IPM Calendar 
Wednesday 4 October 2023   Today  
Events for day: Wednesday 03 May 2023    
           11:00 - 12:00     Wednesday Weekly Seminar - meeting
The origin of magnetic fields during inflation: helicity and a sawtooth coupling



The origin of large-scale magnetic fields in the Universe is one of the long-standing problems in cosmology. An intriguing possibility is that they are remnants of primordial fields that originated during inflation as amplification of quantum vector perturbations. We discuss the generation of helical magnetic fields by considering a departure from Maxwell's theory during inflation: the electromagnetic sector is coupled to a time-dependent function with a sharp feature, hence the name sawtooth coupling. Scale-invariant modified gravity is a suitable framework for testing the model, providing a natural physical interpre ...

           13:30 - 15:00     Weekly Seminar
Diffusion Dominated Stochastic Multiple Field Inflation


In this talk I am going to speak about multiple field inflationary cosmology with the method of stochastic formalism as an effective field theory. At first I will review inflationary cosmology and next I will consider the formalism of stochastic analysis in general. Then the use and advantage of stochastic formalism in inflation will be discussed. After that I will consider the multiple field inflation in which the quantum jumps are larger than the classical drift. At last the implications for generation of primordial black holes are considered. ...

           14:00 - 15:00     Combinatorics and Computing Weekly Seminar
On Chromatic Stability Numbers in Graphs


The chromatic vertex (resp. edge) stability number $vschileft(G ight)$ (resp. $eschileft(G ight)$) of a graph $G$ is the minimum number of vertices (resp. edges) whose deletion results in a graph $H$ with $chi(H) = chi(G)-1$. We have proved that if $G$ is a graph with $chi(G)in left{Delta(G), Delta(G) + 1 ight}$, then $vschileft(G ight)=ivschileft(G ight)$, where $ivschileft(G ight)$ is the independent chromatic vertex stability number. The result need not hold for graphs $G$ with $chi(G) leq left(Delta(G)+1 ight)/2$. It is proved that if $chi(G) > Delta(G)/2 + 1$, then $vschi(G)=eschi(G)$. A Nordhaus-Gaddum-type result on the chromatic vert ...

           16:00 - 17:00     Mathematics Colloquium - online
Perspectives in Scalar Curvature


Manifolds with their scalar curvatures bounded from below display flexibility of shapes similar to what happens in the geometric and in the symplectic topology. The problem of evaluating the limits to this flexibility is inseparable from the index theory of Dirac operators and the geometric measure theory.

Venue: Online via zoom:


Meeting ID: 908 611 6889

Passcode: 362880

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           17:30 - 19:00     Number Theory Webinar
Tame Class Field Theory


As a part of global class field theory, we construct a reciprocity map that describes the unramified (resp. tame) etale fundamental group as a pro-completion of a suitable idele class group (resp. tame idele class group) for smooth curves over finite fields. These results were extended to higher-dimensional smooth varieties over finite fields by Kato-Saito (unramified case, in 1986) and Schmidt-Spiess (tame case, in 2000). We begin the talk by recalling these results. The main focus of the talk is to work with smooth varieties over local fields. The class field theory over local fields is not as nice as that over finite fields. We discuss ...