Commutative algebra seminar

IPDF talk
Friday, 2nd Feb, 3:30-4:30 pm

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Host: Manoj Keshari

Venue: https://meet.google.com/gyb-jfbn-oiu?authuser=0

Speaker: Parnashree Ghosh

Affiliation: ISI Kolkata

Title: Applications of exponential maps to the epimorphism and Zariski
cancellation problem

Abstract: In the first part, we will discuss the Epimorphism Problem and also discuss the famous Abhyankar-Sathaye Epimorphism Conjecture. We will introduce ``Generalised Asanuma varieties" (GAV) of higher dimensions \geq 3 and see some necessary and sufficient conditions for these varieties to be isomorphic to the affine space. We see that this characterization immediately yields a family of higher dimensional hyperplanes satisfying the Abhyankar-Sathaye Conjecture.

In the second part, we see some necessary conditions for two GAVs to be isomorphic and also describe automorphisms of a certain subfamily of GAV. These results show that for each d \geq 3, there is a family of infinitely many pairwise non-isomorphic rings which are counterexamples to the Zariski Cancellation Problem for dimension d in positive characteristic. We further give a complete description of two important invariants called Makar-Limanov and Derksen invariants of a certain subfamily of GAV.

This talk is based on a joint work with Neena Gupta.

Algebraic Groups seminar

Friday, 2 February, 4.00-5.15

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Venue: Room 105

Host: Dipendra Prasad

Speakers: Dibyendu Biswas, Chayan Karmakar, Mohammed Saad and Deep Makadiya

Affiliation: IIT Bombay

Title: Regular elements in semi-simple algebraic groups

Abstract: We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on the paper by ROBERT STEINBERG, Regular elements of semi-simple algebraic groups Publications mathématiques de l'I.H.É.S., tome 25 (1965), p. 49-80

Analysis seminar

IPDF talk

Friday, 2nd Feb. 4 pm - 5 pm 

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Venue: Online, link TBA

Host: Sanjay Pusti

Speaker: Jitendra Kumar Senapati 

Affiliation : BITS Pilani, Goa

Title: Restriction theorem for the Fourier-Dunkl transform and its applications to Strichartz inequalities

Abstract: We define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz’s restriction theorem for the Fourier-Dunkl transform for certain surfaces, namely, cone, paraboloid, sphere, and hyperboloid, and its generalization to the family of orthonormal functions. Finally, as an application of these restriction theorems, we establish versions of Strichartz estimates for orthonormal families of initial data associated with the Schrodinger propagator, wave propagator, and Klein-Gordon propagator for the case of the Dunkl Laplacian. This restriction theorem generalizes Stein-Tomas and Strichartz’s restrictions theorems in special cases. This is a joint work with B. Pradeep, S. S. Mondal, and H. Mejjaoli.