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.