Student APS
Speaker: Pradyumna Poduri, IIT Bombay
Host: S. Krishnan
Title: On 4PC related matrices of complete bipartite graphs
Time, day and date: 10:00:00 AM – 10:40:00 AM, Monday, February 16
Venue: Room 113 
Online: https://meet.google.com/hui-ztpc-khr 
Abstract: In this presentation,  we focus on the $2$-Steiner distance matrix  of the complete bipartite graph $K_{m,n}$. This is  a matrix whose rows and columns are indexed by a 2-sized subset of vertices. The entry indexed by a row 2-sized subset and column 2-sized subset is the minimum number of edges in a connected subgraph that contains the union of the vertices in the row 2-sized subset and the column 2-sized subset.   For $K_{m,n}$, we get a complete set of eigenvectors and eigenvalues of its 2-Steiner distance. Along the way, we consider the $\Max$, $\Min$ and $\Mid$ matrices of $K_{m,n}$ and determine a complete set of eigenvectors for these matrices. We outline a common procedure for generating these eigenbasis. 

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Review of Feed-Forward Neural Networks
Time, day and date: 10:00:00 AM – 11:00:00 AM, Monday, February 16
Venue: Ramanujan Hall
Abstract: This lecture presents an introduction to feed-forward neural networks, emphasizing their mathematical structure and relevance to modern problems in physics. We discuss how neural networks are trained, why they are effec.ve function approximators, and how they can be used to model physical systems governed by differential equations. The lecture serves as a foundation for a lecture series on deep learning methods in mathematical and computational physics

Student APS
Speaker: Kaushik Khamari, IIT Bombay
Host: Ananthnarayan Hariharan
Title: Intermediate extensions of the S_2-ification and connectedness
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, February 16
Venue: Ramanujan Hall
Abstract: In 1994, Hochster and Huneke defined the S_2-ification of a noetherian local ring and established its relation with a connectedness condition on the spectrum. 
In this talk, we will define certain intermediate extensions of the S_2-ification and present a generalization of their connectedness result

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Deep Learning for Solving Equations
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, February 17
Venue: Ramanujan Hall
Abstract: This lecture presents how deep learning can be used to solve a broad class of mathematical equations, including algebraic, functional, integral, and differential equations. We discuss neural-network-based formulations for direct and inverse problems, illustrate solution strategies for ordinary and partial differential equations, and highlight modern techniques such as multiphase resolution and equation discovery. The lecture emphasizes how neural networks provide a unified framework for solving diverse equation types arising in applied mathematics and physics.
The details of the lectures in this series are given in the following PDF document:
https://drive.google.com/file/d/1MyJ-QN_VswUaRcuaztPdG2TgWbvXybhW/view?usp=sharing

Student APS
Speaker: Bhawani Singh, IIT Bombay
Host: Sutanu Roy
Title: Different Perspectives of Quantum Graphs
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, February 17
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss two approaches of Quantum Graphs. First, I will present the definition via an operator on (L^2(B,ψ)), where B is a finite dimensional C*-algebra and ψ is a faithful state. I will then introduce the operator bimodule formulation. The main objective is to show that these two definitions are equivalent in the tracial case, and that with mild additional assumptions the equivalence is also holds for general faithful state.

Student APS
Speaker: Omkar Ramdas, IIT Bombay
Host: Niranjan Balachandran
Time, day and date: 11:00:00 AM - 12:00:00 PM, Wednesday, February 18
Venue: Room 105
Title: Extremal properties of permutations
Abstract: This talk will broadly be divided into two parts. In the first part, I'll define some special families of permutations and we'll see some optimal bounds on the sizes of such families. In the second part, I'll define what caged sequences are, for any given permutation and we'll see their asymptotic properties.

Student APS
Speaker: Swapan Jana, IIT Bombay
Host: Sourav Pal
Title: ANDOˆ ’S DILATION AND BOHR-THEORETIC ASPECTS OF THE MULTIVARIATE VON NEUMANN INEQUALITY FOR BANACH SPACE OPERATORS
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, February 18
Venue: Room 105
Abstract: The celebrated Bela Sz.-Nagy dilation theorem states that every contraction ´ T on a Hilbert space H dilates to an isometry and the minimal isometric dilation space is uniquely determined (up to unitary equivalence) by H ⊕2 `2(DT ), which equals H ⊕2 `2(H ) if T is a strict contraction. In 1963, Ando proved that a commuting pair of contractions on a Hilbert space ˆ H dilates to a commuting pair of isometries on H ⊕2 `2(H ⊕2 H ⊕2 H ⊕2 H ). We show that a commuting pair of strict contractions on a Hilbert space H admits an isometric dilation on H ⊕2 `2(H ⊕2 H ). Moreover, we prove that H ⊕2 `2(H ⊕2 H ) is a minimal isometric dilation space, which shows that minimal isometric dilation space is independent of the choice of the commuting pair of strict contractions on the underlying Hilbert space. An immediate application of our construction is that we extend this mechanism to construct an isometric dilation of a commuting pair of strict contractions on a Banach space. This part is based on a joint work with Prof. Sourav Pal. For c ∈ C n (n ≥ 1), let Gc be the collection of tuples (T1,...,Tn) of Banach space operators satisfying kTik ≤ |ci | for 1 ≤ i ≤ n. Using a multidimensional analogue of Bohr’s theorem, we show that the closed polydisk D n (R) is a spectral set for Gc if and only if c ∈ B(D n (R)), the Bohr zone of D n (R). In contract to the one-variable case, we prove that D n (R) is not a minimal spectral set of Gc for any c ∈ B(D n (R)) when n ≥ 2. This part is based on an ongoing joint work with Prof. Sourav Pal and Dr. Himadri Halder.

Student APS
Speaker: Shivani, IIT Bombay
Host: Neela Nataraj
Title: Discontinuous Galerkin finite element methods for linear and semilinear fourth-order problems in smectic liquid crystals
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: In this talk, we will discuss the analysis and numerical approximation of a regular solution to a semilinear fourth-order partial differential equation defined on a polygonal domain, modelling the density variation of Smectic-A liquid crystals. First, we will discuss the discontinuous Galerkin finite element method for the corresponding linear problem. Building upon this, we will discuss the analysis of the semilinear fourth-order problem. For the nonlinear model, we establish existence, local uniqueness, and optimal order error estimates in the energy norm under the assumption that the exact solution $u\in H^{2+\alpha}(\Omega)$ with $\alpha>0$. Numerical experiments validating the theoretical results will also be presented.

Special Session
Speaker: Madhusudan Manjunath, IIT Bombay
Title: Mathematics for Well-Being
Time, day and date: 4:00:00 PM - 5:15:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: We ask fundamental questions concerning Mathematics and its potential for Well-being. Taking guidance from an ancient school of Indian philosophy, we sketch candidate answers to these questions. The talk assumes no special background in either Mathematics or Philosophy.

Student Seminar
Speaker: Om Milind Joglekar, IIT Bombay
Host: Suman Kumar Sahoo
Title: Perron-Frobenius Theory: Matrices & Graphs
Time, day and date: 5:30:00 PM – 6:30:00 PM, Wednesday, February 18
Venue: Ramanujan Hall
Abstract: This talk examines the Perron-Frobenius theorem, focusing on the existence of a strictly positive eigenvector and the spectral consequences of irreducibility. We will specifically connect these analytic properties to graph-theoretic concepts like connectivity and cycle periodicity.

Student APS
Speaker: Pradip Roy, IIT Bombay
Host: Keshav Aggarwal
Title: Weyl bound for GL(2) in t-aspect via a trivial delta method.
Time, day and date: 11:00:00 AM – 11:45:00 AM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: We use a trivial delta method to prove the weyl bound in t - aspect for the L-function of a hecke holomorphic (or Maass) cusp form of arbitrary level and nebentypus  and also we use voronoi summation formula, Poisson summation formula and stationary phase analysis.

Monge-Ampere equation
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:00:00 AM – 12:00:00 PM, Thursday, February 19
Venue: Room 215
Abstract: We shall show C^1 regularity in 2D for solutions to the weak formulation of the Dirichlet problem for the Monge-Ampère equation when the initial data is locally essentially bounded. Along the way, we shall derive a dichotomy between the existence of regular solutions and the propagation of singularities along an entire line segment. The contents of this lecture are not reliant on that of the previous one.

Student APS
Speaker: Garima Khetawat, IIT Bombay
Host: Niranjan Balachandran
Title: A purely entropic approach to the rainbow triangle problem.
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, February 19
Venue: Room 113
Abstract: In this talk, we will discuss a proof that in a 3-edge colored simple graph with R red edges, B blue edges and G green edges, the number of rainbow triangles is at most \sqrt{2RGB}. This proof, given by Ting-Wei Chao and Hung-Hsun Hans Yu (2024), is different from other entropic proofs in the sense that in other proofs, entropy does not play a central role after all the terms are expressed in terms of probability of certain events. But this proof remains in the realm of the entropy method throughout.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Lagrangian Systems
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: This lecture introduces Lagrangian systems from the perspective of neural-network-based modeling. We study classical variational systems such as the harmonic oscillator, catenary, brachistochrone, simple pendulum, and Euler’s elastica, and show how their dynamics can be learned and reproduced using neural networks. The lecture highlights the connection between variational principles, trajectory optimization, and modern data-driven approaches to classical mechanics.

Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR Bombay *Retd.)
Host: Tony Puthenpurakal
Title: Singularities of plane curves
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: We will consider reduced power series f(X,Y) over an algebraically closed field k of characteristic 0. Following topics about R=k[[X,Y]]/(f) will be discussed.
Algebraicity results of Artin, Hironaka-Rossi, Samuel, Basic intersection theory of place curves, Conductor ideal, Value semi-group of R, Gorenstein's result, Dedekind's Conductor Formula, Jung's formula connecting the Milnor number and conductor, Applications of Dedekind's formula. We will give Abhyankar's proofs of Dedekind and Gorenstein results. If time permits, Abhyankar-Moh result about generators of the value semi-group will be discussed. 

Algebraic groups seminar
Speaker: Shripad M. Garge, IIT Bombay
Title: Basic results on Algebraic Groups. II
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, February 19
Venue: Room No .215
Abstract: We discussed the basics of linear algebraic groups in the first lecture and reached the notion of reductive groups. In this lecture, we will see the structure theory of reductive groups.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S. Baskar
Title: Hamiltonian Systems
Time, day and date: 11:30:00 AM - 12:30:00 PM, Friday, February 20
Venue: Ramanujan Hall
Abstract: This lecture focuses on Hamiltonian systems and their formulation within the Hamiltonian framework. We study classical examples such as the harmonic oscillator, the simple pendulum, and charged particle motion in a magnetic field, and show how neural networks can be used to learn and reproduce Hamiltonian dynamics. Special attention is given to canonical transformations and generating functions, highlighting their role in structure-preserving, data-driven modeling of physical systems.

APS
Speaker: Sourav Khatua, IIT Bombay
Host: Sutanu Roy
Title: On path spaces of quantum graphs
Time, day and date: 4:15:00 PM – 5:15:00 PM, Friday, February 20
Venue: Ramanujan Hall
Abstract: Let (B,\psi_B, A) be a quantum graph, where B is a finite-dimensional C*-algebra equipped with a faithful state \psi_B and A is a quantum adjacency matrix. Using the notion of quantum edge correspondences, we construct path spaces of arbitrary length as C*-correspondences over B. We show that these path spaces form a sub-product system over the center Z(B). Furthermore, we prove that when two quantum graphs are classically isomorphic, then there is a correspondence isomorphism between the respective sub-product systems.

APS
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: Model Category Structures on an n-Cube.
Time, day and date: 4:30:00 PM – 5:30:00 PM, Friday, February 20
Venue: Room 215
Abstract: In this talk we are going to discuss the model category structures on an n-cube using the notion of 'proto-centers' of weak equivalence classes introduced by Droz and Zakharevich(2021). We also try to give an enumeration of model structures on 4-cube having only one 'non-trivial' weak equivalence class.