IPM Calendar 
Sunday 21 April 2024   Today  
Events for day: Wednesday 24 April 2024    
           11:00 - 12:00     Wednesday Weekly Seminar - meeting
Coherent optical phenomena via optical vortex lights



Optical vortex beams are of fundamental interest due to their applications. An optical vortex with a spiral phase carries an orbital angular momentum (OAM) along the propagation axis . There is a phase singularity at the core of the vortex which evolves its doughnut-shaped intensity profile. Optical vortices are routinely created to carry specific values of OAM. When interacting with the matter, their specific characteristics result in various interesting effects, including ultraprecise atom localization, entanglement of OAM states of photon pairs, atom vortex beams, light-induced torque and spatially dependent elec ...

           12:45 - 13:45     Geometry and Differential Equations Seminar
Existence of Radial Positive Solutions for Homogeneous and Non-homogeneous Neumann Problems


Let $B_{1}$ be the unit ball in $mathbb{R}^{n}$. We analyze the positive solutions to the problem egin{equation}label{aaa} left{egin{array} {ll} - Delta u + u = u vert uvert ^{p - 2}, & mbox{ in } B_{1}, %u>0, & mbox{ in } Omega, dfrac{partial u}{partial u} = 0, & mbox{ on } partial B_{1} , end{array} ight. end{equation} where $p > 2$ and $frac{partial}{partial u}$ is the outward normal derivative. This problem, sometimes referred to as the Lane-Emden equation with Neumann boundary conditions, arises for instance in mathematical models which aim to study pattern formation, and more specifically in those governed by diffusion ...

           13:30 - 15:30     Weekly Seminar
Removing point-particle singularity from gravitational theories


Singularities in Newtons gravity, in general relativity (GR), in Coulomb's law, and elsewhere in classical physics, stem from two ill-conceived assumptions that, a) there are point-like entities with finite masses, charges, etc., packed in zero volumes, and b) the non-quantum assumption that these point-like entities can be assigned precise coordinates and momenta. In the case of GR, we argue that the classical energy-momentum tensor in Einstein's field equation is that of a collection of point particles and is prone to singularity. In compliance with Heisenberg's uncertainty principle, we propose replacing each constituent of the gravitatin ...

           16:00 - 17:00     Mathematics Colloquium
Vector Field on Plane in Characteristic Zero and p>0


A polynomial vector field on a complex plane C^2 defines a foliation of the plane and one would like to know when the leaves of this foliation are algebraic, i.e. when the analytic integral curves are algebraic. This is a hard unsolved problem. I will suggest a conjectural approach to this problem which uses the reduction of the vector field modulo primes p. It turns out that the corresponding problem in characteristic p is easy to solve. We then conjecture that the original vector field is algebraic if and only if its reduction modulo a prime p is algebraic for almost all p. We have some partial results towards proving this conjecture. This ...