computational complexity. Our proposed method is particularly useful for directed graphs, with the wellknown results for undirected graphs being special cases. Additionally, we utilize the spectral method for these problems, and we have implemented our algorithms to demonstrate their plausibility and effectiveness.



14:10 to 14:40 
MarieFrancoise Roy (University of Rennes, Rennes, France) 
Alegebraic winding number (ONLINE) Algebraic winding number
MarieFrancoise Roy, emerita professor, University of Rennes, France
Using a new algebraic definition of the winding number we can prove a fully general complex root counting result, improving a former result of [E]. This result is closely related to our previous work on the Quantitative Fundamental Theorem of Algebra PR].
Joint work with Daniel Perrucci, University of Buenos Aires, Argentina.
[E] M. Eisermann, The fundamental theorem of algebra made effective: an elementary realalgebraic proof via Sturm chains. Amer. Math. Monthly 119 (2012), no. 9, 715–752.
[PR] D. Perrucci, M.F. Roy, Quantitative fundamental theorem of algebra. Q. J. Math. 70 (2019), no. 3, 1009–1037.



14:50 to 15:20 
Mousomi Bhakta (IISER Pune, India) 
Stability of PoincareSobolev inequlity in the hyperbolic space (ONLINE) Consider the Poincar\'eSobolev inequality on the hyperbolic space: for every $n \geq 3$ and $1 < p \leq \frac{n+2}{n2},$ there exists a best constant $S {n,p, \lambda}(\mathbb{B}^{n})>0$ such that \begin{align*} S {n, p, \lambda}(\mathbb{B}^{n})\left(~\int \limits {\mathbb{B}^{n}}u^{{p+1}} \, {\rm d}v {\mathbb{B}^n} \right)^{\frac{2}{p+1}} \leq\int \limits {\mathbb{B}^{n}}\left(\nabla {\mathbb{B}^{n}}u^{2}\lambda u^{2}\right) \, {\rm d}v {\mathbb{B}^n}, \end{align*} holds for all $u\in C c^{\infty}(\mathbb{B}^n),$ and $\lambda \leq \frac{(n1)^2}{4},$ where $\frac{(n1)^2}{4}$ is the bottom of the $L^2$spectrum of $\Delta {\mathbb{B}^n}.$ It is known from the results of Mancini and Sandeep (Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (4): 635671, 2008) that under appropriate assumptions on $n,p$ and $\lambda$ there exists an optimizer, unique up to the hyperbolic isometries, attaining the best constant $S {n,p,\lambda}(\mathbb{B}^n).$ In this talk we;ll discuss the quantitative gradient stability of the above inequality and the corresponding EulerLagrange equations. Our result generalizes the sharp quantitative stability of Sobolev inequality in the Euclidean space of Bianchi and Egnell (J. Funct. Anal. 100 (1): 1824. 1991), Ciraolo, Figalli and Maggi (Int. Math. Res. Not. IMRN (21): 67806797, 2018), Figalli and Glaudo (Arch. Ration. Mech. Anal, 237(1): 201258, 2020) to the Poincar\'{e}Sobolev inequality on the hyperbolic space.



15:30 to 17:30 
 
Panel I  Women in Mathematics, the Indian story 

