October 19, 2020 - October 23, 2020
Public Access Category: All |
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- Time:
- 11:30am
- Description:
- Date and Time: Monday 19 October, 11.30am
Speaker: Nitin Tomar
Google Meet Link: https://meet.google.com/afe-nzqz-sgt
Title: Pro C* algebras
Abstract: Pro C*-algebras are the generalisation of C*-algebras in which the C*-norm is replaced by a family of C*-seminorms. In this talk, we discuss the analogy between pro C*-algebra and C*-algebra. Also, we discuss that any pro C* algebra arises as the projective limit of C*-algebras (hence, the name). With this observation, we write the spectrum of a pro C*-algebra and see how it differs from its C*-algebra counterpart. We will also see necessary and sufficient conditions under which a pro C*-algebra isomorphic to a C*-algebra.
- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Joachim Jelisiejew, University of Warsaw, Poland
Time: Monday 19th October 4 to 5pm (joining time 3.45pm IST)
Google Meet Link: https://meet.google.com/qvo-kduy-yco
Title: Questions and recent results on the Hilbert scheme of points.
Abstract: In the talk I will present the open questions and state of the
art on Hilbert schemes of points, focusing on the most accessible
questions. In one sentence: the Hilbert scheme parameterizes deformations
of finite rank algebras, which accounts for its usefulness, while it is
highly singular which accounts for the difficulties, jointly these
features make its investigation a very active area.
- Time:
- 4:00pm
- Description:
- Date and Time: Wednesday 21 October, 04.00pm
Speaker: Saad Qadri
Google Meet Link: https://meet.google.com/tbg-fghh-nmg
Title: Lindemann-Weierstrass theorem
Abstract: A (complex) number is said to be algebraic (over rationals) if it satisfies a nonzero polynomial
equation with integer coefficients. A number that is not algebraic is said to be transcendental. Our goal
in this talk will be to prove the Lindemann Weierstrass theorem which states that if b_j's are distinct algebraic numbers then exp(b_j)'s are linearly independent over the field of algebraic numbers (over Q). This gives as its corollary the fact that pi and e are transcendental.
- Time:
- 6:30pm
- Description:
- Date and Time: 23 October 2020, 6:30pm IST/ 1:00pm GMT / 09:00am EDT
(joining time: 6:15 pm IST - 6:30 pm IST)
Speaker: Jack Jefferies, University of Nebraska-Lincoln, NE, USA
Google meet link: meet.google.com/hzo-wzpe-tht
Title: Faithfulness of top local cohomology modules in domains.
Abstract: Inspired by a question of Lynch, we consider the following
question: under what conditions is the highest non-vanishing local
cohomology module of a domain R with support in an ideal I, faithful as an
R-module? We will review some of what is known about this question, and
provide an affirmative answer in positive characteristic when the
cohomological dimension is equal to the number of generators of the ideal.
This is based on joint work with Mel Hochster.